Modeling microphysical effects of entrainment in clouds observed during EUCAARI-IMPACT field campaign

This paper discusses aircraft observations and large-eddy simulation (LES) modeling of 15 May 2008, North Sea boundary-layer clouds from the EUCAARIIMPACT field campaign. These clouds are advected from the northeast by the prevailing lower-tropospheric winds and featured stratocumulus-over-cumulus cloud formations. An almost-solid stratocumulus deck in the upper part of the relatively deep, weakly decoupled marine boundary layer overlays a field of small cumuli. The two cloud formations have distinct microphysical characteristics that are in general agreement with numerous past observations of strongly diluted shallow cumuli on one hand and solid marine stratocumulus on the other. Based on the available observations, a LES model setup is developed and applied in simulations using a novel LES model. The model features a double-moment warm-rain bulk microphysics scheme combined with a sophisticated subgrid-scale scheme allowing local prediction of the homogeneity of the subgrid-scale turbulent mixing. The homogeneity depends on the characteristic time scales for the droplet evaporation and for the turbulent homogenization. In the model, these scales are derived locally based on the subgrid-scale turbulent kinetic energy, spatial scale of cloudy filaments, mean cloud droplet radius, and humidity of the cloud-free air entrained into a cloud, all predicted by the LES model. The model reproduces contrasting macrophysical and microphysical characteristics of the cumulus and stratocumulus cloud layers. Simulated subgrid-scale turbulent mixing within the cumulus layer and near the stratocumulus top is on average quite inhomogeneous, but varies significantly depending on the local conditions.


Introduction
Numerical simulation of cloud microphysical properties poses significant challenges. This is because of the range of spatial scales involved, from the scale of a cloud or cloud system (hundreds of meters to tens or hundreds of kilometers) down to subcentimeter scales at which cloud microphysical processes operate. Resolving such 5 a range of scales in a numerical model is yet not possible. Cloud-scale dynamics (with help from even larger-scale processes) determine overall cloud characteristics, such as the cloud depth, horizontal extent, lifetime, etc. It also provides energy for smaller-scale turbulent motions, for instance, through the instabilities of the cloud-environment interface Clark, 1991, 1993a,b). Resolving cloud-scale dynamics requires 10 model gridlengths ranging from tens of meters to a kilometer or so depending on the particular case. Processes operating at smaller scales can only be included through the subgrid-scale modeling. This especially applies to cloud entrainment where dry environmental air is brought into the cloud and affects cloud macro-and microphysical characteristics. Entrainment is typically driven by interface instabilities, especially 15 in the case of cumulus clouds, but it may be also affected by other processes, for instance, by the buoyancy reversal due to cloud evaporation (see Kuo and Schubert, 1988;Siems et al., 1990;Grabowski, , 1995. Details of how entrainment affects cloud microphysics are still poorly understood because of difficulties encountered in cloud observations (mostly because of the aircraft speed and response time of aircraft 20 cloud probes) and the limited range of spatial scales resolved in numerical modeling.
Entrainment and mixing typically lead to a reduction of the cloud liquid water content (LWC), but microphysical effects can vary widely. In the homogeneous mixing, the dilution leads to the reduction of the droplet size, with a decrease of droplet concentration only due to changes of the total cloudy volume. When the extremely inhomogeneous 25 mixing takes place, droplet concentration is reduced without effects on the droplet radius. Both droplet radius and concentration are reduced in the intermediate case of the inhomogeneous mixing. The homogeneity of mixing has been argued to depend on the Introduction Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | modeling setup. Model results are compared to observations in Sect. 4, and simulated mixing characteristics are analyzed in Sect. 5. Conclusions are presented in Sect. 6.

