1. Introduction
Stratocumulus clouds play an important role in Earth’s energy balance, hydrological cycle, and applications. Because of the prevalence and high albedo of stratocumulus clouds, small changes in stratocumulus cover and thickness can lead to strong responses in Earth’s climate (e.g., Randall et al. 1984). However, climate models are unable to accurately model stratocumulus clouds (Bony and Dufresne 2005). Because of the stark contrast between cloud albedo and ocean surface albedo, the majority of research on stratocumulus clouds has focused on observing, measuring, and modeling marine stratocumulus clouds in the subtropics [Wood (2012) and references therein] or as part of postfrontal systems (Mechem et al. 2010a,2010b). Although receiving less attention, stratocumulus clouds are also abundant over coastal land areas that are frequently well populated (Hilliker and Fritsch 1999; Iacobellis and Cayan 2013; Mathiesen and Kleissl 2011).
The stratocumulus topped boundary layer (STBL) over ocean and land is characterized by a strong temperature inversion that limits the vertical mixing of cool moist air in the boundary layer with warm dry air aloft (Klein and Hartmann 1993). This inversion forms when warm dry air descending from aloft in a high pressure cell interfaces with cool moist air near the surface. Turbulence in the STBL transports water from surface to the cloud layer and promotes entrainment of dry air from the free troposphere. Nocturnally, cloud-top longwave radiative cooling is the primary driver of turbulence in the boundary layer, often resulting in a well-mixed layer that acts to maintain the stratocumulus cloud layer (Lilly 1968). During the day, solar absorption within the cloud counteracts the longwave cooling, thereby reducing the convective mixing. Thus, stratocumulus clouds over the ocean usually attain maximum coverage and thickness just before dawn, minimum coverage and thickness in the early afternoon, and exhibit a marked diurnal cycle (Wood et al. 2002).
The stratocumulus diurnal cycle is even stronger over land. Since land surfaces have a lower heat capacity than ocean, a significant portion of incoming solar radiation is reemitted as sensible and latent heat flux. The stronger surface flux leads to substantial warming and moistening of the STBL over land compared to ocean. Furthermore, during day the surface buoyancy flux becomes the main driver of turbulence in the STBL, offsetting the decrease in turbulence generated by longwave cooling. Hence, cloud-top entrainment velocities over land can exceed 10 mm s−1 during midday (Mechem et al. 2010b), in comparison to entrainment velocities that rarely exceed 5 mm s−1 over ocean (Stevens 2002). Consequently, warming through solar absorption, surface sensible heat flux, and entrainment of drier warmer air aloft are the main causes of daytime cloud dissipation over land. This strong mixing is in stark contrast to the decoupling frequently observed in the STBL over the ocean.
Less research attention has been given to stratocumulus over land than over ocean, and of those studies, the majority have focused on postfrontal continental stratocumulus clouds (Kollias and Albrecht 2000; Zhu et al. 2001; Ghate et al. 2010; Fang et al. 2014a,b; Mechem et al. 2010a; Mechem et al. 2010b). Stratocumulus clouds over coastal land differ from clouds in the continental interior in two major ways. First, coastal stratocumulus clouds usually form in the summer when there is a strong inversion capping the STBL, whereas continental clouds often occur during the cool season when downwelling solar radiation is smaller (Mechem et al. 2010a). Second, horizontal advection by the sea breeze plays an important role in modulating coastal stratocumulus clouds. The transport of air from and to the ocean and the diurnal cycle of the surface energy budget are important in addition to shear and entrainment of free tropospheric air into the cloud layer (Sandu et al. 2010). An accurate assessment of coastal stratocumulus cloud evolution can only be made if all of these factors are considered.
In this paper, we use large-eddy simulation (LES) and a mixed layer model (MLM) to examine how cloud-top entrainment, surface Bowen ratio, and advection by the sea breeze contribute to cloud breakup during the morning transition of stratocumulus over coastal land. We will first use LES of some idealized cases to obtain a reference state of the cloud evolution that reasonably portrays the breakup of coastal stratocumulus clouds (section 3). Next, we describe modifications to the MLM to more accurately represent how changes in cloud-base and cloud-top temperature affect longwave radiation and to more accurately represent the combined effect of surface and cloud-driven buoyancy on turbulence and entrainment (section 4). Finally, the MLM is applied in conjunction with the LES to understand how STBL turbulence, entrainment, cloud liquid water path (LWP), and cloud thickness respond to the varying initial profiles, wet and dry land surfaces, large-scale advection, and subsidence (section 5).
