Large-Eddy Simulation of Moist Convection during a Cold Air Outbreak over the Gulf Stream

Transcription

1 1274 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 66 Large-Eddy Simulation of Moist Convection during a Cold Air Outbreak over the Gulf Stream ERIC D. SKYLLINGSTAD College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, Oregon JAMES B. EDSON Department of Marine Sciences, University of Connecticut, Groton, Connecticut (Manuscript received 1 February 2008, in final form 16 October 2008) ABSTRACT Cold air outflow over the Gulf Stream is modeled using a cloud-resolving large-eddy simulation model with three classes of precipitation. Simulations are conducted in a quasi-lagrangian framework using an idealized sounding and uniform geostrophic winds based on observations taken on 20 February 2007 as part of the World Climate Research Program Climate Variability and Predictability (CLIVAR) Mode Water Dynamics Experiment (CLIMODE) project. Two cases are considered, one with an increasing sea surface temperature (SST) representing the crossing of the Gulf Stream front, and a second case with constant SST. Cloud systems develop in the model with strong convective plumes that spread into regions of stratus clouds at the top of the boundary layer. Simulated boundary layer growth is forced by a combination of evaporative cooling at the cloud top, upward radiative flux, and mechanical entrainment of the overlying warmer and drier air. Constant growth of the boundary layer acts to maintain a near-constant water vapor level in the boundary layer, promoting high latent and sensible heat fluxes. Frictional surface drag is distributed throughout the boundary layer by convection, causing increased shear at the cloud top, qualitatively agreeing with observed sounding profiles. Overall, the frontal case develops stronger precipitation and turbulence in comparison with the constant SST case. A near-uniform stratocumulus layer and stronger radiative cooling are produced in the constant SST case, whereas the frontal case generates open cumuliform clouds with reduced cloud coverage. Cloud evolution in the frontal case is similar to the transition from stratocumulus to shallow cumulus observed in the subtropics, as cumuliform clouds enhance cloud-top entrainment and evaporation of stratus clouds. 1. Introduction Air sea interaction over the midlatitude oceans is a major component in the seasonal cycle of the atmospheric heat and moisture content. Dry, cold continental air produced over land gains heat and moisture when traveling over the ocean, typically through moist convective processes. As the air warms, rapid cooling of the ocean is forced, which can penetrate to depths of hundreds of meters in the weakly stratified water masses commonly referred to as mode waters that form adjacent to western boundary currents in the subtropical Corresponding author address: Eric Skyllingstad, COAS, 104 COAS Admin. Bldg., Oregon State University, Corvallis, OR skylling@coas.oregonstate.edu gyres (e.g., Dewar et al. 2005). One such mode water is present in the Atlantic basin south of the Gulf Stream at depths of 500 to 1500 m. Atlantic mode water is often named eighteen-degree water (EDW) because it has a temperature range of C. Mode water acts like a long-term memory for the climate system, storing information about the strength of air sea fluxes from previous winter seasons. Because of the importance of EDW mode water as a climate indicator, an extensive observational program the World Climate Research Program Climate Variability and Predictability (CLIVAR) Mode Water Dynamics Experiment (CLIMODE) was undertaken to collect data on atmospheric and oceanic processes that lead to mode water formation (Marshall et al. 2009). Evidence suggests that much of the EDW forms just south of the Gulf Stream during winter storms when DOI: /2008JAS Ó 2009 American Meteorological Society

2 MAY 2009 S K Y L L I N G S T A D A N D E D S O N 1275 latent and sensible heat fluxes are a maximum. Typical high flux conditions are generated when extratropical cyclones intensify and move off the east coast of North America, transporting polar continental air over the offshore Gulf Stream region. Air masses moving off the mainland are cold and dry, setting up a scenario for strong boundary layer mixing and moist convection. These cold air outbreaks generate organized convective systems, usually starting as roll convection and expanding into large-scale convective complexes, as shown by a satellite image in Fig. 1. Cold air outbreaks have been studied extensively in recent years with most of the emphasis placed on understanding the broadening of cells as convection develops downstream. In particular, research on cold advection over the Great Lakes of North America has received considerable attention. Examples include simulations using mesoscale models (Hartmann et al. 1997; Tripoli 2005; Maesaka et al. 2006) and largeeddy simulation (LES; Rao and Agee 1996; Zurn- Birkhimer et al. 2005; Gryschka and Raasch 2005). Over the ocean, studies of cold air outbreaks have concentrated on the structure and dynamics of atmospheric convection in response to the large air sea surface temperature difference. For example, Schröter et al. (2005) examine how moist processes control the broadening of coherent cloud bands, showing that diabatic heating within clouds and cloud-top cooling are necessary for development of convective roll aspect ratios greater than 10. Here, we are interested in the overall budgets of heat and moisture within the marine boundary layer and how modifications of the boundary layer bulk properties affect surface fluxes. It is well known that cold air outbreaks can produce extremely large latent and sensible heat fluxes just offshore of the Gulf Stream front. For example, latent heat values observed and simulated during the Genesis of Atlantic Lows Experiment (GALE) study ranged from 700 to 1200 W m 22 for outflow events (Grossman and Betts 1990; Warner et al. 1990). During leg 2 of CLIMODE, latent heat fluxes often exceeded 400 W m 22 and occasionally topped 1000 W m 22 during strong cold air outbreaks (Marshall et al. 2009). One key to understanding how these fluxes affect EDW formation rates is knowing how quickly the boundary layer warms and moistens, thereby reducing sea surface fluxes. Fluxes are controlled in a moist convective boundary layer by processes at the bottom and top of the layer. At the surface, water evaporates in response to dry air and strong winds. A large fraction of this latent heat is released by cloud formation in the upper half of the boundary layer. Convective clouds generate strong vertical transport, with convective plumes penetrating the overlying dry, stable atmosphere. Growth of the boundary layer, both by evaporation in overshooting convective clouds and by mechanical mixing, provides a sink for the moisture and heat gained through surface fluxes. Consequently, continued growth of the boundary layer is essential for maintaining strong latent heat fluxes at the surface; otherwise, the boundary layer will accumulate moisture and heat, limiting the differences in temperature and moisture across the air sea interface. Large-eddy simulation has become a frequent tool of choice for examining the effects of clouds on the atmospheric boundary layer. In general, these studies have focused on stratocumulus (e.g., Siebesma et al. 2003; Stevens 2007; Savic-Jovcic and Stevens 2008) and shallow trade wind convection (Stevens et al. 2001; Abel and Shipway 2007), with precipitation usually limited to drizzle. Use of LES to examine marine convection with a full range of precipitation is not as common as research involving stratocumulus layers. Studies include lake-effect convective systems (Zurn-Birkhimer et al. 2005) and cold air outbreaks (Schröter et al. 2005; Gryschka and Raasch 2005) with microphysics limited to cloud formation. These simulations have typically examined the roll structure of convection within ;100 km of shore, with less emphasis on the dynamics of the convective clouds or boundary layer structure over open water. None of these LES studies of cold air outbreaks has examined the total water budget of the boundary layer, including the effects of precipitation, or the behavior of convection after rolls break apart to form cellular convection. In this study we apply a cloud-resolving LES model that simulates water and ice clouds along with three classes of precipitation (rain, snow, and graupel), which are commonly observed in midlatitude convective showers. We consider conditions similar to a cold air outbreak observed on 20 February 2007 during leg 2 of the CLIMODE experiment (Fig. 1). Cases are selected to examine how moist convection modifies cold air masses as they move from relatively cool water north of the Gulf Stream to the more tropical waters on the southeast side of the Gulf Stream front. Our focus centers on understanding the role of clouds and precipitation in maintaining the relatively low humidity of the evolving cold air outflow. Specifically, we examine how cloud systems transfer heat and moisture vertically and control the vertical boundary structure. These experiments differ from previous LES cold air outbreak research (e.g., Schröter et al. 2005; Gryschka and Raasch 2005) by focusing on cases with an established boundary layer, well beyond the land or ice transition. Consequently, we do not simulate the evolution of the

