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  • View in gallery
    Fig. 1.

    GOES-10 visible imagery of cellular patterns over northeast Pacific off the coast of California at 1530 UTC 11 Jul 2001. Open cells, POCs, and closed cells in a 0.6° × 0.6° box are enlarged for clarity.

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    Fig. 2.

    Snapshots of cloud albedo fields at t = 3, 6, and 9 h (corresponding to each of the three rows) during the life cycle of the stratocumulus deck for experiments N65, N150, and N500 (corresponding to each of the three columns, with initial CCN concentrations of 65, 150, and 500 mg−1 respectively).

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    Fig. 3.

    Snapshots of 200-m level vertical velocity fields at t = 3, 6, and 9 h with contours of rain rate (0.5, 5, and 20 mm day−1) superimposed. Plots are arranged in the same way as in Fig. 2.

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    Fig. 4.

    Vertical (yz) cross sections of total particle (CCN plus drop) number concentration (shaded colors), perturbation wind vectors (updrafts in red and downdrafts in blue; reference arrow for magnitude), cloud water (qc > 0.01 g kg−1; black lines), and drizzle water outline (qr > 0.002 g kg−1; thin red lines) at t = 9 h for (a) N65 at x = 30 km and (b) N500 at x = 13.5 km. For clarity, yz slices are zoomed in to 30 × 1.2 km2.

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    Fig. 5.

    Vertical profiles of water vapor mixing ratio qv, liquid water mixing ratio ql, rain rate Rr, total particle (CCN plus drop) number concentration Nt, variance of vertical velocity , cloud-average variance of vertical velocity , third moment of vertical velocity , and TKE. Profiles are averaged between t = 3 and 6 h (solid lines) and between t = 9 and 12 h (dotted lines). A cloud optical depth threshold of 2 is used for the calculation of . All other quantities are domain averaged.

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    Fig. 6.

    Time evolution of (a) domain-average (solid) and cloud-average (dotted) LWP; (b) cloud fraction (CF); (c) domain-average inversion base height (solid) and cloud base height (dotted); (d) cloud-average drop number concentration Nd (solid) and total particle number concentration Nt (dotted); (e) domain-average cloud albedo αc; and (f) domain-average rain rate Rr at the surface (solid) and at cloud base (dotted) for the three experiments as indicated in the legend. Cloudy columns are defined by an optical depth threshold of 2 for the calculation of cloud fraction; a criterion of Nd ≥ 20 mg−1 is applied when calculating cloud-average Nd.

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    Fig. 7.

    Normalized frequency distribution of open-cell size and wall width as a function of time. At each time, a threshold cloud optical depth τc of 2 is first used to filter the cloud field, and a collection of cell sizes and wall widths are obtained by scanning each row and column of grids in both x and y directions. Cell size is defined as the distance between two neighboring cloudy grids along the scan line, and cell wall width is the distance between two neighboring cloud-free grids. Results are shown (a) using τc = 2 during scanning and (b) using the median τc of all cloudy grids along each row/column to further remove contamination by optically thin clouds. Solid lines indicate (left) the time evolution of the median value of cell sizes in the range of 3–30 km and (right) the median value of wall widths in the range of 1.5–10 km.

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    Fig. 8.

    Snapshots of 200-m-level vertical velocity fields over a 2-h period for experiment N65. Time since model start is indicated above each panel. Three individual updraft cells are labeled 1, 2, and 3 to track their evolution with time.

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    Fig. 9.

    Cloud-base rain rate Rr as a function of drop number concentration Nd and cloud depth H or LWP in the form of (a) RrH3/Nd and (b) , where Rr, H, and LWP are domain averages. Data are sampled every 30 min after 2-h model spinup.

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    Fig. A1. Snapshot of cloud albedo field at t = 6 h for the four indicated resolution-sensitivity experiments.

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    Fig. A2. Snapshot of cloud albedo field at t = 6 h for the two sensitivity experiments with observed wind shear for comparison with the corresponding panel in Fig. 2 (with no wind shear).

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    Fig. A3. As in Fig. A2, but for 200-m level vertical velocity with contours of rain rate (0.5, 5, and 20 mm day−1) superimposed for comparison with the corresponding panel in Fig. 3 (with no wind shear).

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Modeling Mesoscale Cellular Structures and Drizzle in Marine Stratocumulus. Part I: Impact of Drizzle on the Formation and Evolution of Open Cells

Hailong WangCooperative Institute for Research in Environmental Sciences, University of Colorado, and NOAA/Earth System Research Laboratory, Boulder, Colorado

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Graham FeingoldNOAA/Earth System Research Laboratory, Boulder, Colorado

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Abstract

A new modeling framework is used to investigate aerosol–cloud–precipitation interactions and dynamical feedbacks at the mesoscale. The focus is on simulation of the formation and evolution of cellular structures that are commonly seen in satellite images of marine stratocumulus clouds. Simulations are performed at moderate resolution in a 60 × 60 km2 domain for 16 h to adequately represent the mesoscale organization associated with open cells and precipitation. Results support the emerging understanding that precipitation plays a critical role in the formation and evolution of open cells. Evaporation of raindrops generates a dynamic response that manifests itself in cellular organization of updrafts and downdrafts and promotes and sustains the formation of an open cellular structure in cloud fields. Vertical motion in open-cell centers with thin clouds is minimal. It is shown that a mean surface rain rate as low as 0.02 mm day−1 is, for the case considered, sufficient to promote the formation of open cells. The maximum dimension of individual open cells ranges between 5 and 30 km. Individual cells grow at a mean rate of between 5 and 10 km h−1. Irregularity in the shape of open cells is caused by formation of new precipitating regions at the cell walls and interference with neighboring cells, which erode, and eventually eliminate, the old cells. The typical lifetime of large individual open cells is about 2 h, close to that observed by radar, although a collection of open cells as a whole may last for tens of hours.

Corresponding author address: Hailong Wang, 325 Broadway, R/CSD2, Boulder, CO 80305. Email: hailong.wang@noaa.gov

Abstract

A new modeling framework is used to investigate aerosol–cloud–precipitation interactions and dynamical feedbacks at the mesoscale. The focus is on simulation of the formation and evolution of cellular structures that are commonly seen in satellite images of marine stratocumulus clouds. Simulations are performed at moderate resolution in a 60 × 60 km2 domain for 16 h to adequately represent the mesoscale organization associated with open cells and precipitation. Results support the emerging understanding that precipitation plays a critical role in the formation and evolution of open cells. Evaporation of raindrops generates a dynamic response that manifests itself in cellular organization of updrafts and downdrafts and promotes and sustains the formation of an open cellular structure in cloud fields. Vertical motion in open-cell centers with thin clouds is minimal. It is shown that a mean surface rain rate as low as 0.02 mm day−1 is, for the case considered, sufficient to promote the formation of open cells. The maximum dimension of individual open cells ranges between 5 and 30 km. Individual cells grow at a mean rate of between 5 and 10 km h−1. Irregularity in the shape of open cells is caused by formation of new precipitating regions at the cell walls and interference with neighboring cells, which erode, and eventually eliminate, the old cells. The typical lifetime of large individual open cells is about 2 h, close to that observed by radar, although a collection of open cells as a whole may last for tens of hours.

