1. Introduction
Marine stratus and stratocumulus (Sc) clouds cover a considerable portion of the world’s tropical and subtropical oceans and play a significant role in the global energy balance through modulating the earth’s albedo (e.g., Hartmann and Short 1980). Marine stratus and stratocumulus clouds are characterized by strong temporal (i.e., diurnal, seasonal, interannual, etc.) and spatial variability and remain a challenge to mesoscale, global, and climate models. This is especially true over the southeastern Pacific (SEP), which is frequently covered by the world’s largest subtropical stratocumulus deck due to its relatively cool sea surface temperature. Over the SEP, coupled atmosphere–ocean models often produce significant errors in sea surface wind and temperature, along with the notorious difficulty in modeling its stratocumulus coverage (e.g., Ma et al. 1996; Kiehl and Gent 2004; Wittenberg et al. 2006; de Szoeke et al. 2012).
Because of its importance in weather and climate modeling, Sc has been the subject of extensive numerical and observational studies over the past two decades or so. The complexity of Sc comes from multiple physical, dynamic, and thermodynamic processes at play over a broad range of temporal and spatial scales. For example, the formation and characteristics of Sc are dependent on synoptic-scale conditions as well as small-scale turbulence and microphysical processes, and its cellular structure (approximately tens of kilometers) is clearly mesoscale (i.e., meso-γ). Benefiting from recent advances in computing power, numerics and physical parameterizations, modern large-eddy simulation (LES) models are capable of simulating Sc cells that resemble satellite imagery and aerial photographs, and play an instrumental role in advancing our understanding of Sc structure and variability (Stevens et al. 1998; Kogan 2006; Wang and Feingold 2009; among others). For example, based on LES simulations, Feingold et al. (2010) demonstrated that precipitation and the associated evaporative cooling are essential to the formation of open cells with much reduced albedo.
Over the last decade, several field observations have been conducted over tropical or subtropical oceans with a focus on Sc [e.g., Eastern Pacific Investigation of Climate Processes in the Coupled Ocean–Atmosphere System (EPIC; Bretherton et al. 2004) and Second Dynamics and Chemistry of Marine Stratocumulus field study (DYCOMS II; Stevens et al. 2003)]. More recently, the Variability of American Monsoon Systems (VAMOS) Ocean–Cloud–Atmosphere–Land Study (VOCALS; Wood et al. 2011b), the field observation component of which [VOCALS Regional Experiment (i.e., VOCALS-Rex)] took place over the SEP in the austral spring of 2008, represented a major international effort to improve understanding, model simulations, and predictions of the coupled ocean–atmosphere–land system over the SEP. One of the main goals of VOCALS is to advance our understanding of the marine cloud variability over subtropical oceans, including the formation and maintenance of pockets of open cells (POCs), which significantly reduce cloud fraction and albedo. One of the VOCALS-Rex research flights, research flight 6 (RF-6), drew broad interests because it documented POC embedded in the SEP stratus deck and a transition from closed cells to open cells (Wood et al. 2011a).
Recently, two possible POC formation mechanisms were tested using LES simulations, namely, inhomogeneity in aerosol number concentration (Berner et al. 2011; Kazil et al. 2011) and variations in the stratocumulus-topped boundary layer (STBL) characteristics, such as depth, moisture, and temperature (Wang et al. 2010; Mechem et al. 2012). Using an LES model, Berner et al. (2011) examined the Sc evolution in an elongated domain with different cloud droplet number concentrations in three separate areas that are otherwise horizontally homogenous (i.e., in terms of both initial condition and large-scale forcing). They demonstrated that open-cell-like patterns with reduced albedo form in the clean air area, while the rest domain with a larger droplet number concentration is still overcast. Wang et al. (2010) suggested that the formation of POC was more sensitive to the moisture and temperature perturbations in the STBL than to the aerosol number concentration variations over the range of parameters they examined. This raises an interesting question about the impact of mesoscale waves on Sc variability, as vertical motion associated with gravity waves may introduce larger-amplitude perturbations in moisture, temperature, and STBL depth than those tested in Wang et al. (2010). In fact, diurnal waves that propagate offshore of northern Chile and southern Peru (e.g., Garreaud and Muñoz 2004; Muñoz 2008; Wood et al. 2009) were hypothesized to have a significant impact on the observed diurnal variation of Sc over the SEP (VOCALS-Rex SOP). According to satellite observations and numerical simulations in previous studies, the diurnal waves offshore of the northern Chile coast are characterized by an ascent band nearly parallel to the coastline with a width of about 400 km and a vertical extension of about 5 km (Garreaud and Muñoz 2004). Observations obtained from the VOCALS-Rex provided further evidence for the existence of these waves (Rahn and Garreaud 2010), and their dynamics and offshore decay distance were examined analytically by Jiang (2012).