2. Characterization of coastal stratocumulus
Over midlatitude coastal land areas, stratocumulus clouds usually form at night owing to the advection of cool ocean air onto the coast. They are especially prevalent during the summer months in the Northern Hemisphere owing to strong climatological anticyclones over the adjacent ocean. Using normalized global horizontal irradiance (GHI) observations [percentage of instantaneous clear-sky irradiance computed based on Ineichen and Perez (2002)] from a Li-200SZ (LiCor, Nebraska) pyranometer at the University of California, San Diego, we observe that the averaged irradiance is lowest during mornings in the months of May–September, compared to the rest of the year, corresponding with the occurrence of coastal stratocumulus clouds (Fig. 1a). Clouds begin to dissipate farthest inland first in the morning and at progressively later times closer to the coast, where the clouds often survive into the afternoon (Fig. 1b; Skupniewicz et al. 1991). Schwartz et al. (2014) analyzed six decades of airport observations to find that during the summer months low clouds, including stratocumulus clouds, respond to large-scale forcings, such as Pacific decadal oscillation, coherently across the entire west coast of North America and across a wide range of time scales.
(a) Normalized GHI observations measured using a pyranometer at the University of California, San Diego (32.88°N, 117.23°W, approximately 1 km from the Pacific Ocean) in 2011. (b) Averaged cloud dissipation time derived from satellite solar resource data for 2–9 Jun 2014 (SolarAnywhere 2014) for the state of California and averaged cloud dissipation time for southern California overlaid with METAR stations along the coast. The magenta box represents the domain where METAR wind data are acquired to model advection (32.5–33.3°N, 117°–118°W).
Citation: Journal of the Atmospheric Sciences 73, 8; 10.1175/JAS-D-15-0228.1
Similar to the stratocumulus clouds occurring over the ocean, stratocumulus clouds over coastal land attain maximum coverage at sunrise. After sunrise, solar radiation warms the atmospheric STBL and land surface. Because of the lower heat capacity of land, a significant portion of the solar radiation absorbed at the surface is converted to convective surface fluxes, which in turn warm and moisten the STBL depending on land surface properties such as soil moisture content. Even though the Bowen ratio can be greater than one over land, the larger total available energy can result in a higher latent heat flux over land then over ocean. The surface buoyancy fluxes also drive turbulence in the STBL, which in turn increases the cloud-top entrainment and inversion height. Greater warming of land during day drives a stronger pressure difference between land and ocean boundary layers, which in turn increases onshore advection. The horizontal advection of marine air has a cooling effect on the land STBL and may decrease the absolute humidity over land even though the relative humidity of the advected marine air is higher than that of the onshore air. As the day progresses, surface flux heating/moistening, advection of cool oceanic air, and entrainment of warm dry air into the STBL all increase. Price (1999) studied the breakup of stratocumulus over the coast in the United Kingdom and found that cloud breakup was caused by solar heating in one case and by a combination of solar heating and shear-driven entrainment in another case.
While in reality the inland penetration of the stratocumulus clouds is limited by distance from the coast and by topography, for the purpose of this paper we shall neglect topographical effects. We define three domains: an “over the ocean” domain, a “coupled” domain that consists of an STBL over the land with large-scale advection of cool moist air from the ocean, and a “land” domain that we assume to be sufficiently inland that advection does not play a significant role in modulating the cloud lifetime (Fig. 2). We simulate the ocean case to serve as a baseline analysis to compare against published results as well as to contrast against the coupled and land cases. The coupled case is chosen to study the effects of large-scale horizontal advection on cloud lifetime. Each of the coupled and land domains are further broken down into two cases: one consisting of a STBL over a wet land surface and another case over a moderately dry land surface. The wet and dry surface cases are chosen to study the effects of idealized surface moisture content and vegetation cover on cloud lifetime. Finally, we simulate the cases outlined above for two different initial thermodynamic profiles in order to test how initial STBL depth and inversion strength affect cloud lifetime together with testing how well the proposed MLM performs under different initial conditions.
Schematic description of stratocumulus cloud dissipation. (a) At sunrise, the stratocumulus cloud extends from over the ocean inland, thermodynamic profiles are well mixed, and there is a strong thin inversion. (b) At midday, the stratocumulus cloud begins breaking up inland first and the dissipation propagates toward the coast. The cloud has dissipated inland, giving rise to a clear dry convective boundary layer. Near the coast the cloud has thinned significantly and is near dissipation. Over the ocean the cloud has thinned but less so owing to lower surface warming occurring in the ocean domain. For all three domains the boundary layer remains well mixed driven by longwave cooling in the ocean surface case and surface flux in the land cases. (c) In the evening, the horizontal extent of the stratocumulus is at its minimum. The clear dry convective boundary layer inland begins to collapse as the surface flux driving turbulence decreases. Near the coast, the cloud has dissipated but the inversion is supported by the advection of oceanic air mass inland. Over the ocean, the cloud begins to thicken as solar radiation goes to zero. During the night as the cloud thickens over the ocean it is advected inland.