Corresponding author address: Hailong Wang, 325 Broadway, R/CSD2, Boulder, CO 80305. Email: hailong.wang@noaa.gov

1. Introduction

Marine stratocumulus (Sc) clouds play a prominent role in the climate system by affecting the earth’s radiation and heat and water budgets. Satellite imagery reveals significant morphological structure within the stratocumulus cloud sheets. The recurrence of striking cellular structures exhibiting both closed- and open-cell patterns is illustrated in Fig. 1 with Geostationary Operational Environmental Satellite 10 (GOES-10) imagery from the northeast Pacific (see also Stevens et al. 2003; Bretherton et al. 2004; Garay et al. 2004; Stevens et al. 2005; Wood and Hartman 2006; Wood et al. 2008). These features present themselves as either bright cloudy cells ringed by darker edges (closed cells) or dark cellular regions ringed by bright cloudy edges (open cells). The starkly different reflectance patterns associated with these cellular structures are of great interest from the perspective of planetary albedo.

The satellite imagery also reveals embedded open cells in otherwise unbroken Sc, referred to as pockets of open cells (POCs; Stevens et al. 2005) or rifts (Sharon et al. 2006). A collection of POCs in a Sc sheet has dimensions on the order of hundreds of kilometers (e.g., Fig. 1), and the POC structure may last for tens of hours (Garay et al. 2004; Stevens et al. 2005). Broad regions of open cells may have a large-scale environment (e.g., sea surface temperature, surface sensible and latent heat fluxes, advective tendencies, and mesoscale cellular convection) very different from that of regions of closed cells (e.g., Agee et al. 1973; see Atkinson and Zhang 1996 for a review). In contrast, the POC region has a large-scale environment and thermodynamic profile similar to the adjacent closed-cell or more stratiform cloud field (e.g., Stevens et al. 2005; Sharon et al. 2006).

What are the underlying physical processes that create and determine the evolution of these open cellular structures? Previous observational studies (e.g., Stevens et al. 2005; Petters et al. 2006; Sharon et al. 2006; Wood et al. 2008) have suggested that POCs are associated with precipitation, and modeling studies (Savic-Jovcic and Stevens 2008, hereafter SS08; Xue et al. 2008) have demonstrated that precipitation does indeed promote the formation of open cells. Representation of precipitation in Sc clouds in models is challenging because of the myriad small-scale coupled processes involved. Precipitation is driven by both aerosol and cloud microphysical processes, as well as by dynamics; whether a cloud precipitates depends on both microphysical processes that are influenced by cloud condensation nuclei (CCN) concentrations and the ability of dynamical forcing to generate deeper, wetter clouds. The study of POCs therefore lies at the nexus of aerosol–microphysical–dynamical and radiative feedbacks and represents an especially fertile area of research because of the strong couplings between these components at a range of scales. It is a desire to understand these processes and feedbacks and their potential implications for the earth’s radiation budget that motivates this endeavor.

Aerosol particles may act as CCN on which water vapor condenses to form cloud droplets. An increase in CCN concentration enhances cloud droplet number concentration Nd and reduces droplet size (for a fixed cloud water content). Smaller drops, in addition to creating optically thicker and more reflective clouds (Twomey 1974), are also less apt to initiate collision–coalescence and generate precipitation (e.g., Warner 1968). Suppression of precipitation may result in higher liquid water path (LWP) and higher cloud cover (Albrecht 1989). It has also been suggested that in nonprecipitating or weakly precipitating Sc, the smaller cloud droplets associated with high CCN concentrations evaporate more readily, reduce LWP, and modify cloud dynamics through enhanced evaporative cooling (Wang et al. 2003; Xue et al. 2008; Hill et al. 2009).

Cloud processes, in turn, affect the aerosol size distribution; drop collision/coalescence can significantly deplete cloud droplets and hence the source of CCN from evaporated drops; precipitation removal is a significant sink of CCN. Regions that have experienced precipitation and that are devoid of particles may experience new particle formation from the gas phase. These particles grow to CCN sizes in a matter of hours to days, and the cycle continues.

Precipitation is not only intimately related to aerosol but is also strongly driven by dynamics and, in turn, has a profound effect on boundary layer circulation. More vigorous clouds generate higher concentrations of liquid water, which have the potential to generate more precipitation (all else being equal). Precipitation causes a redistribution of heat and moisture through drop sedimentation and evaporation processes and alters atmospheric stability and cloud dynamics (e.g., Brost et al. 1982; Wang and Wang 1994). With the onset of drizzle, a solid stratocumulus cloud layer capping a well-mixed boundary layer tends to transform into broken, more cumuliform clouds penetrating the stratocumulus and a boundary layer that is less well mixed on average but is tightly coupled by the cumulus (Wang and Lenschow 1995; Stevens et al. 1998). Observations suggest that a characteristic length scale for precipitation in Sc is on the order of 10 km (Paluch and Lenschow 1991) so that precipitation patterns exhibit mesoscale variability.

In this paper the emerging picture of the relationship between precipitation and POCs is explored further through numerical simulation. Numerical models have proven to be a valuable tool for investigating how aerosol, precipitation, and POCs are related. Large-eddy simulation (LES) has been widely used to study marine boundary layer cloud dynamical and microphysical processes. Xue et al. (2008) studied how precipitation and associated dynamical feedbacks affect the organization of shallow cumulus/stratus convection in pristine air. Using LES (including bin microphysics), they showed that precipitation-induced downdrafts, and the subsequent outflow, are responsible for the formation and evolution of open cellular structure. Their results clearly showed the initial formation and growth of open cells. However, their model domain size (12.4 × 12.4 km2) was too small to represent the full growth of cells, which have characteristic dimensions of tens of kilometers and are therefore more appropriately studied at the meso-β scale (20–200 km). With a larger model domain (25.6 × 25.6 km2), SS08 simulated marine Sc clouds and demonstrated that precipitation does indeed initiate the formation of open cells. Many aspects of observed precipitating Sc—such as cumulus-coupled circulations, locally elevated cloud tops, patches of anomalously high subcloud equivalent potential temperature, and a general reduction in cloudiness—are well captured by their simulations. The realism of the open cell structure revealed by both of these modeling studies generates confidence in the simulations and their representation of real atmospheric processes.

The current work extends the aforementioned modeling work by demonstrating that the community Weather Research and Forecasting model (WRF; Skamarock et al. 2008) can successfully simulate the primary features of POCs. Use of WRF opens opportunities for future studies using open boundaries and forced by regional models, as well as the possibility of coupling to an aerosol–chemistry model (WRF-Chem; Grell et al. 2005), which will enable investigation of aerosol cycling and its role in POC formation and maintenance. Using WRF, aerosol–cloud–precipitation interactions and dynamical feedbacks are revisited to study the evolution of marine Sc and the formation of POCs and to examine how these interactions and feedbacks affect POC formation and evolution. Qualitative comparisons with observations are made whenever possible.