3 1276 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 66 FIG. 1. (a) SST (8C) and (b) visible cloud image for 20 Feb 2007 from Geostationary Operational Environmental Satellite 12 (GOES-12) and the Moderate Resolution Imaging Spectroradiometer (MODIS) on Aqua. Ship location varied between and 388N along 548W as shown by the black line in (a) and within the box in (b). boundary layer from roll convection to open cells; rather, we center our experiments on understanding the role of shallow, precipitating convection in controlling the boundary layer structure. By comparing two cases with differing sea surface temperature (SST), representing different sides of the Gulf Stream front, we show that increased latent heat flux on the warm side of the front leads to reduced total cloud cover and more vigorous cumuliform clouds. Precipitation over the warm side of the front is greatly increased and has a significant impact on the boundary layer heat budget. In contrast, cloud systems over the cooler SST are primarily stratiform, with radiative fluxes having a more dominant role in the boundary layer evolution. We find that the overall behavior of the boundary layer in the front case follows an evolution

4 MAY 2009 S K Y L L I N G S T A D A N D E D S O N 1277 similar to the subtropical conversion of stratocumulus cloud layers to shallow convection as described in Wyant et al. (1997). The paper is organized as follows: We begin with a description of the LES model and case study in section 2. Results are presented in section 3, focusing on the boundary layer evolution and budgets of the convective cloud systems. A summary and conclusions are presented in section Model description and case study Experiments are performed using a modified version of the LES model described in Skyllingstad et al. (2007, 2005). Model equations are based on Deardorff (1980) with a subgrid scheme based on the filtered structure function method from Ducros et al. (1996). The equations are solved using third-order Adams Bashforth with a conservative scheme for scalar quantities based on Collela (1990). Pressure is calculated by assuming the anelastic approximation and solving for pressure via a conjugate residual method described in Smolarkiewicz and Margolin (1994). The current version of the model has been expanded to include both cloud and precipitation processes and longwave radiative transfer. Precipitation processes are modeled using the microphysical parameterization described by Reisner et al. (1998), Thompson et al. (2004), and Thompson et al. (2008) and currently used in the Weather Research and Forecast (WRF) model (Skamarock et al. 2005). This scheme uses five variables to describe cloud and precipitation mixing ratios: cloud water, cloud ice, rain, snow, and graupel. An additional variable representing the number concentration of cloud ice particles is also used, effectively introducing a secondmoment model for the formation of ice particles. Longwave radiative transfer is parameterized using the rapid radiative transfer model (RRTM; Mlawer et al. 1997), which is called for each grid column every 30 time steps. Currently, shortwave radiation is not represented in the model. Simulations are conducted over a horizontally periodic domain of 28.8 km in the crosswind direction, 14.4 km in the along-wind direction, and a height of 3600 m, with a grid resolution of 30 m in all directions. The larger crosswind dimension was selected to allow for multiple convective roll structures, which were anticipated based on initial modeling experiments and satellite observations (e.g., Fig. 2). A sponge layer is imposed over the top 720 m with a gradual Rayleigh damping to a constant background state, following Durran and Klemp (1983). FIG. 2. Vertical sounding of (a) temperature and dewpoint temperature along with (b) winds from 2100 UTC 20 Feb 2007 on the R/V Knorr. Also shown are (c) idealized conditions used for model initialization. In previous boundary layer simulations of SST fronts, open boundaries were used to examine flow over changes in ocean SST (Skyllingstad et al. 2007). Here, however, the scales of the Gulf Stream front are too large for this