The EUCAARI-IMPACT field campaign and the 15 May 2008, North Sea case
The EUCAARI-IMPACT (Intensive Observation Period At Cabauw Tower) field campaign was part of the EUCAARI (European Integrated Project on Aerosol Cloud Cli-5 mate and Air Quality Interactions, Kulmala et al., 2011) project funded under the EU Framework Programme 6. The campaign took place in May 2008 in the Netherlands and focused on remote sensing and in-situ ground-based and airborne observations of clouds and aerosols in the vicinity of the Cabauw tower. Because of unexpectedly dry and cloudless conditions that prevail over the Netherlands for most of the EUCAARI- 10 IMPACT campaign, several scientific flights were conducted over the North Sea. These flights targeted clouds and aerosols within the stratocumulus-topped marine boundary layer. The 15 May flight was one of such cases (Puygrenier et al., 2010). Figure 1 shows flight trajectory of the 15 May Meteo-France Safire ATR-42 mission superimposed on the MODIS satellite image at 11:15 UTC. The figure shows a sig- 15 nificant cloud cover over the North Sea and the surrounding land masses. Shallow convective clouds over the eastern England, just to the west of the Greenwich meridian, document the low-level north-easterly flow over the region, in agreement with the aircraft data (see Fig. 2). The stratocumulus deck over the North Sea extends to the north of approximately the 54 • N parallel and appears quite spatially heterogeneous. 20 The stratocumulus topped boundary layer (STBL) and the lower free troposphere were sampled by the aircraft between approximately 07:40 and 09:30 UTC. Figure 2 shows the height of the aircraft as a function of time and depicts in red periods when the aircraft encountered a cloud. The figure shows that besides the stratocumulus cloud (with cloud base and cloud top around 700 and 1150 m), the aircraft often intersected 25 clouds beneath the stratocumulus cloud base. Such a situation, often referred to as the boundary layer with stratocumulus over cumulus, corresponds to a weakly decoupled Introduction relatively deep marine boundary layer, often associated with the transition from shallow STBL to significantly deeper cumulus-topped boundary layer in the subtropics (see Bretherton and Pincus, 1995;de Roode and Duynkerke, 1997;Sandu et al., 2010). The cloud data from the flight track shown in Figs. 1 and 2 were divided into two sets depending on the height of the aircraft to represent the stratocumulus/cumulus 5 clouds. The droplet concentration, cloud water mixing ratio, and mean volume radius for the two cloud types are shown in Figs. 3 and 4. Each data point in the figures represents approximately 100-m average (1-Hz) of cloud droplet counts from the FFSSP (Fast Forward Scattering Spectrometer Probe; Brenguier et al., 1998). The data corresponding to the stratocumulus cloud ( Fig. 3) are shown as a function of height above the cloud base that varies between 650 m and 750 m. Figure 3 shows fairly typical pattern: approximately constant with height droplet concentration (∼ 100 mg −1 ; except near the cloud base where FFSSP may miss small droplets and cloud top where intensive mixing takes place), cloud water mixing ratio not far from the adiabatic (but also with a significant spread, especially in the upper half of the cloud depth), and the mean 15 volume radius increasing gradually with height and consistent with the observed concentrations. In contrast, the data for the cumuli (Fig. 4) show a wide range of droplet concentrations and relatively small values of the cloud water mixing ratio. The mean volume radius is small, in the range of 2 to 8 µm, that is, as in the lower part of the stratocumulus. All these suggest that small cumuli beneath stratocumulus are strongly 20 diluted by entrainment and the 1-Hz data may not represent the small-scale features adequately. Because cumulus cloud fraction is low, there is a significantly lower number of data points in Fig. 4  run for 6 h, and snapshots of model fields saved every 3 min from the last 3 h of the simulation were used in the analysis. Model thermodynamics combines the two-moment warm-rain scheme (i.e. predicting both the mixing ratio and the droplet concentration for the cloud and rain water; Grabowski, 2007, 2008) with the delay of cloud water evaporation result- 15 ing from the subgrid-scale mixing between the cloud and its environment (Grabowski, 2007;Jarecka et al., 2009). Activation of cloud droplets is represented by the approach developed by Khvorostyanov and Curry (2006) with the total CCN concentration set to 200 mg −1 . The latter is based on EUCAARI-IMPACT observations reported in Crumeyrolle et al. (2011). Autoconversion and accretion parameterization follow those pro-20 posed in Khairoutdinov and Kogan (2000) as used in Morrison and Grabowski (2007). The delay of cloud water evaporation during turbulent mixing is facilitated by including two additional model variables, the characteristic scale (width) λ of cloud filaments and the fraction of a gridbox volume occupied by the cloudy air β. The scale λ is assumed to decrease during the stirring phase of the entrainment process from the scale 25 of an initial engulfment Λ (assumed to be of the order of the model gridlength) down to the scale of microscale homogenization λ 0 (i.e. of the order of the Kolmogorov microscale; ∼ 1 mm in atmospheric conditions). The evaporation of cloud water due to Introduction subgrid-scale mixing depends on the scale λ, with virtually no evaporation when λ ∼ Λ, and all evaporation when λ ∼ λ 0 (see discussion in Grabowski, 2007).