In a broad sense, gravity waves are virtually ubiquitous in the troposphere and can be generated by a variety of sources (e.g., topography, hurricanes, frontal activities, and convection). An important and yet open question is how much influence gravity waves have on Sc variability. The objective of this study is to provide some insights into the response of a STBL to mesoscale wave forcing through systematic LES simulations over a range of wave parameters and aerosol number concentrations. The remainder of this paper is organized as follows. section 2 includes a brief description of the LES model, model configuration, characteristics of the sounding profiles, and the mesoscale waves enforced. The numerical results are presented in section 3. Section 4 includes concluding remarks.
2. Numerical configuration
a. LES model and numerical setup
The simulations are performed using a large-eddy simulation model based on the atmospheric component of the Coupled Ocean–Atmosphere Mesoscale Prediction System (COAMPS1; Hodur 1997; referred to as COAMPS-LES). The COAMPS-LES model was described and evaluated in detail by Golaz et al. (2005). This same model was employed by Wang et al. (2008, 2012) for the study of vertical wind shear effects on STBL-top entrainment and turbulence structure. For this study, a selective monotonicity-reserving advection scheme described in Blossey and Durran (2008) is used for the advection of the potential temperature and moisture variables. The two-moment bulk microphysical scheme illustrated in Feingold et al. (1998) and Fu-Liou four-stream radiation code (Fu and Liou 1992) are used for cloud physics and longwave radiation calculation. For simplicity, the aerosol number concentration Na is specified and stays constant for each simulation, while the cloud droplet number concentration Nc can still be changed by microphysical processes, such as activation, evaporation, collection, coalescence, and sedimentation. In addition, to focus on the impact of dynamic wave forcing, the diurnal variation of the shortwave (i.e., solar) radiation is not taken into account.
The computational domain contains 351 × 351 grid points in the horizontal with a grid spacing of Δx = 200 m and periodic conditions applied along lateral boundaries. The grid spacing is chosen based on a set of sensitivity simulations over a smaller domain and in line with other similar studies [e.g., Δx = 300 m in Wang et al. (2010); Δx = 125 m in Berner et al. (2011)]. The relatively coarse horizontal resolution allows us to perform multiple simulations of cell development in a reasonably large domain (i.e., 70 km × 70 km). There are 100 vertical model levels with a uniform grid spacing of 30 m, which is comparable to Wang et al. (2010) and Mechem et al. (2012). It is noteworthy that some previous studies suggested that a finer vertical spacing (i.e., 5 m or less) should be used across an inversion to better resolve smaller-scale eddies and adequately represent the entrainment process (Bretherton et al. 1999; Stevens et al. 2005). We choose to use the relatively coarse vertical spacing because the cloud-top entrainment is not the focus of this study, and the resulted error in the entrainment rate is much smaller than the wave vertical velocity. The model top is located at 3 km, where the potential temperature and water vapor gradients are fixed throughout each simulation.
b. Sounding profiles and mesoscale wave forcing
The model is initialized homogeneously in the horizontal using the wind, potential temperature, and moisture profiles shown in Fig. 1. These profiles are constructed from observations obtained during VOCALS-Rex RF-6 on 28 October 2008 (Wood et al. 2011a), which documented pockets of open cells embedded in a stratocumulus deck over the southeastern Pacific. The mean winds are northwesterly above the STBL and are assumed to be in geostrophic balance. The STBL is approximately 1.3 km deep capped by a sharp inversion of 12.5 K, above which the water vapor mixing ratio decreases sharply. A detailed description of the cloud characteristics and large-scale conditions documented by VOCALS-Rex RF-6 can be found in Wood et al. (2011a). It is noteworthy that these profiles have been used in a few other LES studies (Wang et al. 2010; Berner et al. 2011) as well.
(a) Horizontal wind components (m s−1), (b) potential temperature (K), and (c) water vapor mixing ratio (g kg−1) profiles derived from VOCALS RF-6 measurements.
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-0135.1
(a) Horizontal wind components (m s−1), (b) potential temperature (K), and (c) water vapor mixing ratio (g kg−1) profiles derived from VOCALS RF-6 measurements.
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-0135.1
(a) Horizontal wind components (m s−1), (b) potential temperature (K), and (c) water vapor mixing ratio (g kg−1) profiles derived from VOCALS RF-6 measurements.
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-0135.1
In our simulations, two separate subsidence (i.e., divergence) terms are included, representing the synoptic-scale and mesoscale wave forcing, respectively. Associated with the subtropical Pacific high pressure system, the VOCALS-Rex study area was constantly under the influence of large-scale subsidence over the observational period (Wood et al. 2011b). Previous studies found that the large-scale subsidence exhibits strong diurnal variations and is difficult to derive from in situ measurements (Bretherton et al. 2004; Garreaud and Muñoz 2004; Wood et al. 2009). In LES simulations of this same case, a constant divergence of 1.33 × 10−6 s−1 was used throughout the model depth in Berner et al. (2011) and 1.67 × 10−6 s−1 was used across the depth of the boundary layer in Wang et al. (2010). These values are based on an estimation from the satellite-derived sea level winds (Rahn and Garreaud 2010) and the National Centers for Environmental Prediction reanalysis (Wood et al. 2011b). In this study, we use a constant divergence of 2 × 10−6 s−1 up to the bottom of the inversion Zi. This value is slightly larger than those in Wang et al. (2010) and Berner et al. (2011), and results in a better balance with the growth of the boundary layer depth due to the STBL-top entrainment in our simulations.