Citation: Journal of the Atmospheric Sciences 73, 8; 10.1175/JAS-D-15-0228.1
3. Large-eddy simulations
a. Initial profiles and domain setup
We employ the University of California, Los Angeles (UCLA) LES model for the large-eddy simulations (Stevens et al. 2005; Savic-Jovcic and Stevens 2008). A cloud interactive radiation scheme based on Monte Carlo sampling of the spectral integration in the delta four stream radiation method was coupled with the LES in order to supply the radiative tendencies (Pincus and Stevens 2009). There has been a significant discussion in the literature on how to accurately model cloud-top entrainment velocity and the effects of entrainment flux on the STBL (e.g., Yamaguchi and Randall 2008; Mellado 2010; Stevens 2002). LES is restricted in its representation of entrainment by the vertical resolution, which is on the order of meters, in addition to its limited ability in tracking the cloud-top mixing interface and modeling the mixing (Stevens 2010). Despite these limitations, LES results were found to match those of measurements well for ocean cases (Stevens et al. 2005; Ackerman et al. 2009).
We simulate the CFMIP-GEWEX Global Atmospheric System (GASS) Intercomparison of LES and Single-Column Model (SCM; CGILS) S12 profile and the Dynamics and Chemistry of Marine Stratocumulus (DYCOMS) first research flight (RF01) profiles as they are representative of a well-mixed STBL (Fig. 3) and have been extensively reported on in the literature, including as initializations for LES intercomparisons (Stevens et al. 2003, 2005; Zhang et al. 2012; Blossey et al. 2013). Bretherton et al. (2013) ran LES and MLM initialized using the CGILS S12 profile to study the ocean STBL response to a variety of factors such as inversion strength, CO2 concentration, and free tropospheric relative humidity. Both the CGILS S12 and DYCOMS RF01 profiles were developed for over-the-ocean model intercomparison studies; however, we do not anticipate any major differences in STBL profiles between land and ocean cases at night. While a weak temperature inversion may occur near the land surface due longwave cooling, the surface longwave cooling effect is greatly diminished in the presence of the cloud layer. There are two main deviations between real observations and CGILS S12 and DYCOMS profiles: 1) variations in liquid potential temperature θl(z) and total water mixing ratio qT(z) within the STBL and 2) thicker inversions. We find that LES based on sounding data with significant inversion thickness (but the same inversion strength) exhibits a qualitatively similar evolution of the cloud layer as the CGILS S12 results (not shown). We therefore expect that the LES and MLM simulations based on the CGILS and DYCOMS cases increase our understanding of the processes behind the cloud dissipation in more realistic situations, similar to how the idealized MLM of stratocumulus by Nicholls (1984) generated insight in more realistic marine cloud layers.
(a) Liquid potential temperature and (b) total water mixing ratio for CGILS S12 (black lines) and DYCOMS (gray lines) simulations at the start of the simulation (0000 LST, solid line) and at 1000 LST for the 1.0 Bowen ratio land case (dashed line).
Citation: Journal of the Atmospheric Sciences 73, 8; 10.1175/JAS-D-15-0228.1
We follow the numerical setup of the CGILS LES intercomparison study: the vertical grid spacing is 10 m near the surface and refined (10% per layer) to obtain a 5-m resolution near the inversion, after which the grid is stretched again. The horizontal resolution is 25 m and the domain size is 2.4 km × 2.4 km in the horizontal and 1.6 km in the vertical (Blossey et al. 2013). In the CGILS S12 LES intercomparison study, the different LES were run to equilibrium conditions over 10 days with an interactive radiation scheme, diurnally averaged (constant) solar radiation, and varying sea surface temperature (Blossey et al. 2013). Little or no precipitation was reported for the duration of the 10-day runs. Thus, we do not consider precipitation and employ a simplified microphysics scheme that consists of a simple pure condensation scheme with no rain. We note that despite drizzle not being observed in the CGILS S12 case, drizzle is often observed in subtropical stratocumulus clouds (Leon et al. 2008). Moreover, unlike the CGILS LES intercomparison, we allow solar position to undergo a diurnal cycle over the 24-h simulation starting at 0000 LST. Large-scale mean subsidence is assumed to be steady since it typically does not vary significantly over 24 h. The LES exhibit a characteristic “spinup” period during the first 2 h (0000–0200 LST), during which turbulent eddies develop as a result of unstable conditions in the STBL due to cloud-top longwave cooling.
