Turbulent and Boundary Layer Characteristics during VOCALS-REx

Stratocumulus clouds have a significant impact on climate due to their large spatial extent, with areas of enhanced coverage termed stratocumulus decks. How turbulence evolves with time and influences the stratocumulus deck properties however, in particular throughout the vertical profile of the boundary layer, is still lacking through model parameterizations of the smallscale flow. Collecting in situ data to better understand the turbulence and physical processes occuring within the stratocumu5 lus deck therefore key to better model parameterizations. Boundary layer and turbulent characteristics, along with synoptic scale changes in these properties over time, are examined using data collected from 14 research flights made with the CIRPAS Twin Otter Aircraft. Data was collected during the VOMOS Ocean-Cloud-Atmosphere-Land Study-Regional Experiment (VOCALS-REx) at Point Alpha in October and November of 2008 off the cost of South America (20◦S, 72◦W). Findings show that the influence of a synoptic system on Nov 1 and 2 brings in a moist layer above the boundary layer, 10 leading to a deepening cloud layer and precipitation during passage, and a large increase in boundary layer height and cloud thinning after passage. The maximum value in turbulent kinetic energy (TKE) was measured on Nov. 1 due to precipitation destabilizing the sub-cloud layer while a minimum occurred on Nov. 2 after precipitation had ceased due to turbulent mixing overturning the boundary layer and depleting the initial turbulent energy produced from the evaporation of precipitation below cloud base. Turbulent properties averaged over all 14 flights reach a maximum near cloud middle (between normalized in15 cloud values of 0.25-0.75), with well mixed boundary layers experiencing two peaks in TKE, one near cloud base due to latent heat release and another near cloud top due to evaporational cooling. Overall, it appears that turbulence measured at Point Alpha is weaker than that measured over the open ocean to the west of Point Alpha, and that measured during other scientific campaigns. Synoptic scale analysis suggests that as the geopotential height decreases, the boundary layer height and entrainment zone thickness increases, accompanied by a decrease of in-cloud and below-cloud turbulence, and vice versa. 20 1 https://doi.org/10.5194/acp-2020-104 Preprint. Discussion started: 11 March 2020 c © Author(s) 2020. CC BY 4.0 License.

top, and condensational heating at cloud base (Moeng et al., 1992). Nicholls (1989) observed through aircraft observations that 90 the largest buoyancy fluxes are close to cloud top, with further observations (Caughey et al., 1982;Nicholls, 1989) suggesting that the descending regions of air originating near cloud top are more a result of radiative cooling rather than evaporative cooling.
Vertical velocity variance typically displays the strongest updrafts and downdrafts in the upper half of the STBL (Hignett, 1991), consistent with the largest production of turbulence being contained within the cloud layer. A positive (negative) vertical 95 velocity skewness indicates that strong narrow updrafts (downdrafts) are surrounded by larger areas of weaker downdrafts (updrafts). It has been found that negative vertical velocity skewness is typically contained within most of the cloud layer and below (Nicholls and Leighton, 1986;Nicholls, 1989), whereas a decoupled boundary layer containing cumulus below stratocumulus may contain positive vertical velocity skewness (de Roode and Duynkerke, 1996).
The main source of moisture for the STBL is supplied by the surface latent heat flux, making it an important source of 100 buoyant TKE production (Bretherton and Wyant, 1997), with the surface sensible heat flux typically being a much weaker source of turbulence. The sensible heat and latent heat flux can be compared using the Bowen ratio (the ratio of the sensible to the latent heat flux). The smaller the Bowen ratio, the more proportional the liquid water flux in the cloud layer is to the upward moisture or latent heat flux. This results in a larger latent heat flux leading to decoupling due to the latent heat flux concentrating convective energy generation (through condensational and evaporational heating/cooling) within the cloud layer.
where the aircraft sampled the free upper troposphere and boundary layer in a single ascent or descent. Each flight of five hours originated from Iquique Chile, allowing for roughly three hours of sampling at Point Alpha.
Of the 19 flights performed by the Twin Otter, only 14 are used here due to instrumentation failure on five of the flights (Phase Doppler Interferometer and the cloud/aerosol probe). Table 1 displays each of the Research Flights (RF) used in this paper. All flights occurred during the day, with all but two flights (RF 8 and RF 17) starting around 7:00 AM local time, with the 130 first vertical profile flown around 8:00 AM local time at Point Alpha. Having each flight sample the same location at roughly the same time is critical, as turbulence typically displays diurnal patterns, with the strongest turbulent mixing occurring during the night when longwave radiational cooling dominates due to the absence of the stabilizing effect of shortwave absorption at cloud top (Hignett, 1991). Meteorological variables were collected at 40-Hz (including u, v, and w wind velocity, wind direction, mixing ratio and potential temperature, to name a few) while most cloud and aerosol data were collected at 1-Hz. 135 A more in-depth description of the instrumentation used and values measured on the Twin Otter can be found in Zheng et al. (2010) and Wood et al. (2011).
To analyze the synoptic conditions over the study period, data from the National Centers for Environmental Prediction (NCEP) / National Center for Atmospheric Research (NCAR) Reanalysis Project (NNRP, Kistler et al. (2001)) will be used.
Data resolution of the NCEP/NCAR reanalysis data is 2.5 • x 2.5 • x 17 pressure levels, available at six hour intervals. The 140 resolution of this data is suitable for analyzing synoptic scale patterns, but is not ideal for depicting mesoscale variability that may be present from day to day.