A much larger domain than was used in earlier studies is used here to encompass a wide range of scales. The motivation for doing so emerges from studies such as that by de Roode et al. (2004), who showed that although the vertical velocity field is dominated by horizontal scales on the order of the boundary layer depth, with time all other scalar fields become increasingly dominated by mesoscale fluctuations. In addition to allowing for this mesoscale variability, the large domain also ensures that cell growth is not restricted by the model domain (Schröter et al. 2005). In our case, the larger domain comes at the expense of representation of the small scales resolved by higher-resolution studies. Therefore, the extent to which grid size impacts the results is also explored.

2. Model and numerical experiments

a. Model description

We perform simulations of marine Sc using an LES version of the Advanced Research WRF (ARW) model with a new treatment of aerosol–cloud interactions. By design, the state-of-the-art ARW model is suitable for use in a broad spectrum of applications across scales ranging from tens of meters (e.g., idealized LES) to hundreds of kilometers (e.g., climate simulations). A detailed description of the governing equations, numerical methods, and physics of the ARW model is documented by Skamarock et al. (2008). Moeng et al. (2007) explored the suitability of ARW for large-eddy simulation of dry boundary layer convection and found that modeled turbulence parameters are statistically comparable to observations, laboratory data, and results of other LES studies. Wang et al. (2009) demonstrated that the ARW model is suitable for large-eddy simulations of boundary layer clouds after improvement to scalar advection. In the ARW model, the advection of scalars is performed using the third-order Runge–Kutta integration scheme (Skamarock et al. 2008), which has been shown to cause overestimates of cloud water and precipitation in cloud-scale simulations (e.g., Skamarock and Weisman 2009; Wang et al. 2009) because of a spurious numerical source to the transported scalars. To correct the numerical error, two flux limiters (Skamarock and Weisman 2009; Wang et al. 2009) have been introduced into the ARW (V3.0) model; of the two, the monotonic flux limiter is found to be preferable. In this study the monotonic flux limiter has been applied to the basic advection scheme using fifth (third)-order horizontal (vertical) accuracy for scalar transport as recommended by Wang et al. (2009).

In the released versions of the ARW model (V3.0 and earlier) simple, single-moment, warm-rain microphysical schemes are provided to study boundary layer clouds. To better represent aerosol–cloud–precipitation interactions, a double-moment warm-rain microphysical scheme originally developed by Feingold et al. (1998) has been modified and incorporated into the model. This scheme uses lognormal basis functions to represent aerosol, cloud droplet, and drizzle drop size spectra. For simplicity, aerosol particles are assumed to be composed of fully soluble ammonium sulfate. Activation is jointly determined by the CCN size distribution and the supersaturation, which is predicted in a similar fashion to the bin method by calculating both dynamical and microphysical tendencies (e.g., Clark 1973; Stevens et al. 1996). Condensation/evaporation of a population of drops follows Clark (1976). Transfer of mass and number concentration between cloud and drizzle due to condensation/evaporation is determined by the ambient super- and/or subsaturation. The stochastic collection bin model of Tzivion et al. (1987) is used to generate lookup tables of bin-by-bin mass and number concentration transfer rates for collection tendencies associated with both drop–drop (cloud) interactions and drizzle–drop interactions. Cloud and drizzle drop sedimentation is also size dependent and is based on the bin method. The division of cloud and drizzle spectra into individual bins is done a priori for a range of mean drop sizes and a given breadth parameter and stored in lookup tables. Sedimentation is then calculated based on lookup table entries for each bin and the locally predicted total mass and number concentrations. This allows drops in each bin to fall at the appropriate velocity. Mass and number concentration of drops in all bins are then regrouped into cloud and drizzle to form new lognormal size distributions.

The prescribed geometric standard deviation for the aerosol, cloud, and drizzle modes is 1.5, 1.2, and 1.2, respectively. The CCN spectrum has a median radius of 0.1 μm. The cutoff radius between cloud and drizzle drops is 25 μm. The local mean radius of cloud droplets and rain drops is computed based on the predicted mass mixing ratios and number concentrations.

This double-moment scheme captures the salient features of precipitating marine Sc when compared with a detailed bin microphysical scheme (Feingold et al. 1998). The enhanced computational efficiency enables three-dimensional simulations over much larger domains and/or much longer time scales than is possible with bin microphysics.

Using this configuration of the ARW model, Wang et al. (2009) performed a simulation of the ninth Global Energy and Water Cycle Experiment (GEWEX) Cloud System Study (GCSS) LES intercomparison, with prescribed input conditions, and compared the output to the ensemble of simulations in Ackerman et al. (2009). All quantities lie within the ensemble range, except for the variance of vertical velocity and subcloud rain rate, two quantities that the ensemble members least agree on. The good comparison with Ackerman et al. (2009) provides further confidence in the ability of ARW to run in LES mode.

b. Case description and experiment setup

Thermodynamic conditions and cloud microphysical properties in a POC region were measured during the Second Dynamics and Chemistry of Marine Stratocumulus field study (DYCOMS II) field campaign over the northeast Pacific off the coast of California (Stevens et al. 2003; Stevens et al. 2005). Figure 1 shows that open cells, closed cells, and POCs coexist in the Sc cloud field on 11 July 2001, the day the second research flight (RF02) was conducted. The POCs inside box b were bisected during one of the flight legs, providing an excellent dataset for modeling studies (vanZanten and Stevens 2005). In the present work, initialization of model simulations is mostly based on nocturnal measurements made during RF02. The initial inversion base is at about 800 m. Total water mixing ratio (qt) decreases from 9.45 g kg−1 in the boundary layer to about 5 g kg−1 near the inversion top, and potential temperature (θ) increases from 288.3 to 296.7 K across the inversion. No wind1 is assumed in the initial profile, which is different from Ackerman et al. (2009) and SS08. As boundary conditions, the upward surface sensible and latent heat fluxes are fixed at measured values of 16 and 93 W m−2, respectively, and the surface friction velocity is set to 0.25 m s−1. The Coriolis parameter is 10−4 s−1. A uniform large-scale horizontal divergence of 3.75 × 10−6 s−1 gives large-scale subsidence at each level by multiplying by the altitude. These forcings and surface fluxes are identical to those in the ninth GCSS LES intercomparison study. To reduce the degree of complexity, and because the initial formation of POCs occurs most commonly at night (Wood et al. 2008), no solar radiation is considered here. Radiative forcing is computed every time step, in each model column, using the simple model of net longwave radiative flux following Stevens et al. (2005) to facilitate comparison with previous studies (e.g., SS08; Ackerman et al. 2009). Note that this simple scheme is optimized for the DYCOMS II closed-cell case and is theoretically justified by Larson et al. (2007), but radiative forcing of clear air and optically thin clouds is not well represented. Nonetheless, comparison to sensitivity tests with a more accurate multiband longwave radiation scheme shows that the parameterized radiation performs adequately, although, as expected, radiative cooling in the optically thin cloud region does make a difference in maintaining these thin clouds. (Results are not shown here.)