We carry out LES initialized with both the CGILS and the DYCOMS profiles for five cases. The first three are for STBLs (i) over the ocean, (ii) over a wet land surface, and (iii) over a moderately dry land surface. The next two are “coupled” cases that include advection from ocean to land for (iv) a wet land surface and (v) a moderately dry land surface.
b. Surface fluxes
For the land cases, the convective fluxes are larger and the partitioning of available energy into sensible (SHF) and latent heat fluxes (LHF), described by the Bowen Ratio (β = SHF/LHF), is of primary importance for stratocumulus lifetime. We assume a constant Bowen ratio for simplicity rather than employ a detailed land surface model that lacks generality and introduces many empirical parameters. Although the similarity of exchange coefficients for heat and water and the longer time scale for changes in soil moisture content compared to atmospheric turbulence motivate the use of a constant Bowen ratio, several limitations exist in practice. For large available energy at the surface, the ability of the vegetation to conduct sufficient water to the surface to maintain the Bowen ratio may be limited by stomatal conductance or leaf area; this results in increasing Bowen ratio as the morning progresses during clear days. However, this limitation is largely irrelevant for the cases studied in this paper since stratocumulus clouds attenuate the solar energy at the surface. The Bowen ratio will also vary if surface air is near saturation and inhibits latent heat flux or if the soil moisture in the root zone or top soil layer reaches the permanent wilting point, but neither is the case in our simulations. Typical Bowen ratio values range from 0.1 over irrigated orchards to 0.2 over forests and grasslands to 2 for urban and semiarid regions (EPA 2004). We chose a Bowen ratio of 0.1 to represent the wet surface case and a Bowen ratio of 1.0 to represent the moderately dry surface case.
The parameterized surface fluxes were tested against a more sophisticated land surface model (LSM) described in Heus et al. (2010) and Rieck et al. (2014), where the coupling to the LES is also described in more detail. The parameterized surface fluxes in Eqs. (2) and (3) were found to be in good agreement with the surface flux of the LSM. Furthermore, both ϕ and φ were found to be relatively constant throughout the daytime and equal to 0.9 and 0.04, respectively.
c. Large-scale advection
Surface wind speed (a) magnitude and (b) direction collected from METAR stations along the coast of California (32.5–33.3°N, 117°–118°W; see Fig. 1b).
Citation: Journal of the Atmospheric Sciences 73, 8; 10.1175/JAS-D-15-0228.1
The LES ocean case provided values of liquid potential temperature and total water mixing ratio profiles [
4. Mixed layer model
The MLM is a thermodynamic model that has been applied to various atmospheric boundary layers, including dry convective and the STBL over the ocean (Bretherton and Wyant 1997; Uchida et al. 2010; Dal Gesso et al. 2014). The MLM solves the STBL mass, heat, and moisture budget equations (Lilly 1968; refer to our appendix A for an overview of the equations). Turbulence in the STBL is generated by either longwave radiative divergence across the cloud layer or by surface flux, and unstable conditions are assumed to prevail. Thus, the thermodynamic properties are assumed to follow adiabatic values, and the STBL is taken to be well mixed (Albrecht et al. 1990; Caldwell et al. 2005). The well-mixed assumption breaks down when the STBL becomes decoupled owing to a reduction in turbulence or an increase in the inversion height. We did not observe any significant deviations from the well-mixed assumption in this study since the inversions height does not exceed 1 km for the cases we have chosen. Furthermore, surface buoyancy flux in the land cases is a significant source of turbulence that keeps the STBL well mixed. While the MLM framework and budget equations are taken from the literature, to improve the MLM accuracy for STBL over land several parameterizations are modified or introduced in the following sections.
a. Radiation parameterization
b. Entrainment parameterization
The thickness of the entrainment zone is an active research topic. Studies conducted by Sullivan et al. (1998) and Fedorovich et al. (2004) on clear convectively driven boundary layers considered a single layer to exist within the entrainment zone. More recently, Garcia and Mellado (2014) showed that the entrainment zone consists of two overlapping sublayers: an upper sublayer that is dominated by thermals and stratification and a lower layer dominated by troughs (crests of undulations within the entrainment zone at the cloud top) of mixed fluid. In the case of the STBL over land, defining the entrainment zone is further complicated by an inversion that is rapidly weakening as a result of surface heating and rising in height because of increased encroachment fed by the enhanced turbulence resulting from the land surface flux (Figs. 5d–i and 6c–f). Because of the uncertainties regarding the definition of entrainment zone heights and insufficient resolution in LES to accurately represent the physical processes occurring in the entrainment zone, we utilize the entrainment zone thickness as a tuning parameter to match LES derived entrainment velocity with that of the MLM. Thus, we set two different entrainment zone heights: one for the cloud-top radiative cooling contribution and another for the surface flux contribution, equal to 3.4 and 7.5 m, respectively. The entrainment zone heights remain constant throughout the simulation and do not change between cases.