5 1278 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 66 method. Instead, we use periodic lateral boundary conditions and simulate the effects of Lagrangian motion across the SST front by changing the surface temperature at a rate proportional to the mean flow velocity in the model, following the method of de Szoeke and Bretherton (2004). This assumes that secondary mesoscale circulations generated near the front are relatively small in comparison with the direct response to surface forcing and thus do not have a strong impact on the overall flow characteristics. Numerous studies using satellite data (Hashizume et al. 2001; Chelton et al. 2001; O Neill et al. 2003; Chelton et al. 2004) show that SST variations are strongly correlated with wind stress; however, the exact mechanism for this coupling is not completely clear. Winds are affected in two main ways by SST changes. First, changing boundary layer stratification can decrease or increase the vertical flux of momentum, causing nearsurface winds to decrease over relatively cold water and increase over relatively warm water. Wind speed can also be affected by the hydrostatic pressure gradient that is produced by boundary layer temperature changes over the Gulf Stream front (Song et al. 2004). This effect is more gradual than the momentum flux change, but it dominates for larger-scale SST features. For the advective scales considered here (;200 km) and the strength of the background flow, pressure-gradient driven changes in the wind speed are only a small fraction of the total wind variations and are assumed to be of secondary importance. Surface fluxes in the model are parameterized using the bulk formula algorithm described in Vickers and Mahrt (2006), which is effectively equivalent to the Coupled Ocean Atmosphere Response Experiment (COARE) version 2.5 (Fairall et al. 1996). This method was developed for estimating fluxes given time-averaged values of the wind speed, temperature, and relative humidity at a given height. Surface fluxes were applied at the lower model boundary grid points by replacing the subgrid-scale flux term with the parameterized values defined as u0w0 sfc 5 C d U 2 k51, (1a) w0u0 sfc 5 C h U k51 (u s u k51 ), and (1b) w0q0 sfc 5 C q U k51 (q s q k51 ), (1c) where U is the wind speed, u is the potential temperature, q is the specific humidity, C d, h, q are exchange coefficients, and the subscript k 5 1 denotes the first model grid point level. Exchange coefficients in (1) are computed using Monin Obukhov similarity theory as described in Vickers and Mahrt (2006) and Fairall et al. (1996). Solution of the fluxes at each grid point requires solving an iterative system; however, convergence is typically achieved within five iterations. Convergence problems at low wind speed are eliminated by limiting the minimum friction velocity u* to a value of ms 21, which is typically not an issue in the cold outbreak situation. Field values used in (1) represent both the mean and perturbation quantities produced by convective cells and resolved turbulence, violating the averaging assumption used in the bulk algorithm. However, test simulations using the horizontally averaged wind speed, temperature, and mixing ratio yielded average fluxes very similar to the grid point derived values, indicating that this application is reasonable. Further research is underway aimed at understanding the relationship between parameterized fluxes and fluxes calculated directly from covariance data measured during CLI- MODE; it will be reported in a second publication. Experiments were conducted using idealized initial conditions representing a cold air outbreak that occurred on 20 February Synoptic conditions over the Gulf Stream were dominated by a low pressure system near Newfoundland, which produced a broad swath of cold advection extending from the east coast of North America to a cold front over the central Atlantic Ocean (Fig. 1). Soundings were taken at four different times on this day as the R/V Knorr traversed the Gulf Stream frontal region. We selected a sounding from a point along the ship track just south of the Gulf Stream front as a basis for our experiments (shown in Fig. 2 along with the idealized profile). The observed sounding was typical for cold air outbreak events observed during CLIMODE, showing a thin superadiabatic layer just above the water, a deeper adiabatic layer up to about ;1000 m (900 hpa) capped by a saturated layer, and then a moderate temperature inversion at ;1800 m (790 hpa). The air mass above the temperature inversion was very dry, with dewpoint depressions of about 108C. We built the idealized version of the sounding using elements similar to the observations, but with linear variations over three regions in the vertical: the mixed layer, inversion, and free troposphere (see Fig. 2b). The superadiabatic layer was not initialized; rather, it developed via surface heating during the model execution. Initial wind fields were assumed to be in geostrophic balance with a constant background geostrophic wind, U g 5 28 m s 21, which yielded average LES surface winds similar to the observations. Actual winds shown in Fig. 2 varied in both strength and direction with height, suggesting a geostrophic wind shear associated with the large-scale circulation. However, a significant

6 MAY 2009 S K Y L L I N G S T A D A N D E D S O N 1279 increase in wind speed was evident near the top of the cloud system, indicating that mixing in the cloud-topped boundary layer may have also influenced the wind profiles. Surface fluxes at the time of the sounding were strongly dependent on the position of the ship as a function of the SST front as shown in Fig. 3. For example, when traveling southward across the front around UTC, the latent heat flux increased from ;300 to ;600 W m 22 when the SST increased from ;138 to ;17.58C. Wind speed also controlled the strength of the fluxes, as indicated earlier in the day at 600 UTC when the ship was moving over warm water. Decreased winds around this time caused a drop in latent heat flux of about 200 Wm 22. Interestingly, relative humidity was relatively stable as the ship traversed the SST front, ranging from 60% to 80%. Mixing ratios computed from the relative humidity and temperature ranged from 4 to 5 g kg 21 as shown in Fig. 3b. The stable nature of the relative humidity suggests that water evaporating from the surface was continuously removed from the boundary layer, preventing relative humidity values from increasing significantly. Bulk fluxes estimated using 10-min-average data compare well with direct covariance estimates measured on the R/V Knorr as shown by the wind stress and buoyancy flux in Fig. 4 near the time of the sounding. Good agreement between the 10-min-average data supports our use of the COARE bulk formula in the LES model, although we note that the covariance data shows large variations over short time periods. Forcing for the simulations was prescribed by assuming SST variations similar to the observed frontal structure (e.g., as observed between 1800 and 2000 UTC in Fig. 3). Movement of the LES domain was simulated by changing the surface temperature based on the prescribed geostrophic velocity and the assumed width of the SST front as represented by T sea K for t, t spinup, (2a) T sea K 1 DT(t t spinup)u g for X front t spinup, t, t spinup 1 X front, and (2b) U g T sea K for t. t spinup 1 X front U g, (2c) where T sea is the SST, DT is the temperature change across the front, t is the time, t spinup is the length of time before encountering the front, U g is the geostrophic wind, and X front is the width of the SST front. Values used in the frontal simulation presented below were DT 5 108C, U g 5 28 m s 21, t spinup 5 2 h, and X front km. Our choice for the frontal strength is higher than SST variations measured during the CLIMODE cruise (Fig. 3). However, other locations along the Gulf Stream front were more similar to the conditions used in the idealized case (e.g., see Fig. 1a). Simulations were typically conducted with a Galilean transformation of the domain by subtracting U g from the flow, resulting in a near-zero background flow field and decreased numerical advective smoothing. Unlike most LES studies of stratocumulus (e.g., Stevens et al. 2001), we did not impose a net subsidence in the simulations for two reasons: assigning a strength for subsidence in cold air outflows would be difficult given the lack of data, and the 5-h duration of our simulations limits the growth of the boundary layer that would otherwise occur in the absence of subsidence. 3. Boundary layer evolution Two main simulations are presented in this paper, each with a duration of 5 h. In the first case, referred to as the constant SST case, SST is held at a value of 281 K, representing the water that the continental air mass traverses after leaving the east coast of North America and prior to encountering the Gulf Stream. The second scenario, referred to as the frontal case, departs from the constant SST case after 2 h with the SST increasing according to (2) until it reaches a temperature of 291 K. In both cases, the surface heat flux is multiplied by a random coefficient (uniform random variable between 0.5 and 1.0, spatially and temporally varying) during the first hour of the simulation to accelerate the initial formation of turbulence. The average value of the random coefficient is 0.75, reducing the total flux over the first simulation hour. a. Surface variables We initially focus attention on the evolution of the surface variables over the 5-h simulation period for the frontal and constant SST cases. Plots of the horizontally averaged surface fluxes, wind speed, temperature, and water vapor mixing ratio shown in Figs. 5 and 6 provide a framework for the two experiments. Flux variations over the first hour in both cases coincide with the initial growth of turbulence at about hour 0.5 and the removal of random surface forcing at hour 1. Simulation of the SST front begins at hour 2, with SST increasing 108 over a time period equivalent to the movement of the domain over 120 km distance at the geostrophic wind speed of 28 m s 21 (i.e., just over 1 h). In response, latent heat flux increases linearly by roughly a factor of 5, whereas the sensible heat flux increases by about a