3. Results
To understand the response of Sc and STBL to mesoscale wave forcing over a relatively broad parameter space, 18 simulations have been carried out for a variety of mesoscale wave parameters and aerosol number concentrations (Table 1). These simulations are grouped into three sets, namely, the control set (C), the aerosol concentration sensitivity set (A), and the wave frequency sensitivity set (F), and the results are summarized in sections 3a, 3b, and 3c, respectively.
List of all simulations and the corresponding acronyms and parameters. The simulations are named as follows: the first letter represents wave frequency (i.e., Q, S, and D for quarter-diurnal, semidiurnal, and diurnal, respectively), the second corresponds to wave amplitude (i.e., W, M, and S for weak, moderate, and strong, respectively), the last two denote wave phase (i.e., AD, DA, and AF for ascent–descent, descent–ascent, and ascent–flat), and the number corresponds to the aerosol number. The reference simulations free of mesoscale wave forcing are referred to as NMWF. The simulations are grouped into three sets; refer to section 3 for details.
a. Control set of simulations
We start with comparisons of six 14-h simulations (referred to as the control set for the convenience of description) with Na = 100 cm−3, including a reference simulation free of mesoscale wave forcing (NMWF-100) and five simulations forced by semidiurnal waves. Among them, three simulations are forced by semidiurnal waves with the same phase, φ0 = 0, but with differentwave amplitudes, namely, SWAD-100, SMAD-100, and SSAD-100, corresponding to a maximum divergence Dm0 of 10−5 (weak), 1.5 × 10−5 (moderate), and 2 × 10−5 s−1 (strong), respectively (see Table 1 for a list of parameters and acronyms). The resulted vertical velocity W maxima at the STBL top and aloft are approximately 13, 20, and 26 mm s−1. The maximum W for the weak wave forcing simulations is comparable to those derived from mesoscale numerical simulations over the SEP by Garreaud and Muñoz (2004). It is noteworthy that, in one of their LES simulations, Wang et al. (2010) included a 15-km-wide wavelike upward motion and found that, while the liquid water path (LWP) shows a sizable increase, the impact of the upward motion on cloud structures is relatively insignificant. The mesoscale wave forcing used in this study aims to mimic the upsidence waves offshore of the Chilean and Peruvian coastlines and, accordingly, the wavelength and wave period are much longer (i.e., hundreds of kilometers, quarter-diurnal to diurnal).
For φ0 = 0, the STBL first experiences a 6-h (i.e., 2–8 h) ascent with a W maximum at 5 h, followed by a 6-h descent (i.e., 8–14 h) with the strongest descent at 11 h (Fig. 2). Correspondingly, the STBL depth increases between 2 and 8 h and decreases between 8 and 14 h. The wave-induced STBL depth change (or the vertical displacement of the inversion induced by the mesoscale wave) η reaches its maximum at t = 8 h, given by 
The normalized vertical motion W and the corresponding vertical displacement of the STBL top η for the specified mesoscale waves. The four pairs of curves correspond to semidiurnal waves with ascent–descent (SXAD) and descent–ascent (SXDA) phases, a half semidiurnal wave (SXAF), and a quarter-diurnal wave (QXAD). The letter “X” in the legend denotes wave amplitude (i.e., weak, moderate, or strong). The SXAD pair corresponds to a diurnal wave (i.e., DXAD) when the time axis runs from 2 to 26 h.
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-0135.1
The normalized vertical motion W and the corresponding vertical displacement of the STBL top η for the specified mesoscale waves. The four pairs of curves correspond to semidiurnal waves with ascent–descent (SXAD) and descent–ascent (SXDA) phases, a half semidiurnal wave (SXAF), and a quarter-diurnal wave (QXAD). The letter “X” in the legend denotes wave amplitude (i.e., weak, moderate, or strong). The SXAD pair corresponds to a diurnal wave (i.e., DXAD) when the time axis runs from 2 to 26 h.
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-0135.1
The normalized vertical motion W and the corresponding vertical displacement of the STBL top η for the specified mesoscale waves. The four pairs of curves correspond to semidiurnal waves with ascent–descent (SXAD) and descent–ascent (SXDA) phases, a half semidiurnal wave (SXAF), and a quarter-diurnal wave (QXAD). The letter “X” in the legend denotes wave amplitude (i.e., weak, moderate, or strong). The SXAD pair corresponds to a diurnal wave (i.e., DXAD) when the time axis runs from 2 to 26 h.
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-0135.1
Time series of six domain-average variables derived from the baseline set of simulations. These variables are (a) the proportional increase of the STBL depth (i.e., Zi/Zi0 − 1), (b) cloud fraction, (c) rain rate (mm day−1), (d) vertical velocity maximum (m s−1), (e) sensible heat flux (W m−2), and (f) latent heat flux (W m−2). For NMWF-100, the cloud fraction is nearly unity in (b) and the surface rain rate is virtually zero in (c), which is not visible.