Horizontally averaged temporal evolutions from LES of vertical profiles for the CGILS case of (a),(d),(g),(j),(m) liquid potential temperature 
Citation: Journal of the Atmospheric Sciences 73, 8; 10.1175/JAS-D-15-0228.1
Horizontally averaged temporal evolutions from LES for the CGILS case of vertical profiles of (a),(c),(e),(g),(i) buoyancy flux, and (b),(d),(f),(h),(j) vertical velocity variance 
Citation: Journal of the Atmospheric Sciences 73, 8; 10.1175/JAS-D-15-0228.1
c. Factors contributing to cloud dissipation
5. Results and discussion
We present LES and MLM results for five cases: (i) ocean case, (ii) relatively wet land surface case (β = 0.1), (iii) moderately dry land surface case (β = 1.0), (iv) relatively wet land surface case (β = 0.1) “coupled” to the ocean STBL by horizontal advection, and (v) moderately dry surface case (β = 1.0) “coupled” to the ocean STBL by horizontal advection. The analysis is performed using both the CGILS and DYCOMS initial profiles. In the noncoupled cases (i, ii, and iii), we assume that horizontal heterogeneity is negligible and that the large-scale horizontal advection of heat and moisture does not affect either domain. Conversely, the coupled cases are motivated by actual coastal conditions where temperature and moisture gradients are significant and large-scale advection plays an important role in modulating the cloud lifetime. For each of the cases outlined, we compare the MLM output against the LES results up to the time of cloud dissipation since we are interested in studying the factors affecting cloud lifetime. We apply Eq. (16) to the MLM output in order to understand how each physical process contributes to the cloud thickness tendency.
a. Ocean case—Baseline analysis
The ocean results confirm well-known stratocumulus behavior (Figs. 5a–c). LWP varies diurnally over the ocean with maximum LWP occurring just before sunrise. LWP decreases after sunrise owing to solar radiative heating across the cloud layer that warms the boundary layer, causing cloud evaporation. Minimum LWP occurs at 1340 LST and at a value of 31 g m−2. The solar radiative heating additionally reduces the buoyancy flux (Fig. 6a) generated through longwave radiative cooling within the cloud layer and correspondingly reduces the turbulence within the STBL (reduction in vertical velocity variance; Fig. 6b). Thus, in addition to directly heating the STBL, solar radiative forcing indirectly affects LWP by reducing buoyancy flux generated within the cloud layer and thus entrainment of warm and dry air into the STBL.
The MLM and LES results are in good agreement (Fig. 7). In all LES cases, there is a drop in LWP during 0000–0200 LST possibly because of spinup effects; consequently, LWP in LES is slightly lower than that of the MLM. The MLM results better match those of the LES when the MLM was initiated with LES thermodynamic profiles sampled after the spinup period (not shown). However, we choose to use the CGILS profiles rather than the postspinup LES profiles to initialize the MLM as our goal is to develop a stand-alone MLM. Note that surface fluxes agree exactly because the same ocean surface model is used in the LES and MLM. The moistening effect of surface latent heat flux is stronger than the heating effect of sensible heat flux over the ocean, resulting in net cloud thickening. Subsidence thins the cloud by pushing the inversion downward (Myers and Norris 2013). Entrainment flux, on the other hand, modulates cloud thickness and lifetime by raising the cloud top and thinning the cloud layer through the mixing of warm dry air aloft into the clouds. The magnitude of entrainment flux decreases during the day over the ocean owing to the decrease in buoyancy flux caused by solar heating that offsets the longwave cooling within the cloud layer.
Comparison between LES (solid) and MLM (dashed) for the CGILS case of (a),(f),(k),(p),(u) LWP, (b),(g),(l),(q),(v) cloud base (gray) and inversion height (black), (c),(h),(m),(r),(x) liquid potential temperature of the boundary (θlBL), (d),(i),(n),(s),(y) total water mixing ratio (qTBL), and (e),(j),(o),(t),(z) entrainment velocity (we) for (a)–(e) the ocean case, (f)–(j) land case with Bowen ratio equal 0.1, (k)–(o) land case with Bowen ratio equal 1.0, (p)–(t) coupled case with horizontal advection representing the diurnally varying sea breeze circulation and Bowen ratio equal to 0.1, and (u)–(z) coupled case with horizontal advection representing the diurnally varying sea breeze circulation and Bowen ratio equal to 1.0. Note that for (k)–(o) the land case with Bowen ratio equal to 1.0 and (u)–(z) coupled case with Bowen ratio equal to 1.0, the plots are only from 0000 to 1200 LST as the cloud dissipates soon after sunrise and the MLM simulation ends.