Turbulent Calculations
The randomness of turbulence makes deterministic description difficult, limiting description to statistics and average values of turbulence, in particular that of Reynolds decomposition (or averaging). Reynolds decomposition uses a mean value (over some 145 time period) and subtracts it from the actual instantaneous velocity to obtain the turbulent component (or perturbation value).
Reynolds decomposition is based on the underlying assumption that the turbulence is isotropic and stationary, conditions that are hardy fulfilled for atmospheric boundary layer flows however, especially when working with data spanning larger timeframes. The problem is defining how to average collected data to best represent the mean and turbulent components for the fluid flow (with shorter subsets of data having more stationary properties in general than that of longer subsets of data). 150 Following the methods outlined in Jen-La Plante et al. (2016), who used a 300-point averaging window, a 320-point averaging window is used here for all turbulent analysis. A 320-point averaging window corresponds to 8 second subsets of data (using 40-Hz data), or a roughly 440-m subset of data in the horizontal spatial scale (assuming average aircraft speed of 55 ms −1 ). Linear regression is then applied to each 320-point averaging window to calculate the mean value and determine the perturbation values. Applying the averaging method discussed above leads to the calculation of the fluctuations of the u, v, and w components of the velocity, along with other parameters used to measure various turbulent fluxes. Variables to be obtained include turbulent kinetic energy, which is given by: where u , v , and w are the fluctuations of the velocity components. The turbulent sensible heat, latent heat, and buoyancy 160 fluxes will also be obtained, given by: respectively. Where C p is the specific heat of air (1005 J kg −1 K −1 ), L v is the latent heat of vaporization at 20 • C (2.45 · 10 6 J 165 kg −1 ), ρ is the mean air density, and θ , q , and θ v are the potential temperature, mixing ratio, and virtual potential temperature perturbations, respectively. Note that θ v is commonly used as a proxy for density when calculating the buoyancy.
Just like that of Reynolds decomposition, the calculation of the TKE dissipation rate ( ) is based on conditions that the flow is isotropic (i.e., uniformity in all directions), making the measurement of challenging. In particular, classical turbulence theory in the inertial subrange from Kolmogorov (1941) is based on assumptions of local isotropy. With that said, there are multiple 170 methods to measure the TKE dissipation rate, including the inertial dissipation method, structure functions, and the direct method. Siebert et al. (2006) found that both the inertial dissipation and structure function methods are useful, but the inertial dissipation method sometimes underestimates at low values due to no clear inertial subrange behavior being observed in the power spectral density, which is not the case for the structure function. The structure function method is therefore considered more robust for cases with small values of , and will be used here. Due to questions of isotropy, the TKE dissipation rate 175 will be evaluated on the u, v, and w components of the wind, and an average dissipation rate will be calculated from the three components.
The calculation of the dissipation rate comes from the analysis of the velocity perturbations through n th order structure functions. The perturbations, as for other turbulent parameters, are determined with respect to an averaging window of 320points. Each subset of perturbations is then appended to the end of the previous subset to create a single time series of velocity 180 perturbations. The structure function is given by: where l is the distance (or in the case of a temporal series, l is equivalent to t assuming constant flight speed). From Frisch (1995), the dissipation rate using the n th order structure function can be obtained by using: where C n is a constant of the order 1. The second order structure function will be used here (n = 2), where C 2 is equal to 2 for transverse velocity fluctuations and C 2 is equal to 2.6 for longitudinal velocity fluctuations (Chamecki and Dias, 2004), interactions with the plane and other instrumental artifacts.
3 Synoptic and Boundary Layer Characteristics