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-0135.1
Time series of six domain-average variables derived from the baseline set of simulations. These variables are (a) the proportional increase of the STBL depth (i.e., Zi/Zi0 − 1), (b) cloud fraction, (c) rain rate (mm day−1), (d) vertical velocity maximum (m s−1), (e) sensible heat flux (W m−2), and (f) latent heat flux (W m−2). For NMWF-100, the cloud fraction is nearly unity in (b) and the surface rain rate is virtually zero in (c), which is not visible.
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-0135.1
Time series of six domain-average variables derived from the baseline set of simulations. These variables are (a) the proportional increase of the STBL depth (i.e., Zi/Zi0 − 1), (b) cloud fraction, (c) rain rate (mm day−1), (d) vertical velocity maximum (m s−1), (e) sensible heat flux (W m−2), and (f) latent heat flux (W m−2). For NMWF-100, the cloud fraction is nearly unity in (b) and the surface rain rate is virtually zero in (c), which is not visible.
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-0135.1
Time series of the domain-average (a) LWP (kg m−2), (b) albedo, (c) scaled LWP variances [defined as 
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-0135.1
Time series of the domain-average (a) LWP (kg m−2), (b) albedo, (c) scaled LWP variances [defined as
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-0135.1
Time series of the domain-average (a) LWP (kg m−2), (b) albedo, (c) scaled LWP variances [defined as
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-0135.1
Time–height plots of (a)–(d) cloud water mixing ratio (color, g kg−1) and liquid potential temperature (white contours, interval = 5 K), (e)–(h) RWF (color, mm day−1) and 
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-0135.1
Time–height plots of (a)–(d) cloud water mixing ratio (color, g kg−1) and liquid potential temperature (white contours, interval = 5 K), (e)–(h) RWF (color, mm day−1) and
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-0135.1
Time–height plots of (a)–(d) cloud water mixing ratio (color, g kg−1) and liquid potential temperature (white contours, interval = 5 K), (e)–(h) RWF (color, mm day−1) and
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-0135.1
Plan views of the albedo valid at 5, 8, 11, and 14 h derived from simulations (a)–(d) NMWF-100, (e)–(h) SWAD-100, (i)–(l) SMAF-100, and (m)–(p) SWDA-100.
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-0135.1
Plan views of the albedo valid at 5, 8, 11, and 14 h derived from simulations (a)–(d) NMWF-100, (e)–(h) SWAD-100, (i)–(l) SMAF-100, and (m)–(p) SWDA-100.
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-0135.1
Plan views of the albedo valid at 5, 8, 11, and 14 h derived from simulations (a)–(d) NMWF-100, (e)–(h) SWAD-100, (i)–(l) SMAF-100, and (m)–(p) SWDA-100.
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-0135.1
Horizontal domain-average profiles of (a) water vapor (g kg−1), (b) 
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-0135.1
Horizontal domain-average profiles of (a) water vapor (g kg−1), (b)
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-0135.1
Horizontal domain-average profiles of (a) water vapor (g kg−1), (b)
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-0135.1
In the absence of mesoscale wave forcing (NMWF-100), the STBL depth grows slowly with the integration time (Fig. 3a), implying that the growth of the boundary layer depth due to the STBL-top entrainment is still slightly faster than the specified large-scale subsidence. In accordance with the STBL-top entrainment and growth of the STBL depth, the domain-average LWP and pseudoalbedo (Figs. 4a,b) decrease slowly. The STBL turbulence weakens in accordance with weaker radiative cooling near the cloud top (Fig. 5e). The pseudoalbedo (referred to as albedo for short) is determined by integrating both the cloud and rain spectra for calculating the optical cross-section area in the entire column, following Feingold et al. (1997). Toward the end of the simulation (i.e., t > 10 h), light drizzle precipitation (~1 mm day−1) occurs in the cloud layer, and yet little precipitation reaches the surface (Figs. 3c, 5e). The buoyancy flux is characterized by a positive maximum in the cloud layer, associated with radiative cooling, positive values right above the surface on account of the surface heating, and nearly zero or negative between (Fig. 5i). While the cloud fraction remains nearly unity throughout the simulation, the w maximum (Fig. 3d) as well as the LWP variance and skewness (Figs. 4c,d) increases slowly with time, implying development of mesoscale circulations. Accordingly, cellularization occurs (Figs. 6b,c) and the average cell size tends to grow with time as reported in previous studies (e.g., Wang and Feingold 2009). By the end of the simulation, the cloud morphology is closed cellular (Fig. 6d).
The two simulations forced by semidiurnal waves corresponding to φ0= 0 (i.e., SWAD-100 and SMAD-100) share many similar features that are profoundly different from the reference simulation (NMWF-100). Compared to the reference simulation, the STBL grows faster between 2 and 8 h and slower (or decreases) from 8 to 14 h (i.e., the descending phase, Fig. 2a), associated with the wave-induced stretching or squashing of the STBL. Accordingly, both the LWP and albedo oscillate approximately in phase with the specified wave forcing (Figs. 4a,b). It is noteworthy that the ascent-induced LWP increase includes contributions from the increase of cloud water mixing ratio and the thickening of the cloud layer; the former is approximately proportional to W, and the latter is more in phase with the vertical displacement of the cloud layer. Therefore, if ignoring precipitation and cloud-top entrainment, then the LWP should reach the maximum between 5 and 8 h.