In the double-moment scheme the homogeneity of mixing is controlled by the parameter α (Morrison and Grabowski, 2008). The parameter α is calculated locally based on the predicted turbulent kinetic energy, the scale of cloud filaments λ, mean cloud droplet radius, and the humidity of the cloud-free air entrained into the cloud. Results of direct numerical simulations of the interfacial cloudy and cloud-free air mixing reported in Andrejczuk et al. (2009) are used in the prediction of α. See Appendix A and JGMP13 for more details.
The entire thermodynamics/microphysics scheme operates in the following way. For 10 a gridbox with either λ = Λ or λ = 0, that is, either fully cloudy or cloud-free, respectively, calculations progress as in the standard double-moment scheme of Grabowski (2007, 2008) without any subgrid-scale considerations. For a gridbox with λ 0 < λ < Λ, the expected evaporation or condensation of cloud water δq c is calculated first using the grid-averaged fields as in the standard double-moment scheme. If 15 condensation is predicted, then the gridbox is assumed uniform, δq c is applied in the microphysics scheme, λ is reset to Λ and β is reset to 1. The same procedure is used when λ < λ 0 because molecular homogenization is assumed completed. If needed, activation of new cloud droplets takes place. For the evaporation, δq c is first partitioned into the adiabatic part βC ad ∆t [where C ad is the adiabatic condensation rate, see ap-20 pendix in Grabowski (2007); and ∆t is the model time step] and the contribution due to mixing ∆q c assuming ∆q c = δq c −βC ad ∆t. Note that variable ∆q c , that is a part due to diabatic evaporation, combines impacts of the explicit (due to turbulent mixing terms) as well as the implicit (numerical) diffusion. Because of the delay of the diabatic evaporation during the stirring phase of the entrainment, only a fraction of ∆q c , ∆q * c = λ 0 /λ ∆q c 25 is allowed to evaporate. This formula comes from heuristic considerations concerning droplet evaporation at the edges of cloud filaments. Next, ∆q * c is applied to the cloud water mixing ratio, and the droplet concentration is reduced depending on the homogeneity of the subgrid-scale mixing, that is, through the parameter α (see Appendix A). Introduction In addition, the adiabatic condensation C ad is applied to the β cloudy fraction of the gridbox assuming no change in the droplet concentration. The idealization of observed mean conditions used to initialize the simulation are shown in Fig. 5. The total water mixing ratio, liquid water potential temperature and horizontal wind components are taken as 5.2 g kg −1 , 282.2 K, −3.18 and −3.89 m s −1 5 (E-W and N-S) up to the base of the STBL inversion at 1120 m. The inversion is assumed to be 40 m deep, with the profiles linearly changing to 3.1 g kg −1 , 289.6 K, The model is forced to maintain approximately steady-state conditions throughout the simulation, similarly to other LES boundary layer studies (e.g. Siebesma et al., 2003;Stevens et al., 2005). Forcings required to maintain approximately steady-state conditions are estimated by a trial and error test simulations. The forcings include: 15 (a) surface heat and momentum fluxes; (b) large-scale subsidence; and (c) radiative processes. Surface heat fluxes and subsidence were assumed to be constant in time and space. Surface sensible and latent heat fluxes were derived by applying an estimate of the sea surface temperature (SST) from satellite analysis for this day. After some tests, the values were selected as constant 8 × 10 −3 K m s −1 for the sensible heat 20 flux and 6.5 × 10 −5 m s −1 for the latent heat flux. The surface momentum fluxes were calculated similarly to Siebesma et al. (2003), with the fluxes given by −u 2 * v/|v|, with u * = 0.28 m s −1 . Large-scale subsidence was prescribed as W s = −Dz with the largescale divergence selected as D = 4 × 10 −6 s −1 . For the radiative transfer, only the longwave processes were considered as the key driver of the STBL dynamics and only in an To provide an illustration for the model results, Fig. 7 shows snapshots of the cloud water field in the two vertical cross sections of the computational domain at time of t = 6 h, i.e. at the end of the simulation. The figure also shows local values of the parameter α at points undergoing turbulent cloud-environment mixing. The figure shows that in 15 the model, similarly as in the observations, the stratocumulus layer overlays a layer with shallow convective clouds that either grow into the stratocumulus layer (like the cloud near the center of the upper panel) or remain detached in the layer between 400 and 700 m (see the bottom panel). Such a situation is typical for relatively deep STBL and results from weak decoupling between the two cloud layers (see Bretherton and 20 Pincus, 1995;de Roode and Duynkerke, 1997;Sandu et al., 2010). The figure also shows that mixing characteristics (i.e. the parameter α) vary significantly in various locations, from close to homogeneous (α = 0, dark blue colors in the panels) to not far from extremely inhomogeneous (α = 1, dark red colors).