Mean Synoptic Conditions
The Southeast Pacific Ocean is found on the eastern edge of the south-Pacific semipermanent subtropical anticyclone, characterized by large scale upper tropospheric subsidence leading to a strong temperature inversion with a well-mixed boundary 195 layer below. The surface pressure therefore is controlled in part by the location of the south-Pacific subtropical anticyclone.
This anticyclone is routinely interrupted (especially between fall and spring) by periods of relative low pressure which is associated with localized troughing or the passage of midlatitude cyclones to the south. Several papers (Toniazzo et al., 2011;Rahn and Garreaud, 2010) have analyzed the synoptic characteristics during VOCALS-REx, these papers however tend to focus on the VOCALS-REx region as a whole, and not specifically on Point Alpha, which is done in this section.
200 Figure 1 shows the mean of large-scale meteorological conditions (including sea level pressure, omega, and 700-hPa geopotential height) from NCEP reanalysis data over the study region between October 19 th to November 12 th . The mean sea level pressure (panel ( This is as expected, as Barret et al. (2009) found that synoptic systems tend to weaken as they move towards the coast of South America.
The mean 700-hPa geopotential height is displayed in panel (b), overlaid with omega data. Subsidence (green shading) dominated the VOCALS-REx region, with Point Alpha having an average value of 0.066 Pa s −1 at the 700-hPa level. While 210 enhanced storm tracks were primarily contained within the mid-latitudes, the 700-hPa geopotential height displays midlatitude troughing extending between Point Alpha and the subtropical high (as was found in (Zheng et al., 2011), suggesting that meteorological conditions at Point Alpha were influenced by both midlatitude synoptic systems and the subtropical anticyclone.
The sea-level pressure was also measured using both reanalysis data and aircraft 30-m level horizontal flight legs. Figure 2, panel (a) shows that the reanalysis data at Point Alpha tended to be on average 1.5-hPa greater than the aircraft measured sea 215 level pressure. The pressure decreased by roughly 3-hPa from October 19 th to November 12 th , however, this decrease cannot be considered a seasonal signal because it is within synoptic scale variation. The sea surface temperature (SST) and atmospheric surface temperature (both measured during 30-m horizontal flight legs) increased steadily throughout the observation period, increasing by 2.79 and 2.28 • C, respectively. Synoptic variability at Point Alpha is summarized by time series of geopotential height at various levels. Higher geopotential heights are associated with ridging aloft while decreases in geopotential heights are associated with synoptic disturbances or troughs. The 500-hPa geopotential height (see Figure 2) varied between 5840 and 5900-hPa, with an increase of 9-hPa between October 19 th and November 12 th . Figure 2 also displays enhanced synoptic scale variation during October, with several disturbances effecting Point Alpha. The 500, 700 (panel (c)), 850, and 1000 (panel (d)) hPa geopotential heights 225 alternate between areas of high and low height through November 2 nd . After November 2 nd , the 500-hPa geopotential height is more consistent, with height increasing over Point Alpha until November 10 th , at which point the height begins to decrease.
Besides minor disturbances in October, there are two main disturbances that stand out. The first disturbance occurs on November 1 st and 2 nd (green shading in Figure 2), where both the 500 and 700-hPa heights have minimums (5842 and 3134 m, respectively). The 850 and 1000-hPa heights also have secondary minimums. The second disturbance was the formation of 230 a costal low, which can be seen by decreasing geopotential heights on November 12 th . Both the 850 and 1000-hPa geopotential heights reached minimums on November 12 th (1498 and 104 m, respectively). This costal low reached a minimum (the coastal low was strongest) after the analysis period, on November 15 th (Rahn and Garreaud, 2010). The ridging which formed after November 2 nd leads to the formation of the coastal low through the warming of the lower and middle troposphere (Garreaud and Rutllant, 2003).

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How the boundary layer turbulence changed with the synoptic evolution, particularly the disturbance observed on November 1 st and 2 nd , will be the focus of this paper. The 700-hPa geopotential height map displayed a midlatitude trough developing and extending past Point Alpha from October 29 th through November 3 rd , as is shown in Figure 3.  westerly component (214 • ). Shear within the boundary layer is not common. Zheng et al. (2011) suggest that this shear is linked to coastal processes such as the propagation of the upsidence wave. It should also be noted however that the wind shear within the boundary layer is present on the same day (November 1 st ) that the trough axis is located over point alpha. On the proceeding day, the surface winds experience their most westerly component. According to Rahn and Garreaud (2010), as troughs approach the coast of South America, southeast winds are typically replaced by southwest winds. Between October 255 29 th and November 2 nd , wind direction within the boundary layer shows its most variation, gradually shifting from 153 • (most easterly component measured) to 213 • (most westerly component measured), respectively. While the trough approaches the coast of Chile, southeast winds are replaced by southwest winds, as is typical of synoptic scale disturbances (Rahn and Garreaud, 2010).