The cloud fraction is near unity for the first 8 h and decreases after the wave-induced descent starts (Fig. 3b). Precipitation in SWAD-100 and SMAD-100 is much more intense than in NMWF-100 and is able to reach the surface (Fig. 3c). The domain-average rainwater flux (RWF) is characterized by tilting linear patterns (Figs. 5f,g), associated with the falling of rain drops. The mean rainwater terminal velocity estimated from the slope (i.e., Δz/Δt) of these linear patterns is about 0.5–1 m s−1, which is comparable to typical drizzle falling speeds (e.g., Gerber and Frick 2012). As suggested by previous studies (e.g., Feingold et al. 2010), precipitation has a dramatic impact on the surface sensible and latent fluxes, turbulence, mesoscale circulations, and cloud morphology. Corresponding to the precipitation maxima, the average cloud depth and LWP show abrupt decreases in both simulations (Figs. 4a, 5b,c). The subcloud layer becomes more stratified on account of rainwater evaporation, and consequently, the turbulence (i.e., 
Despite many common features shared by the two simulations, the differences in precipitation intensity, mesoscale circulations, and cloud patterns between them are significant, highlighting the sensitivity of the STBL and clouds to the wave amplitude. When forced by a moderate-amplitude wave (i.e., SMAD-100), the LWP shows a maximum around 4 h, 2 h earlier and about 20% larger than in the corresponding simulation with weak wave forcing (i.e., SWAD-100). The early arrival of the LWP maximum in SMAD-100 implies that precipitation overpowers the condensation induced by wave lifting; compared to SWAD-100, the maximum surface rain rate produced by SMAD-100 is approximately 5 times more (Fig. 3c). As shown in the time–height sections of the RWF (Figs. 5f,g), the SWAD-100 simulation produces an RWF maximum between 5 and 8 h and weak precipitation throughout the rest of the simulation. In contrast, there are two distinctive RWF maxima in the SMAD-100 simulation, centered at 5 and 7.5 h (Fig. 5g), which are substantially larger than from SWAD-100. The surface average rain rate exhibits two maxima in SMAD-100, located at 5.5 and 8 h, respectively (Fig. 3c), about half an hour behind their corresponding RWF maxima aloft. It is also noteworthy that while the two maxima are comparable, the first surface rainrate maximum in SMAD-100 is only half as large as the second maximum, suggesting that a large portion of the rainwater is evaporated during the first precipitation episode before it reaches the surface. The low-level air is closer to saturation during the second precipitation episode due to the moistening and cooling associated with evaporation during the first episode. Accordingly, the positive buoyancy flux maximum corresponding to the first episode is more pronounced. Even with weak wave forcing (i.e., SWAD-100), high albedo clusters appear during the ascent phase (Fig. 6f), corresponding to updrafts driven by evaporative cooling below. In general, during the descent wave phase, the cloud fraction becomes smaller when forced by a stronger wave and accordingly, the Sc cells become more open. For SMAD-100, the cloud fraction decreases to about 0.15 between 11 and 14 h (Fig. 3b) on account of stronger descent, suggesting Sc is largely dissipated except for some cloud filaments associated with narrow but strong updrafts. As expected, the precipitation becomes even more intense between 2 and 8 h in SSAD-100 (not shown) than in SMAD-100, in accordance with the stronger ascent and the cellular patterns develop earlier and are more open during the wave-induced descent.
In the SMAF-100 simulation, only a half-sine wave is enforced during the 2–8 h to mimic an asymmetric wave (i.e., stronger ascent and weaker descent). The SMAD-100 and SMAF-100 simulations are identical for the first 8 h. From 8 to 14 h, the STBL top in SMAF-100 stays aloft (Fig. 2b) after the wave forcing terminates as opposed to the rest of the simulations, in which the STBL approximately returns to its original depth after a whole wave cycle. In absence of the wave-forced descent, the precipitation continues after the wave forcing terminates (not shown) and the w maximum and 
At last, when forced by a wave starting with its descent phase (i.e., SMDA-100), there is little precipitation in the first 11 h (Fig. 5h) and the clouds are largely dissipated during the descent phase. The boundary layer turbulence is much weaker than the reference simulation, in accordance with reduced cloud-top cooling. It is also noteworthy that, compared to NMWF-100 and SWAD-100, the mean BL top of SMDA-100 is about 15% lower, indicative of less STBL-top entrainment (Fig. 3a). Overall, the evolution of the average albedo and LWP is approximately in phase with the oscillation of the wave-induced STBL depth. During the descent period, the w maximum and 
b. Aerosol number concentration
We have demonstrated that, with a moderate aerosol number concentration (i.e., Na = 100 cm−3), gravity wave forcing can significantly modify the albedo and morphology of marine stratocumuli through triggering or enhancing precipitation and dissipating clouds. As reported in previous studies, precipitation of marine stratocumuli is sensitive to the aerosol number concentration. To examine the sensitivity of the stratocumulus evolution under mesoscale wave forcing to the aerosol number concentration, we have performed several pairs of simulations with aerosol number concentrations varying from 30 to 200 cm−3 with or without wave forcing (see set A in Table 1), and the results from the Na = 50 and 200 cm−3 pairs are summarized in Figs. 8–11, representing clean and dirty air examples, respectively.