Citation: Journal of the Atmospheric Sciences 73, 8; 10.1175/JAS-D-15-0228.1
b. Land cases without advection—Effects of surface conditions on cloud lifetime
At night over land, longwave cooling is the main factor driving turbulence and entrainment flux. During day, surface flux is an additional source of turbulence and heating and moistening. For the wet surface case (small Bowen ratio), the stratocumulus layer breaks up at 1400 LST followed by partly cloudy conditions until sunset, after which the cloud cover returns to overcast (Figs. 5d–f). The increase in surface latent heat flux after sunrise moistens the STBL (Fig. 5e). The surface buoyancy flux (refer to section 4b, Fig. 6d) keeps the STBL well mixed despite the increase in inversion height by more than 100 m between sunrise and midday (Fig. 6c). LWP is greater in the MLM than the LES, possibly because of the LWP loss during LES spinup. Consequently, the higher LWP in the MLM attenuates the net surface radiation, thereby reducing the surface turbulent flux (Figs. 7f,k). In particular, the lower latent heat flux in the MLM results in lower STBL moisture content later in the day compared to the LES (Fig. 7i). Despite the substantial moistening effect of surface latent heat flux, the combination of solar absorption and enhanced entrainment flux thin the cloud at a faster rate than the surface latent heat flux thickens the cloud; thus, the cloud layer eventually dissipates in the MLM (Fig. 8b).
Breakdown of the different factors controlling cloud thickness (h) evolution in the MLM for (a) the ocean case, the land surface case with Bowen ratio equal to (b) 0.1 and (c) 1.0, and the coupled case with Bowen ratio equal to (d) 0.1 and (e) 1.0. The entrainment flux across the inversion is denoted by the blue line, SHF 
Citation: Journal of the Atmospheric Sciences 73, 8; 10.1175/JAS-D-15-0228.1
For the dry surface case (large Bowen ratio), we observe rapid cloud dissipation soon after sunrise as the STBL substantially warms because of increasing surface sensible heat flux (Figs. 5g–i). The sensible heat flux drives a strong increase in buoyancy flux (Fig. 6e), resulting in a rapidly increasing entrainment velocity that incorporates more warm dry air aloft into the STBL (Fig. 7o). Stronger warm thermals emitted by the dry land surface substantially enhance STBL height compared to the wet surface case. Pal and Haeffelin (2015) similarly found that inversion height evolution, measured using lidar, had a higher correlation to land surface processes for drier soil conditions. The MLM overestimates LWP compared to the LES, but the difference in cloud lifetime is less than 30 min (Figs. 7k–o). In both simulations, the combination of increasing sensible heat flux and entrainment flux dissipate the cloud shortly after sunrise (Fig. 8c).
c. Land case with advection of oceanic air—Effects of large-scale horizontal advection on cloud lifetime
Similar to the prior cases, the MLM has larger LWP than the LES as a result of spinup effects causing a drop in LWP within the first 2 h for the LES. Thermodynamic values (θl, qT) and entrainment are in good agreement between both simulations (Figs. 7p–z). In both the wet and dry surface coupled cases the cloud layer is mainly controlled by radiation and entrainment flux during the night, similar to the land case without large-scale horizontal advection. Advective cooling and drying are about balanced at night. During the day the prescribed horizontal winds increase as a result of the pressure difference between the warm land and cool ocean air masses (Fig. 4). Combined with the temperature and moisture differences between both air masses, the winds give rise to the advective tendencies.
In terms of temperature, large-scale advection of ocean air produces a strong cooling effect after sunrise that thickens the cloud layer for both dry and wet land surface conditions. In terms of moisture, large-scale advection acts to thin the cloud layer for the wet surface case (Fig. 8d). This is because the land STBL experiences increased latent heat flux from a wet surface at warmer temperature and thus has greater water vapor mixing ratio than air advected from the ocean. The combined effects of large-scale advection of heat and moisture nonetheless provide a net cloud thickening, as expected. Consequently, the cloud layer in the coupled wet land surface case exists in a cooler STBL and persists throughout the day (Figs. 5j–l), unlike the wet land surface case without advection. The cloud thickening effect of horizontal advection of cooler air (with lower saturation mixing ratio) offsets the cloud thinning effects of larger entrainment flux, solar absorption, and the lower mixing ratio of the advected air (Fig. 8d).
For the coupled dry surface case, the clouds dissipate during the day and reform after sunset (Fig. 5o). This case is similar to stratocumulus clouds occurring over the relatively dry Southern California coast during the summer months (Fig. 1). The STBL does not warm as fast in the coupled case as in the uncoupled land case because cooling from large-scale advection acts to offset the strong warming effect of entrainment flux, surface sensible heat flux, and solar absorption. The reduced warming of the STBL results in slower cloud dissipation. The cloud layer begins to thin at 0900 LST, resulting in a broken cloud deck (cumulus clouds) that persists until 1230 LST, followed by clear skies (Figs. 7u–z). The cloud thickening effect of large-scale advection is further enhanced by the attenuation of net surface radiation by the thicker cloud, thus reducing energy available for the surface flux warming. The advective tendencies more strongly support cloud thickening in the dry case compared to the wet case, because (i) the STBL over dry land is warmer, thus increasing land–ocean temperature gradients, and (ii) the STBL over dry land is less moist and therefore advection only causes minimal drying compared to the STBL over wet land.