Conclusions References
The double-layer structure of clouds within STBL is also confirmed by the mean cloud fraction and in-cloud condensed water profiles shown in Fig. 8. To obtain these profiles, gridpoints of the model data were assumed cloudy if the cloud water mixing 1498 Introduction

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Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ratio exceeded 0.01 g kg −1 and the droplet concentration exceeded 5 mg −1 . The cloud fraction within the cumulus layer is small (∼ 0.1), but it is quite high, up to 0.9, within the stratocumulus layer. The cloud water shows that the cumulus layer (roughly between 300 and 700 m above the sea level) features clouds significantly diluted by entrainment, with the mean cloud water increasing with height at a rate lower than the adiabatic one 5 (the latter is ∼ 1 g kg −1 per 500 m). The rate of increase within the lower part of the stratocumulus layer (between approximately 700 and 1000 m) is significantly higher. The reduction of the cloud water close to the cloud top comes from the cloud-top entrainment as illustrated by the number of gridpoints undergoing turbulent mixing (see colored points in Fig. 7). the mixing with the unsaturated air from above the cloud top. Figure 10 shows the CFAD of β, the cloudy fraction of the gridbox volume. As expected, β is seldom different from unity in the stratocumulus layer, but vary widely within the cumulus layer and near the very stratocumulus top. It follows that predicted ACPD 13,2013 Modeling of  gridbox-averaged droplet concentration N c and the local droplet concentration N c /β (i.e. the concentration in the cloudy part of volume) differ significantly in cumuli and near the stratocumulus top. These differences are consistent with the stirring phase of the cloud entrainment and mixing. Figure 11 shows the CFAD of the droplet mean volume radius. The figure clearly 5 shows that the two cloud layers are to a large extent decoupled. The most frequent values increase with height in both layers, and the separation between the layers is evident. The green lines show the adiabatic values of the radius assuming the cloud base height and the adiabatic droplet concentration of 300 m and 60 mg −1 for the cumulus layer, and 700 m and 90 mg −1 for the stratocumulus layer. In the stratocumulus layer, the most frequent values are close to the adiabatic profile. This indicates that the stratocumulus is only weakly diluted by entrainment, an aspect consistent with the observations (Fig. 3). For the cumulus layer, the most frequent values are much smaller than adiabatic, except near the cloud base, with radii smaller than 8 µm. Similar behavior is seen in the observations (see Fig. 4). This is again a consequence of strong dilution 15 of cumulus clouds. Although some cumuli penetrate into the stratocumulus layer (see examples in Fig. 7) Fig. 11 clearly shows that this is not the dominant pattern.

Mixing scenarios
As explained in the previous section, the model predicts locally the mixing scenario at each time step by deriving the parameter α from model variables (see the Appendix A). 20 Figure 7 shows local α values at grid volumes undergoing turbulent cloud-environment mixing. The figure shows that mixing events take place mostly at the edges of cumulus clouds and near the stratocumulus top. They occur less frequently inside the stratocumulus layer, typically at the edges of stratocumulus breaks (or holes) as one might expect (see discussion in Kurowski et al., 2009 Figure 12 shows CFAD of the parameter α for points undergoing turbulent mixing. The figure also shows the number of points (as a fraction of all points at a given level) included in the analysis. The figure shows that α changes from close to 0 (homogeneous mixing) to close to 1 (extremely inhomogeneous mixing) and the distribution is particularly wide near the bottom and top of the cloud layer. The red line shows the 5 average profile. The profile is approximately constant across the cloud layer, except near the very bottom and very top. Although the cloud fraction in the cumulus layer is small, the mixing events occur often, approximately half of the cloudy points within the cumulus layer experience turbulent mixing. In the stratocumulus layer mixing events are rare, except near the cloud top. The most frequent mixing scenarios represent in-10 homogeneous mixing (α ≈ 0.7-0.8) across the most of the cloud layer depth (except of of the 100 m or so near the cloud base and cloud top). The width of the distribution is large, however, with α ranging from 0.3 to 0.9 throughout the most of the cloud field, with even wider range near the cloud base and cloud top. The differences between the two cloud layers seem rather small. This might be viewed surprising considering 15 significant differences between cumulus and stratocumulus clouds, expected levels of turbulence, for instance (e.g. Siebesma et al., 2003;Stevens et al., 2005;Burnet and Brenguier, 2007). The analysis below further explores the similarity and differences.