As in Fig. 3, but for two pairs of simulations for Na = 200 and 50 cm−3 with semidiurnal weak- and moderate-amplitude wave forcing.
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-0135.1
As in Fig. 3, but for two pairs of simulations for Na = 200 and 50 cm−3 with semidiurnal weak- and moderate-amplitude wave forcing.
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-0135.1
As in Fig. 3, but for two pairs of simulations for Na = 200 and 50 cm−3 with semidiurnal weak- and moderate-amplitude wave forcing.
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-0135.1
As in Fig. 4, but for two pairs of simulations for Na = 200 and 50 cm−3 with semidiurnal weak- and moderate-amplitude wave forcing.
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-0135.1
As in Fig. 4, but for two pairs of simulations for Na = 200 and 50 cm−3 with semidiurnal weak- and moderate-amplitude wave forcing.
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-0135.1
As in Fig. 4, but for two pairs of simulations for Na = 200 and 50 cm−3 with semidiurnal weak- and moderate-amplitude wave forcing.
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-0135.1
As in Fig. 5, but for simulations (left to right) NMWF-50, NMWF-200, SMAD-50, and SMAD-200.
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-0135.1
As in Fig. 5, but for simulations (left to right) NMWF-50, NMWF-200, SMAD-50, and SMAD-200.
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-0135.1
As in Fig. 5, but for simulations (left to right) NMWF-50, NMWF-200, SMAD-50, and SMAD-200.
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-0135.1
As in Fig. 6, but for simulations (a)–(d) NMWF-50, (e)–(h) NMWF-200, (i)–(l) SMAD-50, and (m)–(p) SMAD-200.
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-0135.1
As in Fig. 6, but for simulations (a)–(d) NMWF-50, (e)–(h) NMWF-200, (i)–(l) SMAD-50, and (m)–(p) SMAD-200.
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-0135.1
As in Fig. 6, but for simulations (a)–(d) NMWF-50, (e)–(h) NMWF-200, (i)–(l) SMAD-50, and (m)–(p) SMAD-200.
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-0135.1
It is evident that, even under an identical wave forcing, the characteristics of Sc vary significantly with Na. When the air is clean (e.g., Na = 50 cm−3), precipitation occurs even in the absence of wave forcing (Figs. 8c, 10e) and the intensity oscillates with a period of approximately 2 h, which is comparable to those documented in Feingold et al. (2010). As a result of precipitation, the average LWP and albedo are significantly smaller than the corresponding simulations with more polluted air (e.g., NMWF-200 in Figs. 9a,b, 10a,b, and NMWF-100 in Figs. 4, 5). The surface sensible (latent) heat flux is substantially larger (smaller) than in NMWF-200 (Figs. 8e,f), indicative of stronger low-level evaporative cooling in accordance with precipitation. Correspondingly, the w maximum (Fig. 8d), LWP variance and skewness, and 
When the air is polluted (Na = 200 cm−3), there is little precipitation in both the no-wave-forcing reference simulation (NMWF-200, Fig. 10f) and the simulation forced by a moderate-amplitude semidiurnal wave (SMAD-200, Fig. 10h). In the absence of precipitation, the surface sensible and latent heat fluxes show slow monotonic decrease with time. For SMAD-200, the average LWP and albedo are above their initial values (Fig. 9b) and the third-moment of w′ (i.e., 
c. Quarter diurnal and diurnal wave forcing
To some degree, the wave forcing introduces a new external time scale to the already complicated Sc–precipitation–aerosol–turbulence feedback system that involves multiple internal time scales. Naturally, we expect the response of Sc to a monotonic wave varies with the wave period. In this section, we examine two additional pairs of simulations forced by quarter diurnal and diurnal waves, respectively (Figs. 12–14).
As in Fig. 5, but for (left to right) QWAD-100, QWAD-50, DWAD-100, and DWAD-50.
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-0135.1
As in Fig. 5, but for (left to right) QWAD-100, QWAD-50, DWAD-100, and DWAD-50.
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-0135.1
As in Fig. 5, but for (left to right) QWAD-100, QWAD-50, DWAD-100, and DWAD-50.
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-0135.1
Plan views of the albedo valid at t = 3.5, 5, 6.5, 8, 9.5, 11, 12.5, and 14 h derived from the two quarter-diurnal simulations, (a)–(h) QWAD-100 and (i)–(p) QWAD-50.
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-0135.1
Plan views of the albedo valid at t = 3.5, 5, 6.5, 8, 9.5, 11, 12.5, and 14 h derived from the two quarter-diurnal simulations, (a)–(h) QWAD-100 and (i)–(p) QWAD-50.