Fluctuations in coastal wind speed and direction at subhour temporal and 1–10-km spatial scales resulting from variations in ocean–land pressure differences and synoptic conditions could be responsible for the observed day-to-day and spatial differences in stratocumulus cloud cover along the coast. This was observed during the Variability of the American Monsoon Systems Ocean–Cloud–Atmosphere–Land Study Regional Experiment (VOCALS-REx) campaign in which horizontal advection had a strong effect on marine boundary layer height and the advection term (
d. DYCOMS cases—Effects of initial conditions on cloud lifetime
To test how well the MLM performs under different initial conditions and the different physical factors affecting cloud lifetime, we simulate the five cases using DYCOMS initial profiles that consist of higher inversion height and a stronger temperature inversion than that of CGILS (Fig. 3). The LES and MLM results for the DYCOMS case are in good agreement (Fig. 9). In the first 2 h of the DYCOMS case, the MLM overpredicts entrainment velocity compared to the LES owing to a relatively weaker inversion and a stronger entrainment efficiency coefficient, and the stronger entrainment flux causes a rapid decrease in LWP in the MLM that is comparable to the decrease in LES due to the spinup effect. The major difference between the CGILS and DYCOMS cases is that the entrainment velocities are higher in the DYCOMS cases (Figs. 9e,j,o,t,z) than in the CGILS cases (Figs. 7e,j,o,t,z) because of the weaker inversion in DYCOMS initial profile (Fig. 3). Hence, the inversion height increases at a faster rate in the DYCOMS cases compared to the CGILS cases. Despite the higher magnitude of entrainment velocity in the DYCOMS cases, the contribution of entrainment flux to cloud thinning is similar to CGILS (Figs. 8 and 10) owing to the weaker temperature inversion in the DYCOMS case. Despite the difference in initial conditions, the cloud lifetime in both cases behaves similarly in response to the external forcings such as land surface properties and large-scale horizontal advection.
As in Fig. 7, but for the DYCOMS initial conditions.
Citation: Journal of the Atmospheric Sciences 73, 8; 10.1175/JAS-D-15-0228.1
As in Fig. 8, but for the DYCOMS initial conditions.
Citation: Journal of the Atmospheric Sciences 73, 8; 10.1175/JAS-D-15-0228.1
e. STBL feedback loops
The advantage of Eq. (16) applied to a MLM is that we can map the feedbacks between two variables and the interaction between different feedbacks. Although we provide only a qualitative description of the main feedback loops present in the STBL over the coast in this section, the feedback analysis could be expanded to include a quantitative analysis similar to that of Jones et al. (2014), in which the authors used LES and MLM to quantify the adjustment time scale arising from cloud thickness–turbulence–entrainment feedbacks for stratocumulus clouds over the ocean. A positive effect is one in which change (increase or decrease) in a certain variable results in the same type of change (increase or decrease) in a second variable and vice versa for a negative effect. Effects can then be summed to form feedback loops. A positive feedback (reinforcing) loop occurs when a change in a certain variable ultimately comes back to cause further change in the same direction for that certain variable. A negative (balancing) loop, on the other hand, occurs when a change in a certain variable ultimately comes back to cause change in the opposite direction for that certain variable. An example of a positive loop is when the surface sensible heat flux warms the boundary layer and dissipates the cloud layer, thereby increasing the net surface radiation, which feeds the surface flux. An example of a negative feedback loop is when the surface latent heat flux moistens the boundary layer, thereby thickening the cloud layer and reducing the net surface radiation feeding the surface latent heat flux. For the STBL particularly over land, the daytime cloud dissipating feedback loops tend to be more powerful, leading to rapid thinning of the initial cloud layer.
For all five cases, longwave radiative divergence cools the STBL, thereby thickening the cloud layer and increasing the longwave radiative divergence across the cloud layer, thus forming a reinforcing feedback loop (Fig. 11a). Longwave radiative divergence additionally drives the turbulence in the STBL, which feeds cloud-top entrainment which in turn warms and dries the STBL, thereby reducing the cloud thickness and the longwave radiative divergence and thus forming a negative feedback loop (Fig. 11b). Nocturnally, we observe that the stabilizing longwave radiation–entrainment feedback loop dominates and that the LW cooling of the BL saturates for LWPs of around 40 g m−2 (Figs. 7a and 9a).
Feedback loops acting upon the cloud thickness h in the MLM. Solid lines denote positive effects, and dashed lines denote negative effects. Feedback loops are shown separately for (a) radiative divergence, (b) entrainment driven by radiative divergence, (c) surface flux, and (d) surface flux driven by radiative divergence.