7 1280 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 66 FIG. 3. Observations of (a) wind speed and direction, (b) mixing ratio for the air (solid) and for air saturated with a temperature equal to the SST (dashed), (c) air and sea surface temperature, and (d) latent and sensible heat fluxes from the R/V Knorr observed on 20 Feb Fluxes are calculated using the COARE algorithm with observed temperature, SST, humidity, and wind speed. factor of 10. Fluxes decrease slightly over the last 1.5 h of the frontal simulation as the boundary layer deepens and near-surface temperature and moisture content increase. In contrast, fluxes in the constant SST case show almost no variation after the initial spinup period. Surface wind speed in the two cases varies only slightly after the initial spinup period, increasing about 1 2 m s 21 in response to the warming SST in the frontal case. Surface potential temperature and water vapor content rise steadily during the frontal simulation as the boundary layer warms and moistens, in qualitative agreement with observations. In the constant SST case, variations in average surface properties are very small over the entire simulation. Although one might expect this result because of the weak fluxes, there still should be a slight increase in both the boundary layer temperature and moisture content, unless entrainment at the boundary layer top is affecting the bulk layer properties. We address this issue in the next section focusing on boundary layer properties. b. Moisture and cloud properties Bulk boundary layer properties are affected by both the surface fluxes and entrainment at the top of the boundary layer. Analysis of the horizontally averaged potential temperature and cloud water shown in Fig. 7 provides an overview of the boundary layer evolution for the frontal and constant SST cases. Both cases show similar behavior over time with the formation of clouds generating a region of warming near the top of the boundary layer, with entrainment cooling of the overlying atmosphere as the boundary layer grows. These features are greatly enhanced in the frontal case with clouds extending throughout the upper half of the boundary layer and significant warming present above 1000-m height. In contrast, cloud thickness in the constant SST case is limited to about 1/4 of the boundary layer depth. Entrainment is also much greater in the frontal case, with the boundary layer depth increasing about 400 m (from about 1800 to 2200 m) versus a ;200-m increase in the constant SST case.

8 MAY 2009 S K Y L L I N G S T A D A N D E D S O N 1281 Also shown in Fig. 7 is the average water vapor time series, which shows how the deepening boundary layer maintains a fairly uniform moisture profile. Near the surface, the water vapor mixing ratio varies only slightly over time in both simulations, agreeing with observations that maintain relatively dry conditions near the surface even when the latent heat flux is large. Water vapor added to the boundary layer from evaporation is balanced by the expansion of the boundary layer into the overlying inversion where the air is very dry. The water vapor mixing ratio in the cloud layer has a reduced vertical gradient, which is consistent with the clouds having a warmer, moist adiabatic lapse rate and higher saturation vapor pressure. Growth of the boundary layer in both the frontal and constant SST cases is roughly linear with time t. This is in agreement with Stevens (2007), who notes that cloudtopped boundary layers typically exhibit a growth rate proportional to t, rather than the t 1/2 growth rate estimated for dry convection (see, e.g., Fedorovich et al. 2004). Stevens (2007) attributes the greater growth rate of cloud-topped boundary layers to the injection and evaporation of cloud moisture by penetrative cloud elements. This process reduces the stability of the overlying inversion, leading to more rapid boundary layer growth and a continual transport of dry free tropospheric air into the boundary layer. Our results, along with those of Stevens (2007), should be viewed with caution, however, because they are model results and have not been corroborated with observed boundary layer growth rates. Horizontal plots of the total cloud albedo (Fig. 8) and vertical cross sections of cloud water content (Fig. 9) show how the simulated cloud structure differs between the two cases. We calculate albedo using an optical depth estimation method proposed by Savic-Jovcic and Stevens (2008) where albedo is defined as A 5 t t, (3) FIG. 4. Ten-minute-average (a) surface wind stress and (b) sensible heat flux calculated using the COARE bulk algorithm and estimated directly from covariance data taken from the Air Sea Interaction Spar (ASIS) buoy during the CLIMODE experiment. t L 5/6 N c 1/3 is the optical depth, N c m 23 is the cloud droplet number concentration, L is the liquid water path defined as Ð rq c dz, q c is the cloud water mixing ratio, and r is the air density. At hour 2, simulated clouds are organized as convective cells with stratus spreading along the inversion layer. Over time, the two simulations show a divergence in the cloud characteristics apparent by hour 5 (Figs. 8 and 9). In general, the constant SST case produces a nearly uniform stratocumulus cloud deck with a smaller percentage of bright convective clouds than the frontal case. Cloud systems in the frontal case exhibit more cumuliform convective cells (e.g., between y 5 4 and 12 km) and less stratiform structures. Clouds in the constant SST case are somewhat similar to shallow stratocumulus cloud systems (e.g., Stevens et al. 2001, their Fig. 14), but with more vigorous updraft regions that extend deeper into the boundary layer. Figure 9 clearly shows the stratocumulus layer at around 2000-m height in the constant SST case. Thicker, cumuliform clouds are simulated in the frontal case, extending from about 800 m to the stratocumulus layer height at 2200 m in Fig. 9a. These thicker clouds correspond to the bright patches in Fig. 8b (e.g., between y 5 4 and 14 km in the frontal case). As pointed out by one of the reviewers, the evolution of the simulated clouds in the frontal case is quite similar to the stratocumulus to shallow cumulus transition that is common over the subtropical oceans (Bretherton and Wyant 1997; Wyant et al. 1997). For example, at hour 2,