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Boundary layer height is perhaps the most important feature of the marine boundary layer (MBL), with the height being one of the main dictators for boundary layer characteristics such as decoupling and cloud cover (Albrecht et al., 1995). Findings from Rahn and Garreaud (2010) at a separate observation point within the VOCALS-REx region suggests that the boundary layer depth tended to be either low (600-m) or high (1500-m) with periods of high or low depth interrupted by rapid transitions between the two states over 12 to 36 hour periods due to synoptic variability. Figure 5 shows the thickness of the Sc cloud 265 layer, the thickness of the inversion (entrainment zone), and subsequently the MBL height for each flight. The cloud layer was identified using a liquid water content (LWC) greater than or equal to 0.01 g m −3 , while the inversion layer was identified by the region of greatest change in the mixing ratio (change ≥ |0.10 g kg −1 | per measurement) and potential temperature (change ≥ |0.20 K| per measurement) within the vertical profiles. This results in the bottom of the inversion layer characterized by the profiles beginning to lose the boundary layer features, while the top of the inversion layer had lost all boundary layer features.

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The average height of the boundary layer was 1175-m (see Table 2 for boundary layer characteristics), with the average cloud layer and inversion thickness being 239 and 59-m, respectively. The sharp inversion layer suggests that the interaction between boundary layer and free tropospheric air aloft extended over a relatively thin layer. Figure  imum on November 1 st however. This can most likely be attributed to enhanced moisture (see Figure 6) above the boundary 290 layer due to the passing synoptic system. Figure 6 shows vertical profiles (based on a normalized boundary layer height) of potential temperature, mixing ratio, liquid water content, and the aerosol number concentration. Individual flight profiles are in gray, with the red profile representing the mean and the blue profiles representing the flights conducted on November 1 st (RF11) and November 2 nd (RF12). Mean profiles show that on average the MBL is well mixed up to the inversion, which then prevents mixing into the free atmosphere above (as evident by the decrease in aerosol number concentration between the 295 boundary layer and free atmosphere above).
The largest deviations from the mean in the profiles occur during the passage of the synoptic system on November 1 st and 2 nd . At this time, both RF11and RF12 measured (1) The thickest Sc cloud layer, with November 1 st having the largest average cloud droplet size (20.8 µm) and in-cloud drizzle rates, while November 2 nd had the lowest recorded cloud base and largest recorded liquid water content; (2) The largest mixing ratio above the boundary layer. This suggests the presence of a moist layer 300 aloft which may have helped in producing the thickest cloud layers observed; (3) The smallest differences in both potential temperature and mixing ratio from the bottom to the top of the inversion layer. During the passage of strong events as described by Rahn and Garreaud (2010), the inversion defining the MBL erodes, making it hard to define the boundary layer height. This process is partially displayed by the small differences in temperature and moisture across the inversion layer during the passage of the synoptic disturbance.

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The differences in mixing ratio and potential temperature can be better visualized in Figure 7, which shows the differences between below and above inversion values in panel (b). Data between normalized boundary layer height values of 0.85 and 0.95 were used for the averages below the inversion, while data between normalized altitude values of 1.10 and 1.20 were used for the averages above the inversion. Besides November 1 st , 2 nd , and to a lesser degree November 4 th , the average difference in potential temperature across the inversion was 17-K, while the average difference in mixing ratio was -6.2 g kg −1 . On

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November 1 st when both reached a minimum, the difference between the mixing ratio and potential temperature across the inversion was 1.9 g kg −1 and 14-K, respectively.
Analyzing wheather the boundary layer is well mixed or not (as displayed in Table 1) based on potential temperature and mixing ratio can be quantified using the decoupling parameters α θ and α q , respectively (Wood and Bretherton, 2004). The decoupling parameters measure the relative difference in mixing ratio and potential temperature between the bottom (near the 315 surface) and top (near the inversion) portions of the boundary layer, and are given by is the level ∼25 m above (below) the inversion, and θ(0) and q t (0) are the potential temperature and mixing ratio at the surface. Here, z + i is calculated using data between normalized boundary layer heights of 1.03 to 1.05, while z − i is 320 calculated using data between normalized boundary layer heights of 0.95 to 0.97 (this is roughly 25 m above and below the inversion). The closer to zero the decoupling parameters are, the more well-mixed the boundary layer is. Previous observations suggest that if the parameters exceed ∼ 0.30, the boundary layer is decoupled (Albrecht et al., 1995).