Citation: Journal of the Atmospheric Sciences 73, 8; 10.1175/JAS-D-15-0228.1
Over the ocean, solar radiative heating has two opposing effects on cloud thickness: (i) warming of the STBL that thins the cloud and therefore reduces solar heating within the cloud layer (balancing feedback loop) and (ii) warming of the cloud layer that opposes longwave cooling and reduces buoyancy flux, which reduces cloud thinning due to weaker entrainment flux (positive feedback loop; Figs. 11a,b). Over land, the STBL responds much faster to solar heating because the lower heat capacity of the land surface means most of the net surface radiative flux is reemitted by the land surface as turbulent fluxes of sensible and latent heat. Large-scale horizontal advection acts to dampen the effects of solar heating by thickening the cloud layer, thereby reducing the net radiation at the surface.
For the low Bowen ratio case we have two feedback loops: (i) a negative feedback loop that maintains the cloud layer and consists of surface latent heat flux moistening the STBL, thickening the cloud, and thereby attenuating the surface radiation feeding the surface flux and (ii) a positive feedback loop that causes the cloud to dissipate and consists of latent heat flux feeding the cloud-top entrainment flux, dissipating the cloud layer, and thereby increasing surface radiation feeding the surface flux (Figs. 11c,d). We observe a positive feedback loop, in the high Bowen ratio case, in which increased sensible heat flux leads to increased entrainment with both factors then warming and drying the STBL. Both factors decrease the LWP, which in turn increases the net solar radiative flux at the surface thus driving an additional increase of surface flux (Fig. 11d).
6. Conclusions
We employed LES and a MLM to investigate factors controlling stratocumulus clouds over coastal land in general and the timing of daytime cloud dissipation in particular. One necessary development that we expect will improve MLM simulations over land is the parameterization of the entrainment velocity as function of the surface buoyancy flux and the integrated cloud buoyancy flux. The simulated STBL and cloud dissipation time in the MLM was found to be in good agreement with LES results. In particular, the entrainment scheme produced entrainment velocities and inversion heights consistent with the LES results for a variety of cases, including over ocean.
We found that cloud lifetime is sensitive to land surface conditions characterized by the Bowen ratio since the bulk of the net surface radiation over land is converted to convective fluxes into the boundary layer. For wet land surfaces, latent heat flux dominates over sensible heat flux, thus moistening the STBL and thereby thickening the cloud layer. In contrast, for moderately dry surfaces, the sensible heat flux dominates, and it and entrainment flux act together to rapidly dissipate the cloud after sunrise. The stronger surface buoyancy fluxes for both wet and dry land cases (compared to the ocean) indirectly thin the cloud by increasing turbulence in the STBL and increasing the cloud-top entrainment flux. Furthermore, the surface net radiation induces stronger surface buoyancy fluxes and stronger entrainment at larger Bowen ratios.
The sea breeze is an important feature of coastal environments, and onshore winds advect cool air from over the ocean onto the coast, thereby thickening the cloud layer. We represented advection effects by prescribing wind speed obtained from surface wind measurements and using temperature and humidity outputs from LES and MLM simulations over the ocean. The advection of ocean air onto the coast plays an important role in modulating the cloud lifetime. For both dry and wet land surface conditions, large-scale horizontal advection cools and dries the STBL. For the wet surface case, the large-scale horizontal advective cooling contributes to maintenance of the cloud layer throughout the day. For the dry surface case with advection, cloud dissipation time is delayed by roughly 3 h.
We believe that this study and future applications of the MLM modified turbulence and entrainment parameterizations will provide important insights into the factors controlling stratocumulus cloud lifetime over coastal land. This study has additionally highlighted the differences between STBL occurring over oceans and coastal lands. Hence, parameterizations developed for stratocumulus clouds over the ocean might not succeed in capturing the physics of those clouds occurring over coastal lands. An analysis benchmarking the capability of the different parameterizations, notably entrainment, in representing the STBL over coastal lands remains to be explored in future work.
Acknowledgments
We acknowledge funding from the California Solar Initiative RD&D program. The authors thank Patrick Mathiesen for providing the Normalized GHI observations at the University of California, San Diego in Fig. 1 and Handa Yang for processing the SolarAnywhere data.
APPENDIX A
Mixed-Layer Model Governing Equations
The heat budget equation is formulated in terms of the liquid potential temperature (θl = θ − (1/Π)(Lυ/cp)ql), where ql represents the liquid water mixing ratio, θ represents the potential temperature, 
APPENDIX B
Parameterization of Longwave Radiation for the MLM
Comparison of longwave radiation derived from LES (solid) and MLM (dashed) computed using the CGILS S12 temperature and liquid water vertical profiles.
Citation: Journal of the Atmospheric Sciences 73, 8; 10.1175/JAS-D-15-0228.1
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