9 1282 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 66 FIG. 5. Domain-averaged (a) latent (solid) and sensible (dashed) heat fluxes, (b) wind speed, (c) potential temperature, and (d) water vapor mixing ratio at 15-m height for the frontal case. the cloud systems behave like a stratiform system, similar to marine stratus beneath subtropical high pressure systems. By hour 5 in the frontal case, much of the stratus has evaporated because of entrained, dry tropospheric air. Clouds at this time are more cumuliform, similar to trade wind cumulus, but with greater precipitation and ice processes. In the subtropics this transition occurs over a period of days as the subtropical marine boundary layer is drawn into the intertropical convergence zone (Wyant et al. 1997). Here, the process is greatly accelerated by the strong surface fluxes, as compared with the radiative forcing in the subtropical case. Cloud evolution in the simulations differs significantly from previous simulations of cold air outflow because the model is initialized with a sounding that has already been greatly modified by flow over relatively warm water off the coast of North America. Consequently, we do not see a strong roll structure as simulated, for example, by Gryschka and Raasch (2005), who initialize their simulation with conditions typical for flow of arctic air off of an ice surface (i.e., with no initial mixed layer) and use a fixed simulation domain. In our simulations, cloud systems generally start out as cumulus cloud structures that are loosely aligned and progressively increase in scale until reaching the irregular convective cells shown in Fig. 8b at hour 5. Continuation of this simulation leads to a single dominant cloud structure over time, suggesting that the preferred circulation size is considerably larger than the current domain. This larger scale is supported by satellite observations from 20 February 2007 that show organized convection with scales from 20 to 500 km over the Gulf Stream region (box insert, Fig. 1). Because of the limitations of the model domain size, we cannot rule out the potentially important role that larger-scale features have in controlling the flow evolution in the real system. Ideally, experiments would be conducted for a much larger domain scale with a fixed domain, as in Gryschka and Raasch (2005). However, at this time computational resources are insufficient to perform such an experiment using LES.

10 MAY 2009 S K Y L L I N G S T A D A N D E D S O N 1283 FIG. 6. As in Fig. 5, but for the constant SST case. c. Turbulence Turbulence in the boundary layer plays a key role in determining the entrainment rates and transport of moisture. We can quantify the intensity of turbulence by plotting the turbulent kinetic energy (TKE; Fig. 10) defined as TKE (u92 1 y9 2 1 w9 2 ), (4) where u, y, and w are velocities in the x, y, and z directions, and primed variables represent the difference between the total velocity component and the horizontal average. As Fig. 10 shows, the vertical extent of turbulence in the simulations closely follows the boundary layer top as indicated by the cloud-top height. Both cases have maximum values of TKE near the top of the boundary layer and near the surface. This pattern is typical for cloud-topped boundary layers, as shown by Deardorff (1980) and Moeng (1986). In the constant SST case, the vertical wind speed gradient is fairly uniform over time with increased shear near the surface consistent with similarity theory. Shear near the top of the boundary layer in this case is weak. In contrast, vertical wind shear in the frontal case at hour 5 increases to large values near the surface and at the boundary layer top. For example, at hour 4.5 the 24 m s 21 isotach is located at ;250 m in the frontal case versus ;450 m in the constant SST case. Increased lowlevel TKE in the frontal case could be mostly a consequence of this increased shear or could indicate a separate process that is increasing the shear via strong vertical momentum transport. Analysis of the TKE budget in the next section shows that both buoyancy production and feedback from shear production are responsible for increased TKE. At the top of the boundary layer, observed winds (Fig. 2b) suggest a profile similar to the frontal case results, namely, wellmixed momentum in the boundary layer between 500 and 1800 m, with shear confined to the cloud tops.

11 1284 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 66 acts to transport moisture vertically, balancing a large portion of the surface evaporative flux. Here we analyze the physical processes that govern moisture in this system by computing the budgets of heat, moisture, and turbulence. Our analysis focuses on the horizontal and timeaveraged fields over the last hour of the simulations. Plots are presented relative to the height scaled with boundary layer depth estimated by the level at which TKE decreases to near zero (about 2300 m in the frontal case in and 2000 m in the constant SST case), allowing for ease in comparison of the cases. We did not scale fields according to the surface fluxes or integrated buoyancy flux as previously reported in Deardorff (1980) and Moeng (1986) for LES experiments on stratustopped boundary layers. In those studies, radiative cloudtop cooling was the primary source of instability and precipitation processes were not modeled. As pointed out in Moeng (1986), boundary layers with cloud processes exhibit quite different statistics between cases, unlike dry convective boundary layers where almost universal scaled profiles are commonly observed and modeled. The budget of horizontally averaged heat is calculated using u t w9u9 Æw99u99æ 5 1 F moist 1 F radiation, (5) z z where u is the potential temperature, Æw99u99æ is the subgrid-scale parameterized heat flux, F moist is the change in potential temperature from evaporation and condensation, F radiation is the change in potential temperature from radiative effects, primes denote perturbations from the horizontal average, and the overbar represents the horizontal average. A similar equation is used for the horizontal budget of water vapor: FIG. 7. Horizontally averaged cloud water mixing ratio (shading) and potential temperature (contours) for (a) the frontal case and (b) the constant SST case, along with water vapor mixing ratio (g kg 21 ) for (c) the frontal case and (d) the constant SST case. 4. Budgets One of the main questions that we wanted to answer concerns how moisture fluxes, particularly latent heat flux, are maintained as the boundary layer air moves over warmer water. Large latent heat fluxes imply that the moisture content of the boundary layer must increase unless other factors remove water from the system. As shown by the time evolution of boundary layer properties in Fig. 7, increasing boundary layer depth q y t 5 w9q9 y z Æw0q0 yæ 1 Q z moist, (6) where q y is the water vapor mixing ratio and Q moist represents evaporation and condensation processes (e.g., evaporation of rain or condensation of cloud water). Individual terms from the heat and moisture budget equations for both cases are presented in Fig. 11. Terms in the heat budget are for the most part dominated by condensation and evaporation of moisture. For example, condensation associated with cloud formation produces net warming between z/h and 0.8. Cooling from evaporation of precipitation is evident below z/h and near the top of the boundary layer above z/h 5 0.8, where cloud water and precipitation evaporate into the overlying dry inversion. Radiation also produces a