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The vertical variation in turbulent properties and fluxes can be conveniently discussed in terms of dividing the boundary layer into vertical layers. Here, we will quantify the amount of turbulence occurring within the boundary layer. In particular, analysis includes: (1) Determine average turbulent values throughout the vertical structure of the STBL, classifying the STBL based on different turbulent profiles analyzed; (2) Analyze day to day variability in turbulent measurements and boundary layer characteristics, relating them to synoptic changes in meteorological conditions. For each flight analyzed here, the Sc deck lies 335 directly below a strong inversion. This extreme vertical gradient can cause instrument response issues with the measurement of both the dry bulb and dew point temperature for some distance beneath cloud top (Nicholls and Leighton, 1986). Therefore, data collected during both vertical profiles and horizontal legs will be used and compared. to its secondary minimum on Nov. 2 nd (note that mean values of surface fluxes can be found in Table 3). The Bowen ratio is typically small (less than 0.20), especially for the first half of the campaign. The Bowen ratio has a sharp increase on Nov 1 st to match the increase in the latent heat flux (and remains above 0.20 for the remainder of the analysis period), suggesting that the liquid water flux in the cloud layer should not be taken to be proportional to the upward latent heat flux after Nov 1 st . Figure 9 gives the surface friction velocity (vertical transport of horizontal momentum), vertical velocity variance, TKE, and the TKE dissipation rate in Panels (a) through (d), respectively. One commonality between each parameter is that the maximum value is reached on Nov. 1 st followed by the minimum value on Nov. 2 nd (see Table 3 for the mean and range of the values).