Three numerical experiments (N65, N150, and N500) assuming initial CCN number concentrations of 65, 150, and 500 mg−1 (equivalent to units of cm−3 when air density is 1 kg m−3), respectively, are designed to examine the impact of aerosol–cloud interactions on the evolution of cloud cellular structures under different aerosol conditions. Aside from transport, activation of cloud droplets is the only sink and evaporation of droplets is the only source of CCN in a given grid box. No replenishing source of CCN is applied. Simulations are performed in a 60 × 60 × 1.5 km3 domain for 16 h. To cover such a large domain for an extended simulation and yet be computationally manageable, a relatively coarse grid size of 300 m in the horizontal and ∼30 m in the vertical is used. The relatively coarse horizontal grid size means that these simulations do not strictly fall into the realm of LES. Nevertheless, it will be shown that they produce useful and realistic results, from which much can be gleaned regarding open-cell formation and growth. In addition, we perform sensitivity tests at finer (100 m) resolution to test the robustness of the results (see section 4 and appendix). The 1.5-order turbulent kinetic energy (TKE) closure is used to calculate the subgrid-scale scalar diffusion (Deardorff 1972). Periodic boundary conditions are assumed in both the x and y directions. A damping layer is employed in the upper 250 m to minimize the accumulation of gravity wave energy.

3. Results

a. Formation and evolution of cellular structures

Cellular structures of marine Sc are usually characterized by the cloud albedo or reflectance fields to mimic those in satellite imagery. A simple two-stream approximation is used to calculate daytime-equivalent, visible wavelength albedo from cloud optical depth, which is calculated explicitly by integrating the total cross-sectional area contributed by cloud and rain drops in the entire column, following Feingold et al. (1997). Snapshots of cloud albedo fields at different stages during the life cycle of the Sc deck are shown in Fig. 2 to visualize the formation and evolution of cellular structures. Although the three experiments are initialized with the same conditions (except for CCN concentration), clouds acquire very different morphology. Initially (t = 3 h) cloud fields in all three cases have a similar closed-cell structure but on average the cloud field in N65 is 60% (0.2 versus 0.5) less reflective than that in the N500 case, where droplets are smaller and liquid water content is larger. At t = 6 h, open cellular structures characterized by highly reflective cell walls surrounding less reflective or dark areas are seen in N65 and N150, whereas in the N500 case, clouds appear in the form of closed cells, characterized by more reflective cell centers than edges. Closed cells are so well defined that each cell is essentially detached from its neighbors. At this stage, the cell sizes and the contrast in albedo between open and closed cells look very similar to those in the earlier finer-resolution simulations of SS08. The advantage of the larger domain used here is that it enables the closed cells to grow by about a factor of 2 in a few hours and the open cells to expand and organize in a qualitatively similar way to those in the satellite imagery shown in Fig. 1. At t = 9 h, the size of some large open cells in N65 increases to about 25 km and to about 20 km for closed cells, clearly necessitating the large domain. The size of open cells (those ringed by bright walls in Fig. 2) in N150 tends to be larger than in N65, but the cells are less distinct than those in N65. Although the open-cell walls in N65 are brighter, the domain-average cloud albedo is 74% smaller than in N500 (0.11 versus 0.42) because the large area of open-cell centers is nearly cloud-free (defined here as having a visible optical depth <2). Note that surface albedo is not considered here.

The evolution of cellular structures in the cloud albedo field shows that the open-cell walls originate from the bright centers of closed cells. Why do these bright spots tend to organize in the clean cases but not in the polluted case? The ringlike structures in vertical velocity fields and the relative locations of precipitation clusters in these rings (Fig. 3) provide a qualitative explanation for this. The shape and organization of open cells in the cloud albedo fields (Fig. 2) derives from variability in the vertical velocity fields. In the subcloud layer, nearly all major precipitating clusters coincide with relatively strong downdrafts because downdrafts facilitate the sedimentation of raindrops, and cooling from subcloud evaporation of falling raindrops intensifies the downdrafts. SS08 have demonstrated that evaporation of raindrops plays a crucial role in modifying the turbulent flow and creating open cells. As a result of this positive feedback and mass conservation, convergent ascending flows develop spontaneously at the boundaries of adjacent precipitating clusters. When initially formed, they appear as regular updraft rings and then later spread and compete for space with neighboring updraft rings.

Water vapor is channeled to the cloud layer in the updrafts as indicated by a significant positive correlation between water vapor perturbations and vertical velocities (figure not shown; see Figs. 3 and 4 in SS08). Hence, these updraft rings can sustain open-cell walls, from which new precipitating clusters emerge. These new precipitating clusters distort or split the “parent” ring by generating new ones (Xue et al. 2008). Such interferences and the chain of feedbacks explain why the open cells exhibit irregular shapes rather than simple geometrical shapes such as hexagons. The less intense and spatially variable precipitation in N150 means that there is less “jostling for space” by open cells. This enables further expansion of some open cells, which acquire larger sizes than in N65 where precipitation is spatially more frequent. This suggests a relationship between the size of an open cell and the spatial distribution of rain intensity in its surroundings.

In the N65 case, during the transition from closed to open cellular structure (t = 3 h), precipitation clusters are larger in number but smaller in size than in the later open cellular stage (e.g., t = 6 h and 9 h). This is consistent with observations reported by Comstock et al. (2007), who found that during this transition, the radar-observed small drizzle cells (<10 km2) exceeded by over 5 times the number of cells in open cellular periods when larger (>10 km2) drizzle cells developed. It is also of note that the individual drizzle cells of about 2–20 km in size observed in their radar observations also appear in our simulations.

These results show that precipitation is critical to the formation and evolution of open cells in the clean cases and support earlier studies. In the polluted case, updrafts also tend to form ringlike or spokelike structures, evident in Fig. 3; however, lacking the driving force from precipitation and subcloud evaporation, they are much less organized.

b. Vertical structure in open and closed cells

The cellular structures shown in Fig. 3 are not just a feature of the subcloud layer; rather, they extend all the way up to the inversion base. Figure 4a shows the vertical structure of open cells and circulations in the boundary layer. The open-cell wall clouds are narrow, yet deep. Ascending and descending branches of in-cloud circulation are connected, as also shown in Fig. 3, because the updrafts are associated with, and benefit from, precipitation in the adjacent downdrafts. The strong surface outflow driven by downdrafts and precipitation can distort updrafts (e.g., at y = 13 km in Fig. 4a). The apparent horizontal flow into the open-cell walls near cloud base and outflow near cloud top (e.g., at y = 2 km and 13 km) is remarkably consistent with C-band radar observations made during the East Pacific Investigation of Climate (EPIC) stratocumulus field experiment (Comstock et al. 2007). Evaporation of raindrops in the lower boundary layer cools and moistens the air in N65, leading to a lower cloud base and the formation of cumulus-like clouds (Wang and Lenschow 1995; Stevens et al. 1998; SS08). These cumuli are sustained by heat and moisture transported in the updrafts and manifest themselves as open-cell walls. Hence, on average the open-cell walls are deeper than the closed-cell clouds.