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-0135.1
Plan views of the albedo valid at t = 3.5, 5, 6.5, 8, 9.5, 11, 12.5, and 14 h derived from the two quarter-diurnal simulations, (a)–(h) QWAD-100 and (i)–(p) QWAD-50.
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-0135.1
Plan views of the albedo at t = 5, 8, 11, 14, 17, 20, 23, and 26 h for (a)–(h) DWAD-100 and (i)–(p) DWAD-50.
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-0135.1
Plan views of the albedo at t = 5, 8, 11, 14, 17, 20, 23, and 26 h for (a)–(h) DWAD-100 and (i)–(p) DWAD-50.
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-0135.1
Plan views of the albedo at t = 5, 8, 11, 14, 17, 20, 23, and 26 h for (a)–(h) DWAD-100 and (i)–(p) DWAD-50.
Citation: Journal of the Atmospheric Sciences 69, 12; 10.1175/JAS-D-12-0135.1
The aerosol number concentrations for the pair of simulations with quarter-diurnal wave forcing are 100 and 50 cm−3, referred to as QWAD-100 and QWAD-50, respectively. The wave period is T = 6 h, and the divergence amplitude in the STBL is Dm0 = 2 × 10−5 s−1. It is noteworthy that we refer to the wave as weak, as it produces the same maximum vertical displacement of the STBL top (i.e., ηm) as the weak semidiurnal waves with Dm0 = 10−5 s−1. However, the vertical velocity maximum Wm of the weak quarter-diurnal wave is twice as large as that of the weak semidiurnal wave. The integration time for the two quarter-diurnal simulations is 14 h, including a 2-h spinup period, 3-h ascent phase, 3-h descent phase, and 6 h free of wave forcing (Fig. 2). To accommodate a whole diurnal cycle, the integration time for the two diurnal simulations, DWAD-100 and DWAD-50, is 26 h, including 2-h spinup, 12-h ascent, and 12-h descent. The maximum divergence is Dm0 = 5 × 10−6 s−1 for the diurnal simulations, which gives the same maximum vertical displacement of the STBL top as in the SWAD and QWAD simulations.
The domain-average cloud water and RWF for the simulations with quarter-diurnal wave forcing (Figs. 12a,b,e,f) are evidently different than the corresponding simulations forced by semidiurnal waves (Figs. 5b,f). During the 3-h ascent phase, QWAD-100 produces a precipitation (i.e., RWF) maximum comparable to those by SMAD-100, probably because the two simulations have the same maximum wave vertical velocity. Unlike SMAD-100, there is only one RWF maximum in QWAD-100, likely due to the shorter ascent time (i.e., 3 h, comparable to the precipitation oscillation period, ~2 h). In accordance with the precipitation during the ascent phase, the domain-average 
It is interesting to compare the cloud patterns in the quarter diurnal wave runs and those in the corresponding no-wave-forcing runs over the last 6 h. For the period of 8–14 h, the cloud morphology is closed cellular in NMWF-100 and open cellular in QWAD-100 (Figs. 6b–d, 13d,f,h) The difference is likely due to the much enhanced precipitation between 2 and 5 h in the QWAD-100 simulation, which significantly reduces liquid water and cloud fraction. In addition, low-level cold pooling and subcloud-layer decoupling occur in QWAD-100, associated with the more intense precipitation. The differences between QWAD-100 and NMWF-100 in terms of the average LWP, albedo, and cloud coverage decrease with time between 8 and 14 h. In general, after the wave forcing is over, the STBL tends to relax slowly toward the corresponding no-wave-forcing simulation and the characteristic time scale for such relaxation is on the order of 6 h. Both NMWF-50 and QWAD-50 are characterized by typical open-cellular networks for t > 6.5 h, associated with precipitation substantially more intense than in simulations with Na = 100 cm−3. There are some noticeable differences in the cloud morphology during the period of 8–14 h between the two simulations. First, the cells are more open in QWAD-50 due to the ascent-enhanced precipitation. Similar to the pair with Na = 100 cm−3, the reduced albedo and cloud coverage in the simulation with wave forcing slowly increase with time and the relaxation time is comparable to the Na = 100 cm−3 pair. Second, while the horizontal dimensions of the Sc cells grow with time in both simulations, the average cell sizes in QWAD-50 are smaller than those in NMWF-50 at the same hours, likely associated with more intense precipitation, which interrupts the cell growth. The third pair of such simulations for Na = 200 cm−3 (not shown) indicate that, for polluted air, the impact of a passing mesoscale wave on a STBL and cloud morphology is more transient because of the lack of precipitation. In polluted air with overpopulated aerosol particles, the albedo shows a small increase during the ascent phase of the enforced wave and a decrease during the descent phase.