Parameter α is a function of the characteristic time scales of the droplet evaporation, τ evap , and of the turbulent mixing, τ mix . The Appendix A presents formulas that are used 20 to locally derive α from τ evap and τ mix , and the time scales from model variables. More in-depth discussion is provided in JGMP13.
CFADs of the time scale τ evap and τ mix are shown in Fig. 13. The figure shows that the two cloud layers differ more significantly in the time scales than in α. CFADs are wider within most of the stratocumulus layer when compared to the cumulus layer. 25 The mixing time scale τ mix is smaller in the cumulus layer. This is caused mostly by differences in TKE predicted by the model, which is higher in cumulus layer and close to the top of the stratocumulus. This agrees with previous modeling studies (Siebesma et al., 2003;Stevens et al., 2005) same within the two layers (except near the cloud base and stratocumulus top where the distribution is particularly wide). This is consistent with the fact that droplet radii are similar in both layers (Fig. 11). Cumulus clouds are shallow and very diluted, so droplets cannot grow to large sizes. This is against a common assumption that cloud droplets within stratocumulus are smaller and thus evaporation is faster. The small values of the 5 evaporation time scale near the stratocumulus top are due to lower humidities of the entrained air, as shown below. Figures 14 and 15 show scatter diagrams of model variables (in appropriate powers, see the Appendix A) that determine the actual values of the τ evap and τ mix at the height of 500 m (i.e. within the cumulus layer) and 1200 m (i.e. near the stratocumulus 10 top), respectively. There are systematic differences between Figs. 14 and 15, consistent with expected differences between entrainment in cumulus and stratocumulus. For instance, there are more points with higher TKE in the cumulus layer, as well as larger droplet sizes near the stratocumulus top (that was already pointed out in the previous analysis). The relative humidity RH d of air involved in the subgrid-scale turbulent mix- 15 ing is typically quite high (0.9 and above so that 1/(1 − RH d ) is larger than 10), but it is shifted towards lower humidities for the stratocumulus layer. This is consistent with the fact that stratocumulus entrains significantly drier air from above the inversion. and featured low LWC, typically below 0.2 g kg −1 , droplet radii between 2 and 8 µm, and a wide rage of droplet concentrations, between a few to about 100 mg −1 . No systematic variation of these parameters with height was observed. Small-scale structure of these cumuli were unlikely resolved by the observations. In contrast, stratocumulus deck observations were consistent with results of previous studies of such clouds. Stratocu-5 mulus is only weakly diluted, droplet concentrations ranged between 50 and 150 mg −1 and were approximately height-independent (except near the cloud top where lower concentrations were observed). The mean droplet radius is observed to increase with height in a manner consistent with the close-to-adiabatic LWC and the mean droplet concentration.

10
To simulate cloud field sampled on 15 May, the LES model with a double-moment warm-rain microphysics was setup based on available observations and trial and error test simulations. The simulation reproduces the stratocumulus-over-cumulus cloud formations and contrasting macro-and microphysical characteristics of the two cloud layers. The LES model used in this study also includes the delay of cloud water evap-15 oration resulting from the turbulent stirring (Grabowski, 2007;Jarecka et al., 2009) and is capable of predicting homogeneity of the subgrid-scale mixing between the cloud and its cloud-free environment (JGMP13). The homogeneity of the subgrid-scale mixing within the microphysics scheme is controlled by a single parameter α, with the range of values between 0 to 1. The limiting values represent the homogeneous and 20 the extremely inhomogeneous mixing scenarios, respectively. The parameter α depends on the characteristic time scales of the droplet evaporation and of the turbulent homogenization. In the model, these scales are derived locally based on the subgridscale turbulent kinetic energy, spatial scale of cloudy filaments, the mean cloud droplet radius, and the humidity of the cloud-free air entrained into the cloud. As a result, pa-25 rameter α is locally predicted. Subgrid-scale mixing turned out to be on average quite inhomogeneous, with the mean parameter α around 0.7 across the entire depth of the cloud field. However, local variations of α at a given height were large and covered almost the entire range, especially near the base and the top of the cloud field. The

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Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | uniform mixing characteristics across the entire depth of the cloud field were explained by small changes of the mixing and evaporation time scales between cumulus and stratocumulus layers.