12 MAY 2009 S K Y L L I N G S T A D A N D E D S O N 1285 FIG. 8. Simulated albedo (a) after 2 h for both cases, and (b),(c) after 5 h for (b) the frontal case and (c) the constant SST case. strong cooling signal near the top of the cloud layer where infrared heat is lost to space above the cloud. Turbulent fluxes of heat act to balance the changes forced by moisture and radiative processes, for example, near the cloud top where vertical heat transport warms the local atmosphere. Similarly, sensible heat flux in the lower atmosphere offsets the cooling produced by evaporation of precipitation. Changes in the water vapor content are consistent with the thermal forcing as shown by the evaporation andcondensationterminfig.11b.forexample,inmidlevels the water vapor decreases because of condensation,

13 1286 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 66 FIG. 9. Cloud liquid water content (shaded) and potential temperature (contours) at hour 5 from (a) the frontal case and (b) the constant SST case for location x 5 1 km. whereas near the top and bottom of the boundary layer, evaporation adds to the water vapor content. Much of the evaporation and condensation is balanced by turbulent transport, except for near the boundary layer top where the two cases are significantly different. In the frontal case, water vapor budget terms combine to moisten the free tropospheric air that is entrained into the boundary layer. In contrast, budget terms in the constant SST case are not consistently aligned in the positive sense; the peak in evaporation/condensation is countered by a negative value for the eddy transport. In both the frontal and constant SST cases, moist processes act to warm the middle of the boundary layer and cool the atmosphere at the top and bottom of the boundary layer. This general pattern, however, is complicated by the effects of cloud and precipitation formation on the heat and moisture budget as demonstrated, for example, by the dual maxima in moist process heating near z/h and 0.6. Variations in the water vapor budget (Fig. 11b) follow the general pattern of moist heating. However, the budget of total liquid water shown in Fig. 12 presents a more complex picture. At z/h 5 0.3, increasing liquid water corresponds reasonably well with the peak in moist heating noted above at the same level. This is not the case at z/h where the budget for liquid water is, overall, slightly negative. Here, transport processes such as convective momentum and particle settling are dictating the net budget of liquid water by moving cloud and precipitation vertically. In the net, condensation is not keeping up with transport, and the local storage of liquid water is decreasing over the 1-h period (this is shown by the cloud water decrease in Fig. 7 between hours 4 and 5). Although the liquid water budget does not completely explain the two heating maxima, cloud cross sections shown in Fig. 9 suggest that new clouds form at the heights of the two heating maxima; that is, convective cloud elements form at z/h and z/h 5 0.6, with the upper clouds spreading laterally to form stratocumulus. Heat and moisture budgets from the constant SST case show a much smaller influence of moist processes on the boundary layer structure in comparison with the frontal case profiles. In particular, cooling of the air near the surface in the constant SST case is much weaker because of

14 MAY 2009 S K Y L L I N G S T A D A N D E D S O N 1287 FIG. 10. Horizontally averaged turbulent kinetic energy (shaded) and wind speed for (a) the frontal case and (b) the constant SST case. less precipitation. At the same time, greater cloud thickness near the top of the boundary layer in this case produces stronger radiative cooling, suggesting that boundary layer growth in the constant SST case is influenced more by radiative instability in comparison with the frontal case. A key component in the heat and moisture budgets is the turbulent transport term, which represents circulations by convective eddies and smaller-scale turbulence structures. We can evaluate the forcing of turbulence by examining the TKE budget determined using TKE t u i 5 u i u 3 u 3 g r9 1 Æu0 i u0 3 æ u i (u 3 TKE 1 u i Æu0 i u0 3 æ 1 u 3 P), ~ x 3 r o x j x 3 (I) (II) (III) (IV) (7) where u i Æu0 i u0 j æ 5 K m 1 u j, ~ p P u j u i r o 3 q2, double primes denote subgrid-scale fields, p is the pressure, r o is the background density, and q is the subgrid-scale turbulence kinetic energy, which is solved as part of the pressure field. Subscripts 1, 2, and 3 represent directions x, y, and z, respectively, and summation over repeated subscripts is implied in (7). Terms in (7) are (I) shear production, (II) buoyant production or destruction, (III) dissipation, and (IV) vertical transport.

15 1288 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 66 FIG. 11. Horizontal and time-averaged budget terms from the frontal and constant SST cases for (a) heat and (b) moisture. Time averaging is performed over hour 5. Terms are described in the text. Plots of the terms in Eq. (7) are shown in Fig. 13 and demonstrate how the cloud system strongly controls the boundary layer structure in both experiments. We focus first on the frontal case. Buoyancy forcing in this case is positive through most of the boundary layer with three peaks, the largest being near the surface where the action of the surface heat flux combines with destabilization by rainfall evaporation. Secondary maxima near FIG. 12. Horizontal and time-averaged liquid water budget terms for (a) the frontal case and (b) the constant SST case, accounting for all changes in the liquid water mixing ratio except for transport and diffusion. These terms represent changes from microphysical processes (e.g., collision and coalescence), condensation, melting, freezing, settling velocity, and evaporation/sublimation.

16 MAY 2009 S K Y L L I N G S T A D A N D E D S O N 1289 FIG. 13. Horizontal and time-averaged turbulence kinetic energy budget terms for the frontal and constant SST cases. Time averaging is performed over hour 5. z/h and 0.7 are most likely produced by moist heating, as shown in Fig. 11. Vertical exchange of momentum by convection produces significant shear near the surface and a commensurate increase in the shear production to values that are off the scale of the plot. Vertical transport of turbulence is generally a loss term in the lower half of the boundary layer and a source term near the boundary layer top (also noted in Deardorff 1980). Turbulence reduction at the top of the boundary layer through buoyancy destruction and dissipation is FIG. 14. Horizontally averaged (a) heat budget terms and (b) TKE budget for the simulations without thermal effects of precipitation (i.e., evaporation, fusion).