Synoptic Variability of Turbulence
For all four variables, there is very little variation between measurements, except for between Oct 30 th and Nov 2 nd , where a large increase in turbulence is observed before a rapid decrease. Overall, there is good agreement between mean values for the same flight, with the exception of Nov 12 th , which contains the largest difference between mean values for each variable legs, there does not appear to be a large difference in the buoyancy flux between the below cloud and in-cloud sections of the boundary layer, which is not as expected. In-cloud buoyancy in general is enhanced due to latent heating and cooling effects.
There is no statistical significance between the in-cloud and below-cloud data, with a p-value of 0.39. While the medians in the data populations are similar, the buoyancy flux in-cloud has a much larger range, suggesting isolated occurrences of extremely large buoyancy fluxes within the cloud. Connecting back to concepts discussed in the introduction, the coefficient correlation 375 between the surface latent heat flux and the in-cloud buoyancy is 0.40, suggesting some evidence that a larger surface latent heat flux leads to a larger in-cloud buoyancy flux, as suggested by Bretherton and Wyant (1997) and Lewellen et al. (1996). Figure 11 displays the same information as that of Figure 10, except for TKE (Panel (a)) and TKE dissipation (Panel(c)).
The total mean TKE was 0.132 ± 0.03 m 2 s −2 , with a below-cloud mean of 0.133 ± 0.05 m 2 s −2 and an in-cloud mean of 0.132 ± 0.04 m 2 s −2 . The total mean was 3.97 ± 1.28 cm 2 s −3 , with a below-cloud mean of 4.14 ± 2.45 cm 2 s −3 and an 380 in-cloud mean of 3.80 ± 1.81 cm 2 s −3 . Overall, very consistent values (when looking at the means) between below-cloud and in-cloud exist, resulting in statistical similarity between the data populations for both TKE and . However, in looking at the boxplots, one can see that there are several cases (including Nov 1 st and Nov 2 nd ) where the entire turbulent distribution of the below-cloud data is shifted to larger values than those of in-cloud data, with minimal overlap. This implies that the two layers have limited mixing between them, perhaps due to a more turbulent decoupled lower boundary layer. This will be explored in further detail in Section 4.2. Along with having different turbulent distributions between in-cloud and below-cloud, both the It is important to analyze turbulent fluxes of energy, momentum, and moisture as they act to determine boundary layer structure and characteristics, along with analyzing how these variables are related to synoptic scale properties such as geopotential height. The correlation coefficients between boundary layer characteristics and synoptic scale properties can be found in Table   4. The 700-hPa geopotential height is fairly correlated with the boundary layer height, although this correlation is negative with 400 a value of -0.37, suggesting that as the geopotential height increases, the boundary layer height decreases. The rate of change in the boundary layer height can be governed by: where h is boundary layer height, ω e is the entrainment rate and ω is the synoptic scale vertical velocity (positive upwards).
This suggest that if the rate of subsidence increases to the point that it is larger than ω e , then the boundary layer height will 405 decrease with time. However, periods of ridging which lead to stronger synoptic scale subsidence aloft will also act to increase entrainment, resulting in a higher lifted condensation level (LCL) for entrained air, and a resulting increase in boundary layer height as a result. Given that h acts to decrease as the geopotential height increases, this suggests that the subsidence becomes the dominating component that governs h over that of entrainment. The correlation between entrainment zone thickness and the boundary layer height is 0.22, in other words, as the geopotential height increases, both the boundary layer and the entrainment 410 zone thickness decreases, and vice versa. Both TKE and increase in-cloud with respect to the geopotential height (correlation coefficient of 0.23 and 0.24, respectively) and decreases with respect to boundary layer height (-0.32 and -0.34, respectively).
As the cloud droplet number concentration and aerosol number concentration increase (accompanied by a decrease in average droplet size), the TKE and increase. Physically this makes sense, as precipitation is suppressed due to larger number concentrations and smaller droplet sizes, a reduced moisture loss from the STBL can result, leading to thicker clouds, a larger 415 buoyancy flux, and a larger TKE. Smaller droplets will also evaporate more readily, leading to enhanced latent heating effects and a resultant increase in turbulence. The correlation between the sensible heat flux and wind is the largest, with a value of To summarize, the correlation coefficient values found here imply that the sensible heat flux is strongly correlated with wind 420 speed, boundary layer height, and geopotential height, in agreement with Palm et al. (1999). It is found that as the boundary layer height decreases, TKE and tend to increase, along with the sensible and latent heat flux. The increased geopotential height (or decrease in boundary layer height), which is most strongly correlated with the sensible heat flux (0.56 and 0.49 for in-cloud and below-cloud, respectively), leads to enhanced values of sensible and latent heat and stronger turbulent values. The various correlation coefficients indicate that (1) as the geopotential height decreases, the boundary layer height and entrainment 425 zone increase, accompanied by a decrease of in-cloud and below-cloud turbulence; (2) as the geopotential height increases, the boundary layer height and entrainment zone decrease, accompanied by an increase of in-cloud and below-cloud turbulence.
The observed decrease in boundary layer turbulence with increasing boundary layer height could be due to decoupling and an inability for the entire boundary layer to be mixed (leading to a subsequent decrease in turbulence), while a shallow boundary layer can be easily mixed through cooling at cloud top.

Vertical Profiles
It has been shown through the boundary layer vertical structure in Figure 6 that the boundary layer is, on average, well mixed when considering thermodynamic variables. Figure (Bretherton et al., 2010). Nocturnal measurements of the Californian Sc deck during DYCOMS-II also revealed a stronger 445 turbulent structure than that measured at Point Alpha, with observations showing in-cloud w w larger than 0.4 m 2 s −2 with a maximum of 0.5 m 2 s −2 near the base of the Sc deck (Stevens et al., 2005). As discussed in Wood (2012), w w is typically more vigorous at night due to the buoyancy production being larger from the lack of shortwave radiation absorption, which acts to stabilize the layer. As is found here, Hignett (1991) and Nicholls (1984) also found that w w peaked in the upper half of the STBL away from any boundaries such as cloud top. Note that the TKE mirrors that of w w in terms of vertical spatial 450 tendencies.
variance, w-variance, and the TKE are displayed in Figure 13 Panels ( and Bourcy, 2001). A slight decoupling can lead to less moisture transport into the Sc layer, resulting in less latent heat release due to condensation. This could be why only one flight has two peaks in TKE within the cloud when the turbulence maximum is reached below cloud, due to latent heat release at cloud base being suppressed. The latent heat flux peaks at the surface, but also sees a secondary maximum at a normalized boundary layer height of 0.99. The maximum at cloud top is due to entrainment of drier air from above the inversion down into the cloud (i.e., also a positive flux since both w and q are negative).