For the closed-cell case (Fig. 4b), the major ascending branch of the vertical circulation is located at the center of cells, making the center thicker and therefore brighter (higher albedo). The inflow near the base of the closed-cell center (e.g., at y = 8 and 16 km) and the outflow near the top exhibits a similar pattern of circulation in the vertical cross section to that of open-cell walls. This is also consistent with observations (Comstock et al. 2007). The closed-cell case, however, does not exhibit near-surface outflow associated with precipitation as in the open-cell case.

Figure 4 also shows that in both open- and closed-cell cases, air is mixed through the depth of the boundary layer (although, as discussed in previous studies, this mixing is less effective in precipitating boundary layers). The subcloud-layer CCN are transported into clouds in the updrafts. Horizontally, the inflow–outflow circulation and the propagation of open-cell walls transport CCN through the domain. Hence, depletion of CCN in clouds through drop collision/coalescence also reduces CCN below clouds indirectly through transport and mixing, particularly in the precipitating case (Fig. 4a). Regions between open-cell walls that have just experienced a drizzle event are the loci of minima in CCN number concentration and of very weak vertical motions, indicating that the cloud-free or optically thin cloud condition is only partially caused by a CCN shortage; rather, it is primarily the result of a lack of dynamical support. With the upward movement of the inversion base and/or cloud top, free-tropospheric CCN are entrained into the boundary layer. However, mixing of CCN through the strong inversion is inefficient, as indicated by the strong gradient in total particle number concentration Nt near the inversion. As can be seen in Fig. 5, the domain-average Nt below the inversion base (zi) decreases with time, but it is constant above the inversion.

Moisture profiles in Fig. 5 show that precipitation in open cells moistens the lower boundary layer (N65 and N150) and offsets the drying from large-scale subsidence while the closed-cell boundary layer (N500) becomes drier. As a result, the liquid water content in clouds in N65 is highly reduced. The long tails in ql profiles toward the surface further reflect the overall cumulus-like open-cell wall. For both open- and closed-cell cases, the peak of the domain-average rain rate Rr (which is calculated based on the sedimentation flux of all drops) is located near cloud top, indicating a substantial contribution from cloud droplets. However, in the strongly precipitating open-cell walls the peak is near cloud base (not shown). The shape of the rain rate profiles changes with time as more rain reaches the surface; this is a result of less evaporation, owing to increasing drop size and a more humid environment.

The domain-average vertical velocity variance and TKE profiles show that at the early stage of open cell formation (solid lines; t = 3–6 h), convection is weaker in the upper part but stronger in the lower part of the boundary layer than in the closed-cell case. The weaker domain-average convection in the cloud layer in the open-cell cases results from a lack of cloud in the open-cell center and commensurately weak radiative cooling to drive vertical motions (Figs. 3 and 4). The stronger convection below cloud base is largely contributed by downdrafts associated with precipitation, as suggested by the slightly negatively skewed vertical velocity (see the profiles). The cloud-average vertical velocity variance profiles show that vertical circulation in open-cell walls is much stronger than in closed cells and it becomes stronger as the open cells grow. The predominance of positively skewed vertical velocities in the open-cell cases is consistent with the cumuliform convection.

c. Time series of cloud properties

Figure 6 shows the time evolution of cloud properties, boundary layer depth, and surface rainfall rate. In the N65 and N150 cases, cloud fraction drops quickly from 100%, reflecting the fast breakup of an overcast Sc deck. For N500 there is only a slight decrease in cloud fraction over the course of the 16-h simulation as a result of the formation of optically thin clouds near closed-cell edges. After the transient spinup of convection in model simulations, the domain-average LWP in N500 is nearly constant. This is consistent with other modeling studies of the same case (e.g., Ackerman et al. 2009; SS08). The domain-average LWP decreases with time in N65 and N150 because of the Sc breakup and thinning in the open-cell center, whereas the cloud-average LWP (dotted lines) increases owing to the formation of thick cell walls (bright features in Fig. 2). The boundary layer deepens in all cases but does so more rapidly in the more polluted case. This is because a larger entrainment rate is favored by stronger cloud-top radiative cooling, which is proportional to LWP. Studies have shown that sedimentation of cloud water can cause a reduction in entrainment (Stevens et al. 1998; Bretherton et al. 2007), implying that sedimentation of cloud water may also have caused differences in the entrainment rate in the three cases. On the other hand, precipitation in open-cell cases tends to suppress the growth of the boundary layer. In spite of a lower cloud top in N65 than in N500, a much lower cloud base contributes to a thicker cloud layer on average. This is consistent with the higher cloud-average LWP in N65 than in N500.

After the transient spinup, Nd (averaged over grids with concentrations ≥20 mg−1) and Nt decrease because of the depletion of CCN via drop coalescence (Fig. 6d). The reduction becomes progressively stronger with decreasing initial CCN because collision–coalescence and precipitation become more efficient. When below-cloud CCN concentrations are highly reduced in N65, vertical circulations can no longer transport a sufficient concentration of CCN to the clouds. By t = 13.5 h, Nd drops below the threshold value, indicating that all clouds have Nd lower than 20 mg−1. The time variation of domain-average cloud albedo (Fig. 6e) is highly correlated with domain-average LWP and Nd. The domain-average cloud albedo is significantly lower in N65 than in N500, consistent with the visual impression from Fig. 2. The temporally averaged values of albedo, after model spinup (2 h), are 0.12 and 0.43, respectively. Although domain-average cloud albedo in N65 is high (up to 0.55) initially, it drops as low as 0.08 because of the formation of larger, less reflective drops, precipitation removal of water, and the resultant open-cell structure.

The combination of low Nd and high cloud-average LWP sustains the relatively strong drizzle in N65. The simulated mean cloud-base (surface) rain rate of 1.44 ± 0.4 (0.31 ± 0.11) mm day−1 is close to the measured 1.29 ± 0.14 (0.35 ± 0.11) mm day−1 (vanZanten et al. 2005). On average, 23% of the cloud-base drizzle reaches the surface, which is also close to the observed 27%. However, in N150 the mean rain rate reduces from 1.05 mm day−1 at cloud base to about 0.02 mm day−1 at the surface, representing a 98% loss of drizzle in the subcloud layer. The trend of greater loss when drizzle is less intense is also consistent with observations (vanZanten et al. 2005) and other simulations (e.g., Ackerman et al. 2009).

d. Rate of growth of open cells

Figure 7 presents the time evolution of the open cell size and wall width for N65. All cloudy grids (cloud optical depth τc > 2) are considered in Fig. 7a, whereas only the upper 50% of cloudy grids are taken into account in Fig. 7b to remove contamination by optically thin clouds in the open-cell center. In the latter case, only the bright rings are considered to be open-cell walls and, as can be seen, the open-cell size is larger and wall width is narrower (Fig. 7b). Open-cell size tends to increase with time in both scenarios. The aspect ratio (cell size divided by the boundary layer depth) of some large open cells is up to 30, which is typical for mesoscale shallow convective cells (Atkinson and Zhang 1996; Wood and Hartmann 2006). The wall widths tend to decrease with time in Fig. 7a whereas they are quite stable in Fig. 7b. During the early “blooming” stage, when all open cells form and expand (see snapshots in Fig. 3), the median size increases with time substantially and monotonically at about 1 km h−1. After t = 6 h some significant fluctuations appear on the median-size lines, reflecting the influence of the formation of new open cells.