Appendix A Summary of model formulas determining the homogeneity of mixing 5 A Homogeneity of the subgrid-scale turbulent mixing in the double-moment microphysics scheme is determined by the parameter α. This parameter is used to calculate the final droplet concentration after entrainment and turbulent mixing according to the Eq. (11) in Morrison and Grabowski (2008), that is: 10 where q i c and N i c are values of the cloud water mixing ratio and droplet concentration before including effects of evaporation due to the subgrid-scale mixing. These values include all other processes, such as the resolved (advective) and parameterized (subgrid-scale) transport and evaporation due to the advective changes of ther-15 modynamic properties, the vertical advection in particular; q f c is the final cloud water mixing ratios (i.e. after the microphysical adjustment). Note that, in the Morrison and Grabowski (2008) scheme, the microphysical adjustment of the cloud water mixing ratio q c takes place before adjusting N c , and it is dictated by the predicted supersaturation, and characteristics of the cloud droplet population (i.e. the droplet concentration and Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 0 for the case of the homogeneous mixing (i.e. no change to N c ) to 1 for the extremely inhomogeneous mixing (i.e. when N c changes in the same proportion as q c and thus the mean volume radius remains unchanged).
To predict the local value of parameter α, we first relate it to the slope δ from the r 3 − N diagram applied in Andrejczuk et al. (2004Andrejczuk et al. ( , 2006. In this diagram, the total number 5 of droplets is plotted against the mean volume radius cubed, similarly to the diagram used in Burnet and Brenguier (2007). The vertical line (reduction of the number of droplets without changing the size; δ → ∞) implies extremely inhomogeneous mixing. The homogeneous mixing corresponds to the horizontal line (i.e. changing droplet size without changing the number of droplets; δ = 0). The slope δ is related to the parameter 10 α in Eq. (A1) as: Based on a large set of DNS simulations, δ can be assumed to be approximately equal to the ratio of the time scales of turbulent homogenization and droplet evapora- where τ mix and τ evap are the turbulent mixing and droplet evaporation time scales respectively. The turbulent homogenization time scale, following Andrejczuk et al. (2009), 20 is approximated by the eddy turnover time (e.g. Jensen and Baker, 1989): where u(λ) is the characteristic velocity at the filament scale λ. It can be related to the model-predicted TKE (E ) as u(λ) = (E ) 1/2 (λ/Λ) 1/3 . This relationship assumes the iner-25 tial range scaling for subgrid-scale turbulence and considers TKE to be dominated by where r is the mean volume radius of cloud droplets, RH d is the relative humidity of the 5 cloud-free portion of the gridbox, and A ≈ 10 −10 m 2 s −1 is the constant in the droplet diffusional growth equation (i.e. dr/dt = AS/r, where S = RH − 1 is the supersaturation). RH d can be estimated using the mean (model-predicted) relative humidity of a gridbox RH and assuming that the cloudy part of the gridbox is saturated. These assumptions lead to Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Lock, A., Müller, F., Stevens, D. E., Whelan, E., and Zhu, P.: Evaluation of large-eddy simulations via observations of nocturnal marine stratocumulus, Mon. Weather Review, 133, 1443-1462, 2005. 1497, 1498, 1501  height droplet concentration (∼ 100 mg −1 ; except near cloud base where FFSSP may miss small droplets and d top where intensive mixing takes place), cloud water ng ratio not far from the adiabatic (but also with a signift spread, especially in the upper half of the cloud depth), the mean volume radius increasing gradually with height consistent with the observed concentrations. In contrast, ata for the cumuli (Fig. 4) show a wide range of droplet entrations and relatively small values of the cloud water ng ratio. The mean volume radius is small, in the range to 8 µm, that is, as in the lower part of the stratocumulus. number of data points in Fig. 4 compared to Fig. 3. Some of these cumuli are likely to penetrate into the stratocumulus 190 layer; this may explain data points with cloud water exceeding the adiabatic value in Fig. 3    Model thermodynamics combines the two-moment warmrain scheme (i.e., predicting both the mixing ratio and the the approach developed by Khvorostyanov and Curry (2006) 220 with the total CCN concentration set to 200 mg −1 . The latter is based on EUCAARI-IMPACT observations reported in Crumeyrolle et al. (2011). Autoconversion and accretion parameterization follow those proposed in Khairoutdinov and Kogan (2000) as used in Morrison and Grabowski (2007).