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Well-mixed STBLs tend to show characteristics of downdrafts that are spatially smaller, but stronger, than updrafts. This results in a negative vertical velocity skewness (from here on w w w ) through most of the cloud and sub-cloud layer (Nicholls, 1989;Hogan et al., 2009). Panel (c) displays that w w w on average is negative throughout the cloud layer and through most of the subcloud layer, having a maximum value near the surface. The minimum values in w w w occurs at cloud base (normalized in-cloud value of 0.04), suggesting that overall, the downdrafts are smallest, yet strongest at cloud base while updrafts are 495 spatially larger, yet weaker. samples near the surface for the profile method). Conversely, the profile method observed a large increase in TKE at cloud top from evaporative cooling due to entrainment mixing, which is not observed in the horizontal leg method. Another example is the buoyancy flux, which is seen to have a large increase in-cloud as compared to below cloud using the profile method. The horizontal leg method displays a maximum in the top-middle region of the cloud, but the overall buoyancy flux increase incloud vs. subcloud is compressed as compared to the profile method. In analyzing Table 5, it is clear that the average turbulence deviate from its surface value, decreasing significantly. Normalizing the potential temperature from 0 to 1 (where the surface is 530 0 (the minimum temperature) and the top is 1 (the maximum temperature), we find that the value of the potential temperature is 0.32 at cloud top and 0.10 at cloud base, inferring significant entrainment of the warmer, less buoyant air aloft. However, the mixing ratio within the boundary layer stays relatively constant. This is due to the fact that the entrainment of the warmer air aloft has a larger mixing ratio that that near the surface of the boundary layer. Significant decoupling is occurring in the subcloud layer, near a normalized boundary layer height of 0.60 (where the largest TKE and are located) and 0.40 (secondary 535 maximum in the TKE and ). It is suggested here that precipitation acts to decouple the boundary layer and enhance subcloud turbulence due to evaporative cooling of precipitation from the Sc deck above. Zheng et al. (2011) states that the cloud liquid water path reached a maximum on Nov, 1 st and Nov 2 nd due to the total-water specific humidity above the inversion being larger than that within the boundary layer. The inversion strength became significantly weaker on these two days (as evident from Figure 7 and the boundary layer was decoupled due to drizzle.

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As discussed previously, drizzle acts to warm the cloud layer and stabilizes the STBL, which reduces turbulent mixing and induces stratification. However, drizzle also evaporates readily below cloud base, resulting in evaporative cooling and enhanced instability for the subcloud layer (Wood, 2012). Precipitation promotes STBL decoupling by reducing the diabatic cooling in the cloud layer through in-cloud latent heating effects. The subcloud evaporation leads to cooling below cloud and a resultant local minimum in the buoyancy flux is created (Bretherton and Wyant, 1997). The sensible heat flux (proxy for buoyancy) 545 is observed to be negative from a normalized boundary layer height of ∼0.4 up to cloud base, with the minimum and local minimum outlined in the orange envelopes. The fact that turbulence peaks in the subcloud layer on this day is driven by the instability created from the cool layer below cloud base from precipitation. Normally, this will result in the cloud layer being decoupled form the surface moisture source, leading to a thinning cloud layer. However, the Sc deck is receiving moisture from the upper atmosphere (as seen in the negative latent heat flux above cloud (where w is negative but q prime is positive). This 550 process acts to moisten the boundary layer, which will lower the LCL, and assuming that the boundary layer height does not change, this will thicken the cloud (Randall, 1984). Note that the cloud layer on Nov. 2 nd is thicker than that on Nov. To summarize, it appears that the subcloud layer is decoupled from the Sc deck due to the evaporative cooling of precipita-560 tion. This increases turbulence within the subcloud layer, while reducing turbulence in the cloud layer. However, the cloud layer is still supplied with moisture through the entrainment of the more moist air aloft, driving cloud deepening and sustaining the Sc deck. The wind direction shifts from the south in the lower portion of the boundary layer to from the north near a normalized boundary layer height of 0.60. Seeing as the free atmosphere wind direction extends into the subcloud layer, this indicated that significant entrainment mixing has occurred, resulting in the upper 40% of the boundary layer to share characteristics with the 565 free atmosphere. Note that the maximum value in TKE that is measured on Nov. 1 st at a boundary layer height of 0.60 (see the blue profile line in Figure 12), matching the location at which the wind shear is occurring. However, this spike in TKE cannot be attributed to the wind shear alone, as wind shear that occurs at the inversion for each flight day and within the boundary layer on Nov 4 th do not result in large increases in turbulence. The increase in turbulence seen on Nov 1 st is related to latent heating affects and the resulting changes in the buoyancy fluxes. Although not displayed here, profiles for Nov 2 nd (the day 570 with the lowest average turbulence) shows a very consistent turbulent profile (no large spikes within or below the cloud layer), suggesting that precipitation has ceased and the boundary layer has been turned over, resulting in little energy remaining for mixing until cooling at cloud top becomes strong enough to support mixing again.
Comparing RF11 to a well-mixed boundary layer, Figure 17 displays the same information as that of Figure 16, except for RF03 (Oct. 19 th ). Both potential temperature and mixing ratio appear to be well-mixed throughout the boundary layer, with a 575 slight decrease in the potential temperature throughout the cloud layer. TKE, , the latent heat flux, and the sensible heat flux all have two peaks near cloud base and cloud top, suggesting latent heating near cloud base and evaporative cooling near cloud top. The sensible heat flux also has a negative value above cloud top due to the entrainment of warm, dry air down into the cloud from the stable air above the inversion. The droplet number concentration flux increases near cloud base owing to droplet activation, and sees a sharp decrease near a normalized boundary layer of 0.50, suggesting most of the activation is occurring 580 in the bottom half of the cloud layer. The vertical velocity skewness has a maximum negative value near cloud base, and never has an increase to positive values. The negative TKE flux within the cloud layer suggest that upward moving air is transporting less TKE than that of downward moving air. This negative TKE flux is proposed as evidence of the cloud top entrainment instability (CTEI) process, as proposed in Pasquier and Jonas (1998).