17 1290 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 66 offset somewhat by this vertical transport and corresponding increased shear production at z/h A similar pattern in the TKE budget terms is noted in the constant SST case; however, the amplitude of the terms is generally smaller and buoyancy production is markedly different. Buoyancy production in this case is a maximum at z/h in the stratocumulus cloud system, with a peak value similar to the frontal case. Buoyancy production in the constant SST case is much weaker in the near-surface layer because of lower surface heat fluxes. Decreased buoyancy and vertical momentum flux leads to stronger low-level shear, producing more dominant shear production in the middle layers between z/h 5 0 and 0.4 in comparison with the frontal case. Reduction in the buoyancy term below z/h in the constant SST case tends to force a decreasing profile of dissipation rate, whereas dissipation in the frontal case is relatively constant between z/h and 0.8. Shear production near the boundary layer top in the constant SST case is much less than in the frontal case, suggesting that the increased eddy mixing in the frontal case water vapor budget (Fig. 11b) results from stronger shear. We note that in both cases the total transport term does not vertically integrate to zero, suggesting a flux of energy out of the boundary layer. Closer examination of the pressure transport term (not shown) suggests that w 0 p 0 has a positive value above the boundary layer, indicating a loss of energy from vertically propagating internal waves. Although this energy loss is relatively unimportant for the boundary layer structure, the role of convectively forced internal waves on the global circulation is not negligible (e.g., Alexander et al. 1995). One of the main differences between the current work and previous LES studies of cloud-topped boundary layers concerns the role of precipitation in controlling the boundary layer structure. In particular, we note above that precipitation tends to evaporate below cloud level, cooling and moistening the low levels of the boundary layer. To better understand the role of precipitation, we conducted experiments with precipitation processes turned off. In these experiments, all processes that remove cloud water by forming precipitation particles were removed from the model, limiting moist processes to condensation and evaporation of cloud droplets and deposition and sublimation of ice crystals. Plots of the heat and TKE budget for these cases are presented in Fig. 14. Overall, the profiles look similar to the full heating case; however, the energy levels without precipitation heating are larger in magnitude in the frontal case and slightly smaller in the constant SST case. Most notable is the increase in the TKE buoyancy term above z/h in the frontal case. Without precipitation heating, buoyancy forcing is about 50% larger in the upper portion of the boundary layer. In contrast, buoyancy production in the frontal case below z/h is noticeably smaller without evaporation of precipitation. In the constant SST case, removal of precipitation heating produces relatively minor changes in the heating profiles. Comparing the constant SST cases in Fig. 14 with Fig. 11, we note that moist heating is slightly smaller in the cumulus cloud layer between z/h and 0.6 and slightly larger in the stratocumulus layer at z/h 5 0.8, suggesting that precipitation formation in the cumulus layer removes moisture, limiting stratocumulus cloud formation at the cloud top. This result is similar to previous stratocumulus simulations showing that drizzle precipitation reduces the strength of stratocumulus clouds (Stevens et al. 1998; Jiang and Cotton 2000). Precipitation also affects the surface fluxes by cooling the surface layer temperature, which produces an increase in sensible heat flux of about 20 W m 22. This is about a 10% increase and is important because of the role surface buoyancy has in triggering turbulent eddies. The increase in sensible heat is nearly offset by a 15 Wm 22 decrease in the latent heat. Evaporation of rain near the surface increases the water vapor content of the air, which decreases the evaporation of water from the ocean surface. 5. Summary and conclusions Experiments using LES are conducted for a moist convective boundary layer generated by heating from the Gulf Stream. Two cases with geostrophic forcing of 28 m s 21 are considered, one with SST increasing 108 over a 120-km advective distance representing passage over the Gulf Stream front, and a second with SST held constant. Results from the simulations indicate that cloud and precipitation processes greatly affect the dynamics of the boundary layer and indirectly control the surface fluxes by maintaining low surface humidity. Differences between the frontal and constant SST cases are clearly shown in the cloud liquid water content and growth characteristics of the boundary layer. As expected, the frontal case generates more active convective cells and boundary layer growth. However, the increase in boundary layer water vapor in the frontal case is tempered by loss of moisture as the boundary layer entrains dry air, leading to large cloud-free regions. Clouds in the constant SST case form a more uniform stratocumulus layer with higher cloud coverage in comparison with the frontal case. Growth of the boundary layer in both cases is produced by entrainment of warmer air from the inversion layer, cooling by evaporation of cloud and precipitation