To illustrate the details of the formation, growth, and dissipation of open cells, we examine the evolution of vertical velocity fields because they demonstrate more regular ringlike structure than do the cloud albedo fields. Figure 8 illustrates the evolution of individual open cells that are bordered by updrafts in red. Three individual cells are labeled 1, 2, and 3 and tracked over a 2-h period. During the early formation stage (6:45–7:15), they are initiated at strong “updraft-knots” at the juncture of three convergence zones (the “Y shape” in red). Strong convection and precipitation is promoted, which leads to strong downdrafts (blue) and opening of a cell. During the growing stage (7:30–8:00) the previous Y-shaped updraft-knot changes into a downdraft-knot as precipitation becomes stronger and pushes out a new convergence ring. During the mature stage (8:15–8:45), the downdraft-knot and precipitation inside the cells start to diminish. Cell growth depends strongly on the growth of neighboring cells. Finally, the cells are distorted and split when new precipitating clouds form on their border.

The interference among neighboring cells occurs continuously because they share borders. Although the three labeled cells are initiated at about the same time, they end up having different sizes and shapes that are partly determined by the intensity and distribution of precipitation and competition with neighboring cells. The maximum dimension of updraft cells 1, 2, and 3 increases from 5 km in their infancy to about 25, 15, and 20 km, respectively, in 2 h, representing a mean growth rate of between 5 and 10 km h−1. The approximate 2-h life cycle of the individual updraft cells and the precipitation clusters inside them matches quite well the wavelength of major periodic oscillations on the median-size line in Fig. 7b. Moreover, the time period is consistent with the typical lifetime of 2 h for mesoscale drizzling open cells (100 km2) in southeast Pacific Sc clouds as observed by C-band scanning radar (Comstock et al. 2005). The authors also observed the splitting, spreading, and dissipating process of drizzling cells over the course of their lifetime, consistent with our simulations.

4. Discussion

a. Effect of grid size on cloud morphology and turbulence

The relatively coarse resolution used in these simulations raises the question of how different the boundary layer and cloud fields might be at higher resolution. To this end, four more simulations were performed at coarse (300 m) and fine (100 m) horizontal grid size over a smaller (25 × 25 km2) domain (see appendix). The essential differences between closed- and open-cellular morphology are well captured by the coarse-resolution simulations, with the finer-scale simulations clearly capturing more detail. Closer examination of vertical profiles of , total water mixing ratio qt, and liquid water potential temperature θl emanating from these simulations, as well as comparison with even higher-resolution results in Wang et al. (2009; Δx = Δy = 50 m; Δz = 12 m), indicates that a progressive increase in resolution results in a concomitant increase in and LWP and better vertical mixing of qt and θl. The high-resolution nonprecipitating simulations exhibit the typical well-mixed, solid-Sc-topped boundary layer (i.e., negative in-cloud , no cumulus penetrating Sc, no decoupled Sc), as opposed to the closed-cell case in the present study. This suggests that resolution is the fundamental cause of this discrepancy.

Comparison of the GCSS intercomparison results (Ackerman et al. 2009) with DYCOMS II measurements of vertical velocity variance (vanZanten and Stevens 2005) shows that those high-resolution models also tend to underestimate . At similarly high resolution, the ARW model has a tendency to generate smaller compared to many of the ensemble members of the GCSS study (Wang et al. 2009). Thus, the tendency for simulation to underestimate is a little stronger in the ARW simulations. Future work will endeavor to explain why.

b. Is a strong surface rain necessary for the formation of open cells?

Although the mean surface rain rate in N150 is only about 0.02 mm day−1, subcloud precipitation also causes cellular structures in the turbulent flow (Fig. 3), suggesting that strong surface precipitation is not necessary for the formation of open cells in Sc clouds. Substantial evaporation of drizzle in the subcloud layer is critical to cooling and moistening the air and driving the circulations that sustain open-cell walls. In the N150 case 98% of cloud-base drizzle evaporates before reaching surface, compared to 77% in N65. The higher evaporative losses are attributed to the higher cloud base in N150 compared to N65 (∼100 m) and to the relatively small drop sizes and drier subcloud layer. On average, the loss rate of drizzle below clouds is 1.86 (1.46) mm day−1 km−1 in N65 (N150). With less drizzle and less evaporated water in N150, the formation of open cells and the breakup of the Sc deck is not as complete as in N65, but it is still sufficient to significantly change cloud morphology and albedo.

SS08 simulated a 2.4 mm day−1 km−1 loss rate of drizzle (estimated from their figures) but a less complete breakup of Sc deck than in our N65 case. These model results therefore suggest that neither surface rain rate nor cloud-base rain rate alone can be used to characterize the relationship between precipitation and open-cell formation. The extent to which this is true in natural cloud systems still needs to be established.

c. The low cloud droplet number concentration

SS08 prescribed Nd = 25 cm−3 to produce a significant amount of drizzle to break up the Sc deck, whereas Xue et al. (2008) initialized their model with a CCN concentration of 25 mg−1 in their bin-microphysical scheme to mimic the open-cellular structure in a trade wind boundary layer. In the present study, the open cellular structure forms in both N65 and N150 cases, which have initial CCN concentrations of 65 and 150 mg−1, respectively, but at the onset of open-cell formation, the respective mean Nd is as low as 25 and 40 mg−1 (Fig. 6). Why are such low values of Nd required for the formation of precipitation? With the measured Nd of 55 cm−3, Ackerman et al. (2009) simulated nearly as much drizzle as in our N65 case. After comparing simulation results among the aforementioned studies and ours, we find that the answer again points to LWP, which is underestimated in our simulations and in precipitating cases of SS08, as well as in some ensemble members of Ackerman et al. (2009). The underestimated LWP in the model has to be complemented by a lower Nd to yield a similar amount of precipitation at cloud base.