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Variations in turbulent and meteorological properties within the boundary layer on a flight by flight basis (synoptic variation) have been examined. It has been shown that the influence of a synoptic system on Nov. 1 st and Nov. 2 nd leads to a deepening of the cloud layer during passage and a large increase in boundary layer height after passage. TKE is shown to be rather weak as compared to other observational studies of Sc decks. TKE is shown to vary around 0.13 m 2 s −2 , except on the days leading up to and following the synoptic system passage, where the TKE increases rapidly to a maximum on Nov. 1 st due to precipitation 590 leading to enhanced turbulence in the subcloud layer and then decreases significantly to a minimum on Nov. 2 nd . Vertical profiles of turbulent fluxes indicate: -As the geopotential height decreases (increases), the boundary layer height and entrainment zone thickness increases (decreases), accompanied by a decrease (increase) of in-cloud and below-cloud turbulence.
-A maximum in TKE on Nov. 1 st (both overall average and largest single value measured) is due to precipitation acting 595 to destabilize the subcloud layer, while acting to stabilize the cloud layer. This is observed in both the vertical profiles of RF11 and the TKE and values in Figure 11, where it is shown that the distributions of turbulence for the subcloud and cloud layer are completely offset from one another, with the TKE in the subcloud layer maximizing for the analysis period, while the TKE in the cloud layer is below the average value for the analysis period.
-Six of the fourteen flights have a maximum TKE within the cloud layer. Seven of the fourteen flights display two peaks 600 in TKE within the cloud layer, one near cloud base and another near cloud top, signifying evaporative cooling near cloud top and latent heating near cloud base. Of the six flights that have a maximum TKE within the cloud layer, all six display two peaks in the TKE within the cloud layer, one near cloud base and one near cloud top.
-Analyzing different layers of turbulence over the 14 flights shows that TKE, , and the buoyancy flux, on average, all reach maximum values near cloud middle (between normalized in-cloud values of 0.25-0.75).

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The results presented here represent a snapshot of data through 14 aircraft flights, with at least a day between any two flights.
Therefore, the results presented represent boundary layer conditions that were present at the time of measurement, limiting any analysis of continuously evolving boundary layer and turbulent conditions, for example, being able to analyze the changing thermodynamic and dynamic conditions that resulted in large turbulent changes between Nov 1 st and Nov 2 nd . It has also been displayed that how turbulence is analyzed is important to understanding the true extent of how turbulence varies within 610 the boundary layer. Taking large scale averages of turbulent parameters (such as over entire horizontal flight legs) may lead to important smaller resolution variations being averaged out. For example, the vertical profiles presented in Figures 16 and   17 show much more detail in the vertical trends as compared to the averaged results of horizontal leg means displayed in Figure 12. Future work will involve using the turbulent analysis presented here to better understand the interactions between droplet clustering (or preferential concentration) and turbulence within Sc clouds, including variables that may influence the 615 components just mentioned, such as aerosol number concentration, cloud height, and precipitating vs. non-precipitating regions of cloud.  Table 3. Mean and range of values for select surface variables over the 14 flights analyzed, with standard deviation and the research flight number in parentheses for column mean and range, respectively.