225
The delay of cloud water evaporation during turbulent mixing is facilitated by including two additional model variables, the characteristic scale (width) λ of cloud filaments and the fraction of a gridbox volume occupied by the cloudy air β. The scale λ is assumed to decrease during the stirring phase 230 of the entrainment process from the scale of an initial engulfment Λ (assumed to be of the order of the model gridlength) down to the scale of microscale homogenization λ 0 (i.e., of the cloud water mixing ratio exceeded 0.01 g kg −1 and the 355 droplet concentration exceeded 5 mg −1 . The cloud fraction within the cumulus layer is small (∼ 0.1), but it is quite high, up to 0.9, within the stratocumulus layer. The cloud water shows that the cumulus layer (roughly between 300 and 700 m above the sea level) features clouds significantly di-360 luted by entrainment, with the mean cloud water increasing with height at a rate lower than the adiabatic one (the latter is ∼ 1 g kg −1 per 500 m). The rate of increase within the lower part of the stratocumulus layer (between approximately 700 and 1000 m) is significantly higher. The reduction of the 365 cloud water close to the cloud top comes from the cloud-top entrainment as illustrated by the number of gridpoints undergoing turbulent mixing (see colored points in Fig. 7).  are approximately constant except close to the c cloud base and the transition layer between cumulu tocumulus. The mean concentration for the strat layer is around 90 mg −1 , and it is around 60 mg − cumulus layer. These are in a good agreement w 380 vational values (see Fig. 4 and 3). The CFAD show spread inside the cumulus layer, with the most freq ues around 20 mg −1 and some points with concent high as 150 mg −1 . Because of the strongly skew the gridbox volume. As expected, β is seldom different from unity in the stratocumulus layer, but vary widely within the cumulus layer and near the very stratocumulus top. It fol-395 lows that predicted gridbox-averaged droplet concentration Nc and the local droplet concentration Nc/β (i.e., the concentration in the cloudy part of volume) differ significantly in cumuli and near the stratocumulus top. These differences are consistent with the stirring phase of the cloud entrainment 400 and mixing. Figure 11 shows the CFAD of the droplet mean volume radius. The figure clearly shows that the two cloud layers are to droplet concentration of 300 m and 60 mg −1 for the cumulus layer, and 700 m and 90 mg −1 for the stratocumulus layer. In the stratocumulus layer, the most frequent values are close 410 to the adiabatic profile. This indicates that the stratocumulus is only weakly diluted by entrainment, an aspect consistent with the observations (Fig. 3). For the cumulus layer, the most frequent values are much smaller than adiabatic, except near the cloud base, with radii smaller than 8 µm. Similar be-415 havior is seen in the observations (see Fig. 4). This is again a consequence of strong dilution of cumulus clouds. Although some cumuli penetrate into the stratocumulus layer (see ex-               . 13. CFADs of the mixing time scale τmix and the evaporation time scale τevap. Red lines show the average profiles. As in Fig. 12, only cloudy points where subgrid-scale mixing takes place are included; the frequencies of mixing events are shown on the right hand sides of the panels.

Conclusions
This paper presents aircraft observations and LES modeling of the May 15, 2008, boundary-layer clouds over the North Sea observed during the EUCAARI-IMPACT field campaign. These clouds were advected from the north-east 505 by the prevailing lower tropspheric winds and were sampled by the aircraft between approximately 7:40 and 9:30 UTC. Almost-solid stratocumulus deck was present in the upper part of the relatively deep weakly decoupled marine boundary layer. Small cumuli, with a cloud fraction of ∼10%, were 510 sampled beneath the stratocumulus. The two cloud formations featured distinct microphysical characteristics. Small cumuli were significantly diluted and featured low LWC, typically below 0.2 g kg −1 , droplet radii between 2 and 8 µm, and a wide rage of droplet concentrations, between a few 515 to about 100 mg −1 . No systematic variation of these parameters with height is observed. Small-scale structure of these cumuli were unlikely resolved by the observations. In contrast, stratocumulus deck observations were consistent with results of previous studies of such clouds. Stratocu-520 mulus is only weakly diluted, droplet concentrations ranged