18 MAY 2009 S K Y L L I N G S T A D A N D E D S O N 1291 water, and cooling through radiative transfer. Evaporative cooling at the cloud top in the constant SST case is less than the frontal case, but this is offset somewhat by greater radiative cooling generated by more widespread cloud cover (see Fig. 8). Overall, water vapor flux at the boundary layer top is greater in the frontal case because of the combined effects of cloud and precipitation evaporation and stronger turbulent moisture flux. A significant difference between the two cases is noted in the near-surface layer below z/h 5 0.2, where increased precipitation in the frontal case generates evaporative cooling. Simulations without the thermal effects of precipitation indicate that evaporation of precipitation alters the heating and TKE buoyancy term profiles in the frontal case. Evaporation of precipitation decreases the buoyancy production term in the main cumuliform cloud layer and increases buoyant production in the subcloud layer in this case, in part by increasing the sensible heat flux by 20 W m 22. In the constant SST case, removal of precipitation thermal effects causes an increase in the strength of heating at the level of the stratocumulus layer, indicating that precipitation removes moisture, limiting cloud-top stratus formation. We find that relatively low humidity values near the surface, which are necessary for strong latent heat fluxes, are maintained by the continual expansion of the boundary layer in the entrainment layer. Clouds play a critical role in this process by generating both strong radiative and evaporative cooling of the relatively warmer air above the boundary layer, thereby providing a sink for increased boundary layer moisture. The simulated boundary layer structure can be summarized using a three-layer schematic based on results from the frontal case (Fig. 15). This schematic is similar to the description given in Wyant et al. (1997) for subtropical cloud transitions. In the first layer between the surface and z/h 5 0.2, surface fluxes generate unstable air parcels that converge to form new convective cloud elements. These convective systems generate precipitation, which cools and moistens the lower layer through evaporation. The second layer, between z/h and 0.8, is identified by large latent release as moisture forms clouds and precipitation in relatively isolated cumuliform clouds. Cooling from evaporation, entrainment, and radiative flux from stratocumulus clouds defines the third layer, which extends from z/h to 1.0. This schematic applies for both the frontal and constant SST cases; however, the impact of moist processes is greatly reduced in the constant SST case, and cloud-top radiation plays a much larger role. In general, simulated cloud cover is inversely related to the strength of surface fluxes. Strong convection in the frontal case generates relatively isolated, thick clouds with large open areas between cloud systems. In contrast, convection in the constant SST case is weaker and cloud systems tend to spread out when reaching the top of the boundary layer. Subsidence surrounding the convective elements in the constant SST case is not strong enough to evaporate the clouds. The net effect is a greater radiative cooling in the constant SST scenario relative to the frontal case because of widespread cloud coverage. Satellite imagery (e.g., Fig. 1b) qualitatively supports this result, showing a more open cloud structure downwind from the Gulf Stream front, as shown by the box insert. Maintenance of the cloud systems in our simulations is more clearly dominated by surface fluxes than in typical stratocumulus clouds (e.g., Stevens et al. 2001; Siebesma et al. 2003); however, cooling by radiation and evaporation at the boundary top is also important, particularly in the constant SST case. Growth of the boundary layer proportional to t (e.g., Stevens 2007) rather than t 1/2, noted for dry convection (e.g., Fedorovich et al. 2004), is consistent with the continual evaporation of water at the boundary layer top, which decreases the stability of the free tropospheric air and maintains a near-steady value of specific humidity in the boundary layer. Simulations presented here differ somewhat from Stevens (2007) in that penetrative cumulus clouds are not the only mechanism for moistening and cooling the capping inversion. Radiative cooling of the stratocumulus layer and evaporation of precipitation also play an important role in the boundary layer growth rate. Our results suggest that the cloud-topped boundary layer associated with cold air outbreaks behaves similarly to the subtropical, cumulus-under-stratocumulus regime discussed in Wyant et al. (1997). In the subtropical regime, stratus clouds at the top of the boundary layer are maintained by detrainment of moisture from cumulus clouds that tap into the surface layer. As the boundary layer deepens, moisture supplied to the stratocumulus layer by cumulus clouds is depleted through entrainment of free-tropospheric air. Eventually, the stratocumulus layer dissipates because of the lack of moisture. Convective cloud systems play a similar role in the cold air outflow cases as surface fluxes increase. In the frontal case, stratocumulus layers form at the top of the boundary layer and slowly dissipate as the boundary layer deepens. Transition from stratocumulus to cumulus occurs over a period of days in the subtropics. However, in cold air outbreaks, this transition happens over a period of hours. The similarity between the cold air outbreak boundary layer evolution and subtropical stratocumulus to cumulus transitions is critical because both of these

19 1292 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S VOLUME 66 FIG. 15. Schematic structure of the boundary layer over the warm side of the Gulf Stream. common processes occur over large areas of the World Ocean and most likely represent the primary way the lower troposphere gains moisture. The experiments presented here indicate a complicated interaction between cloud and precipitation formation and turbulent transport that is difficult to validate at this time, given the general lack of data on midlatitude shallow convection. For example, measurements of the evaporative fluxes of cloud water and precipitation both above and below the cloud systems are needed to verify whether the model microphysics is within the realm of actual precipitating cloud systems. Direct measurements are also needed to test the threelayer structure discussed above. Nevertheless, our results point out the complexity of shallow convection, which needs to be accounted for in large-scale atmosphere models. Accurate representation of cumulus and stratocumulus cloud systems will likely require submodeling systems similar to the cloud-resolving LES presented here and, for example, as applied in Wyant et al. (2006) using a two-dimensional framework. Care must be taken in defining a general conclusion regarding the effects of SST variability on the evolution of the marine boundary layer during cold air outbreaks. Our results suggest that increasing SST will generally force stronger convection and boundary layer growth through moist evaporative cooling coupled with radiative heat loss and entrainment at the cloud top. Conditions without SST variability tend to evolve into stratocumulus-capped boundary layers where radiative cooling plays a more active role in the boundary layer growth. However, because the size of convective elements increases over time to scales much larger than our domain, results concerning cloud type and coverage may be unreliable. Acknowledgments. We would like to acknowledge the supercomputer time provided by the National Center for Atmospheric Research, which is funded by the National Science Foundation. This research was supported by the National Science Foundation Grant OCE and the Office of Naval Research, Grant N REFERENCES Abel, S. J., and B. J. Shipway, 2007: A comparison of cloudresolving model simulations of trade wind cumulus with aircraft observations taken during RICO. Quart. J. Roy. Meteor. Soc., 133, Alexander, M. J., J. R. Holton, and D. R. Durran, 1995: The gravity wave response above deep convection in a squall line simulation. J. Atmos. Sci., 52, Bretherton, C. S., and M. C. Wyant, 1997: Moisture transport, lower-tropospheric stability, and decoupling of cloud-topped boundary layers. J. Atmos. Sci., 54, Chelton, D. B., and Coauthors, 2001: Observations of coupling between surface wind stress and sea surface temperature in the eastern tropical Pacific. J. Climate, 14, , M. G. Schlax, M. H. Freilich, and R. F. Milliff, 2004: Satellite measurements reveal persistent small-scale features in ocean winds. Science, 303, Collela, P., 1990: Multidimensional upwind methods for hyperbolic conservation laws. J. Comput. Phys., 87, Deardorff, J. W., 1980: Stratocumulus-capped mixed layers derived from a three-dimensional model. Bound.-Layer Meteor., 18, de Szoeke, S. P., and C. S. Bretherton, 2004: Quasi-Lagrangian large eddy simulations of cross equatorial flow in the east Pacific atmospheric boundary layer. J. Atmos. Sci., 61, Dewar, W. K., R. M. Samelson, and G. K. Vallis, 2005: The ventilated pool: A model of subtropical mode water. J. Phys. Oceanogr., 35, Ducros, F., P. Comte, and M. Lesieur, 1996: Large-eddy simulation of transition to turbulence in a boundary layer developing spatially over a flat plate. J. Fluid Mech., 326, Durran, D. R., and J. B. Klemp, 1983: A compressible model for the simulation of moist mountain waves. Mon. Wea. Rev., 111, Fairall,C.W.,E.F.Bradley,D.P.Rogers,J.B.Edson,andG.S. Young, 1996: Bulk parameterization of air sea fluxes for Tropical