Recent observational and modeling studies have shown that rain rate Rr decreases with Nd but increases with LWP (or cloud depth H) in the form of RrH4/Nd (Pawlowska and Brenguier 2003), Rr ∼ (LWP/Nd)7/4 (Comstock et al. 2004), RrH3/Nd (vanZanten et al. 2005), and (Feingold and Siebert 2009). Wood (2005) compared different relationships among LWP (or H), Nd, and Rr using data collected from various field campaigns around the globe. In spite of a clear dependence of Rr on LWP (or H) and Nd, no simple relationship is suitable for all datasets. These relationships are examined using our results from the N65 and N150 cases to evaluate the values of α and β in the Rr ∼ LWPαNdβ relationship. Two of them are shown in Fig. 9. One is a comparison with the relationship derived from DYCOMS II measurements (RrH3/Nd; vanZanten et al. 2005) and the other is the best fit among all, , which is similar to Feingold and Siebert’s (2009) modeling study. For linearly stratified (adiabatic) clouds, LWP is proportional to H2, which gives H3/Nd ∼ LWP3/2/Nd. Given the very different approaches to derivation of these relationships, their agreement is noteworthy. All of these relationships show a nonlinear dependence of Rr on LWP and Nd and agree that Rr is more strongly dependent on LWP than on Nd. This further reinforces why Nd has to be reduced to such low values to generate a certain amount of rain.

5. Conclusions

Aerosol effects on precipitation and the formation of open cells in marine Sc sheets over the northeast Pacific are simulated using the three-dimensional ARW model with a double-moment microphysical scheme that utilizes bin-by-bin collection and sedimentation under the assumption of fixed basis functions for aerosol, cloud, and rain. Three experiments with different CCN number concentrations are performed in a 60 × 60 km2 domain for 16 h to simulate the open-cell, transitional, and closed-cell structure in the cloud albedo field and associated turbulence and microphysical characteristics.

Simulations produce the distinct morphological, optical, and microphysical differences between open- and closed-cell cloud fields similar to those seen in prior studies (Stevens et al. 2005; Sharon et al. 2006; SS08) and support the hypothesis that drizzle plays a critical role in the formation and evolution of open cells in marine Sc clouds. Prior modeling studies (SS08; Xue et al. 2008) elucidated the processes by which a solid cloud deck can transform into an open-cell structure. Those studies were performed in horizontal domains of up to 25.6 × 25.6 km2 in size, so that representation of the meso-β-scale organization associated with open cells and precipitation was somewhat restricted (de Roode et al. 2004). In this study, we have presented results using a significantly larger domain of 60 × 60 km2 to enable interactions between neighboring cells throughout their life cycles and an analysis of the rate of growth of open cells.

The dynamic response to evaporative cooling and moistening associated with precipitation manifests itself in cellular organization of updrafts in the turbulent flow and promotes and sustains the formation of an open cellular structure in cloud fields. The circulation pattern in vertical cross sections of precipitating cells is remarkably consistent with radar observations (Comstock et al. 2007). The cloud-free region in open-cell centers is due to a temporary lack of vertical mixing and dynamical support rather than a shortage of CCN because clouds do develop there whenever the dynamical forcing supports them. In the case under consideration, a mean surface rain rate as low as 0.02 mm day−1 is sufficient to promote open cellular structure in the turbulent flow and cloud fields.

The maximum dimension of individual open cells ranges between 5 and 30 km. The largest cells clearly need large domains in which to grow. The irregular shape of open cells is caused by the formation of new cells in the old cell walls and interference with neighbors, which erode and eventually eliminate the old cells. A cell tends to grow larger if it has significant precipitation (and negative buoyancy) within its center and is surrounded by weakly precipitating cells that cannot compete as effectively for space. This indicates a relationship between the size of an open cell and the spatial distribution of rain intensity in its surroundings.

The typical lifetime of large individual open cells is about 2 h, close to that observed by radar. They grow at a mean rate of between 5 and 10 km h−1. A collection of the simulated open cells lasts for over 10 h. There is no evidence of them collapsing entirely through the course of the simulations, although domain-average liquid water path and cloud fraction do decrease with time. Longer simulations with a diurnal cycle of solar radiation are required to realistically characterize the growth and duration of POCs.

The large domain has necessitated the use of a relatively coarse horizontal grid (300 m). We have performed sensitivity studies at higher resolution in smaller domains to show that the coarser-resolution simulations capture the essential features of the open-cell patterns. The coarser resolution does, however, tend to generate a boundary layer that is less vigorous and not as well mixed as in the finer-resolution simulations (section 4a and appendix). For example, our nonprecipitating boundary layers tend, at coarser resolution, to exhibit some of the features of decoupling usually associated with precipitating boundary layers. Simulations with the model at higher resolution show that this is alleviated at fine resolution (Wang et al. 2009). Regardless, this does not compromise the robust morphological differences between polluted and clean conditions and their manifestation as closed and open cells. As in many applications, the balance between domain size and a desire for detail needs to be borne in mind (e.g., Schröter et al. 2005) and choices must be appropriate to the problem at hand.

Since open cells do not form in the polluted simulations, the question is posed as to whether additional aerosol particle sources can close open cells that have already formed in a clean environment. In a companion paper (Wang and Feingold 2009), we show how a substantial increase in CCN transported from a neighboring polluted environment or from ship emissions influences the cloud microphysics and dynamics at the boundary between open and closed cells.

Acknowledgments

We acknowledge support from NOAA’s Climate Goal. HW was supported by Cooperative Institute for Research in Environmental Sciences (CIRES) Visiting Fellowship. The constructive suggestions from Bjorn Stevens, Robert Wood, and an anonymous reviewer helped improve the manuscript. We thank the NOAA ESRL High Performance Computing Systems team for computational and technical support. GOES-10 data are provided by NCAR/EOL under sponsorship of the National Science Foundation.

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APPENDIX

Summary of Sensitivity Tests for Horizontal Grid Size and Wind Shear

To show that the relatively coarse horizontal grid (i.e., Δx = Δy = 300 m) and a lack of wind shear do not have a significant impact on the simulated formation of cellular structures, six additional sensitivity experiments are conducted. Four experiments (N65_d300, N65_d100, N500_d300, and N500_d100) are performed in a 25 × 25 km2 horizontal domain for N65 and N500 cases with grid sizes of 300 and 100 m. Two other experiments (N65_ws and N500_ws) have the same settings as the N65 and N500 but are initialized with the observed wind shear (e.g., SS08).

Grid size

Figure A1 compares snapshots of the cloud albedo field at t = 6 h for the four sensitivity experiments related to horizontal grid size. As expected, the high-resolution simulations resolve finer details of clouds and vertical velocity (not shown). Nonetheless, both low- and high-resolution simulations capture the patterns of cellular structures in turbulent flow and clouds. It is clear, however, that by t = 6 h a single open cell (with some new cells forming on the walls) tends to fill the entire domain; its growth is limited by the domain size. Unlike open cells in the large domains (Figs. 2 and 3), the isolated open cell cannot sustain itself as a complete ringlike cell wall because of a lack of dynamic interactions with neighboring cells. Quantitatively, relative differences in time-averaged LWP, cloud fraction, Nd, and cloud albedo between N65_d300 and N65_d100 are less than 5%. Note that the high-resolution simulation for the N500 case (N500_d100) has a more distinct closed-cell structure (i.e., clear gaps between cells; see Fig. A1) so that the time-averaged cloud fraction, LWP, and cloud albedo are about 20% smaller than in the low-resolution simulation (N500_d300). However, this does not change the distinct morphological, optical, and microphysical differences between open- and closed-cell cloud fields for both low- and high-resolution simulations.