Finally, we show two simulations forced by a diurnal wave while keeping in mind that the shortwave radiation is not considered in this study. The DWAD-100 produces a similar evolution of RWF with a maximum at 8 h when W reaches its maximum and reduced WRF throughout the rest of the simulation. Similarly, 
4. Summary and concluding remarks
The objective of this study is to shed some light on the impact of gravity waves on marine stratocumuli and stratocumulus-topped boundary layer. We have carried out 18 simulations using an LES model initialized with a composite sounding from VOCALS-Rex measurements and forced by gravity waves with different amplitudes, frequencies, and phases. The results indicate that the cloud morphology and albedo often exhibit dramatic changes in response to the wave-induced vertical motion. A transition from closed cells to open cells occurs in several simulations associated with gravity wave forcing, implying that gravity waves may play a role in the formation of POCs over the open ocean. In general, wave-induced ascent tends to increase the liquid water content and therefore enhance precipitation under proper conditions. On the contrary, during the descending phase of a wave, the cloud albedo decreases significantly as the cloud dissipates, associated with subsidence and adiabatic warming. Depending on the aerosol concentration, the descent may break up overcast clouds or lead to a transition from closed cells to open cells.
Our simulations confirm the crucial role of precipitation and the associated evaporative cooling in driving mesoscale circulations in an STBL, as suggested by previous studies. Wave-induced ascent tends to increase the cloud water mixing ratio as well as the cloud depth and therefore facilitate the growth of rain droplets. Consequently, precipitation can be significantly enhanced during the ascent phase of a wave. In accordance with the enhanced precipitation, the surface sensible heat flux increases, the latent heat flux decreases, and low-level relative humidity increases, indicative of evaporative cooling below the cloud level. The evaporative cooling or cold pooling is accompanied with strengthened mesoscale circulations, as evidenced in the increased w maximum and scaled LWP variances and LWP skewness. Precipitation also leads to a sudden increase of 
The timing and intensity of precipitation, and therefore the cloud morphology, vary with the wave characteristics. In general, when forced by a larger amplitude wave, the precipitation is more intense and tends to occur earlier, which leads to stronger mesoscale circulations and fast development of cellular patterns. If the wave period is long enough, a large-amplitude wave may cause episodic precipitation with a characteristic life span on the order of 2 h. The impact of a mesoscale wave on an STBL varies with the wave phase and period as well. An ascent–descent wave cycle has stronger influence on an STBL through enhancing precipitation, and its modification on the cloud morphology and albedo is irreversible. For the parameters examined in this study, it takes about 6 h to replenish the Sc through vertical turbulence transport of water vapor after the wave forcing is over. On the contrary, the influence of a descent–ascent wave cycle on an STBL is more transient and nearly reversible due to the overall negative change in the STBL depth and accordingly little or negative contribution to the precipitation. The dependence of precipitation and cloud cellularization on the wave period is more complicated. When the wave period is longer, the enhanced precipitation time is longer, and accordingly it allows more time for Sc cellularization. In contrast, a longer wave usually corresponds to a weaker vertical velocity (i.e., W) and consequently weaker precipitation.
The impact of gravity waves on precipitation is found to be more significant when the air is moderately polluted (i.e., Na ~ 75–150 cm−3). When Na is low, precipitation could occur even in the absence of wave forcing, and the increase in cloud water content due to wave lift could enhance the precipitation and accelerate the formation of open cells. For an intermediate Na, the increased cloud water during the ascending phase may trigger or significantly enhance precipitation and therefore lead to strengthened mesoscale circulations, cloud cellularization, and sometimes the transition from closed to open cells. For polluted air (i.e., Na ~ 200 cm−3 or larger), no substantial precipitation is observed even with relatively strong wave forcing. The wave-induced ascent (descent) only enhances (dissipates) the stratocumuli temporarily. However, the cloud water content may be modified by the enhanced entrainment during the ascent phase and reduced water vapor supply during the descent phase.
There are a few noteworthy limitations of this study. First, some of the results in this study might be significantly modified by the diurnal cycle of solar radiation, which is not considered here for simplicity. Presumably, the solar radiation may interfere with gravity wave forcing constructively or destructively in terms of their impacts on stratocumulus, depending on the phase difference between the two, which will be investigated in a future study. Second, the Na is fixed throughout each simulation. In the real world, Na can be reduced by precipitation and replenished by processes such as entrainment, turbulence mixing, and advection. The temporal and spatial variations of Na shall add an additional layer of complexity to the already complicated problem and will be examined in a future study. Furthermore, the gravity wave forcing is approximated as a sinusoidal vertical oscillation in time. Accordingly, the advection effect associated with wave-induced horizontal gradients is not discussed.
Acknowledgments
This research is supported by NRL Base Program PE 0601153N. Dr. A. Reinecke helped us with the implementation of the selective monotonic advection scheme. The authors also want to thank Drs. H. Wang and G. Feingold for the helpful discussions about the two-moment cloud microphysics. The primary sponsor of VOCALS is the U.S. National Science Foundation. The simulations were performed using the LES component of the Coupled Ocean–Atmosphere Mesoscale Prediction System (COAMPS-LES) developed by the U.S. Naval Research Laboratory. Computational resources were supported by a grant of HPC time from the Department of Defense Major Shared Resource Centers.
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