Wind shear

Results for experiments N65_ws and N500_ws show that while cellular structures do appear in the presence of wind shear, the shape of the cells is, as expected, more irregular. To illustrate this, Figs. A2 and A3 present snapshots of cloud albedo and vertical velocity and precipitation fields at t = 6 h for the two experiments with the observed wind shear. These can be compared to the corresponding plots in Figs. 2 and 3. Closed cells are elongated in the direction of the mean wind and become brighter than in N500, but no notable change exists in the vertical velocity field as a result of wind shear. At a glance, the pattern of domain-wide open cellular structure in N65_ws is similar to that in N65; however, individual open cells are not as well defined in N65_ws, and the visual relationship between precipitation clusters and updraft rings is not as clear. In the absence of shear, individual open cells exhibit more distinct ringlike structures, making it easier to size and track them and thus prompting our decision to remove shear.

Fig. 1.
Fig. 1.

GOES-10 visible imagery of cellular patterns over northeast Pacific off the coast of California at 1530 UTC 11 Jul 2001. Open cells, POCs, and closed cells in a 0.6° × 0.6° box are enlarged for clarity.

Citation: Journal of the Atmospheric Sciences 66, 11; 10.1175/2009JAS3022.1

Fig. 2.
Fig. 2.

Snapshots of cloud albedo fields at t = 3, 6, and 9 h (corresponding to each of the three rows) during the life cycle of the stratocumulus deck for experiments N65, N150, and N500 (corresponding to each of the three columns, with initial CCN concentrations of 65, 150, and 500 mg−1 respectively).

Citation: Journal of the Atmospheric Sciences 66, 11; 10.1175/2009JAS3022.1

Fig. 3.
Fig. 3.

Snapshots of 200-m level vertical velocity fields at t = 3, 6, and 9 h with contours of rain rate (0.5, 5, and 20 mm day−1) superimposed. Plots are arranged in the same way as in Fig. 2.

Citation: Journal of the Atmospheric Sciences 66, 11; 10.1175/2009JAS3022.1

Fig. 4.
Fig. 4.

Vertical (yz) cross sections of total particle (CCN plus drop) number concentration (shaded colors), perturbation wind vectors (updrafts in red and downdrafts in blue; reference arrow for magnitude), cloud water (qc > 0.01 g kg−1; black lines), and drizzle water outline (qr > 0.002 g kg−1; thin red lines) at t = 9 h for (a) N65 at x = 30 km and (b) N500 at x = 13.5 km. For clarity, yz slices are zoomed in to 30 × 1.2 km2.

Citation: Journal of the Atmospheric Sciences 66, 11; 10.1175/2009JAS3022.1

Fig. 5.
Fig. 5.

Vertical profiles of water vapor mixing ratio qv, liquid water mixing ratio ql, rain rate Rr, total particle (CCN plus drop) number concentration Nt, variance of vertical velocity , cloud-average variance of vertical velocity , third moment of vertical velocity , and TKE. Profiles are averaged between t = 3 and 6 h (solid lines) and between t = 9 and 12 h (dotted lines). A cloud optical depth threshold of 2 is used for the calculation of . All other quantities are domain averaged.

Citation: Journal of the Atmospheric Sciences 66, 11; 10.1175/2009JAS3022.1

Fig. 6.
Fig. 6.

Time evolution of (a) domain-average (solid) and cloud-average (dotted) LWP; (b) cloud fraction (CF); (c) domain-average inversion base height (solid) and cloud base height (dotted); (d) cloud-average drop number concentration Nd (solid) and total particle number concentration Nt (dotted); (e) domain-average cloud albedo αc; and (f) domain-average rain rate Rr at the surface (solid) and at cloud base (dotted) for the three experiments as indicated in the legend. Cloudy columns are defined by an optical depth threshold of 2 for the calculation of cloud fraction; a criterion of Nd ≥ 20 mg−1 is applied when calculating cloud-average Nd.

Citation: Journal of the Atmospheric Sciences 66, 11; 10.1175/2009JAS3022.1

Fig. 7.
Fig. 7.

Normalized frequency distribution of open-cell size and wall width as a function of time. At each time, a threshold cloud optical depth τc of 2 is first used to filter the cloud field, and a collection of cell sizes and wall widths are obtained by scanning each row and column of grids in both x and y directions. Cell size is defined as the distance between two neighboring cloudy grids along the scan line, and cell wall width is the distance between two neighboring cloud-free grids. Results are shown (a) using τc = 2 during scanning and (b) using the median τc of all cloudy grids along each row/column to further remove contamination by optically thin clouds. Solid lines indicate (left) the time evolution of the median value of cell sizes in the range of 3–30 km and (right) the median value of wall widths in the range of 1.5–10 km.

Citation: Journal of the Atmospheric Sciences 66, 11; 10.1175/2009JAS3022.1

Fig. 8.
Fig. 8.

Snapshots of 200-m-level vertical velocity fields over a 2-h period for experiment N65. Time since model start is indicated above each panel. Three individual updraft cells are labeled 1, 2, and 3 to track their evolution with time.

Citation: Journal of the Atmospheric Sciences 66, 11; 10.1175/2009JAS3022.1

Fig. 9.
Fig. 9.

Cloud-base rain rate Rr as a function of drop number concentration Nd and cloud depth H or LWP in the form of (a) RrH3/Nd and (b) , where Rr, H, and LWP are domain averages. Data are sampled every 30 min after 2-h model spinup.

Citation: Journal of the Atmospheric Sciences 66, 11; 10.1175/2009JAS3022.1

i1520-0469-66-11-3237-fa01

Fig. A1. Snapshot of cloud albedo field at t = 6 h for the four indicated resolution-sensitivity experiments.

Citation: Journal of the Atmospheric Sciences 66, 11; 10.1175/2009JAS3022.1

i1520-0469-66-11-3237-fa02

Fig. A2. Snapshot of cloud albedo field at t = 6 h for the two sensitivity experiments with observed wind shear for comparison with the corresponding panel in Fig. 2 (with no wind shear).

Citation: Journal of the Atmospheric Sciences 66, 11; 10.1175/2009JAS3022.1

i1520-0469-66-11-3237-fa03

Fig. A3. As in Fig. A2, but for 200-m level vertical velocity with contours of rain rate (0.5, 5, and 20 mm day−1) superimposed for comparison with the corresponding panel in Fig. 3 (with no wind shear).

Citation: Journal of the Atmospheric Sciences 66, 11; 10.1175/2009JAS3022.1

1

Using the observed winds, our simulations do produce open cells, but the cells are more irregular and less distinct. This, and the fact that it is more difficult to track individual cells when horizontal advection exists, has prompted our decision to remove the horizontal winds. We do, however, show additional simulations including wind shear in the appendix.

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