Top-down and Bottom-up aerosol-cloud-closure: towards understanding sources of uncertainty in deriving cloud radiative flux

Top-down and bottom-up aerosol-cloud-radiative flux closures were conducted at the Mace Head atmospheric research station in Galway, Ireland in August 2015. This study is part of the BACCHUS (Impact of 15 Biogenic versus Anthropogenic emissions on Clouds and Climate: towards a Holistic UnderStanding) European collaborative project, with the goal of understanding key processes affecting aerosol-cloud-radiative flux closures to improve future climate predictions and develop sustainable policies for Europe. Instrument platforms include groundbased, unmanned aerial vehicles (UAV), and satellite measurements of aerosols, clouds and meteorological variables. The ground-based and airborne measurements of aerosol size distributions and cloud condensation nuclei (CCN) 20 concentration were used to initiate a 1D microphysical aerosol-cloud parcel model (ACPM). UAVs were equipped for a specific science mission, with an optical particle counter for aerosol distribution profiles, a cloud sensor to measure cloud extinction, or a 5-hole probe for 3D wind vectors. UAV cloud measurements are rare and have only become possible in recent years through the miniaturization of instrumentation. These are the first UAV measurements at Mace Head. ACPM simulations are compared to in-situ cloud extinction measurements from UAVs to quantify 25 closure in terms of cloud radiative flux. Two out of seven cases exhibit sub-adiabatic vertical temperature profiles within the cloud, which suggests that entrainment processes affect cloud microphysical properties and lead to an overestimate of simulated cloud radiative flux. Including an entrainment parameterization and explicitly calculating the entrainment fraction in the ACPM simulations both improved cloud-top radiative closure. Entrainment reduced the difference between simulated and observation-derived cloud-top radiative flux (RF) by between 30 W m and 30 40 W m. After accounting for entrainment, satellite-derived cloud droplet number concentrations (CDNC) were within 30% of simulated CDNC. In cases with a well-mixed boundary layer, RF is less than 25 W m after accounting for cloud-top entrainment, compared to less than 50 W m when entrainment is not taken into account. In cases with a decoupled boundary layer, cloud microphysical properties are inconsistent with ground-based aerosol measurements, as expected, and RF is as high as 88 W m, even after accounting for cloud-top entrainment. This 35 1 The regulatory term for UAV is Remotely Piloted Aircraft (RPA). Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2017-201, 2017 Manuscript under review for journal Atmos. Chem. Phys. Discussion started: 21 March 2017 c © Author(s) 2017. CC-BY 3.0 License.

2 work demonstrates the need to take in-situ measurements of aerosol properties for cases where the boundary layer is decoupled as well as consider cloud-top entrainment to accurately model stratocumulus cloud radiative flux.

Introduction
One of the greatest challenges in studying cloud effects on climate are that the clouds are literally out of reach. Many ground-based measurement sites have a long historical record that are useful for identifying climatological trends, 40 however, it is difficult to quantify such trends in cloud microphysical and radiative properties at these stations based solely on remote sensing techniques such as radar and lidar. In-situ aerosol measurements at the surface are often used to estimate cloud properties aloft, but the simulations used to estimate above surface conditions require many idealized assumptions such as a well-mixed boundary layer and adiabatic parcel lifting. Satellites have the advantage to infer cloud properties over a much larger area than ground-based observations; however, they can only see the upper most 45 cloud layer and satellites need in-situ observations to improve their retrievals. In this study, we combine ground-based and airborne measurements with satellite observations to determine cloud radiative properties and compare these results to an aerosol-cloud parcel model (ACPM) to identify sources of uncertainty in aerosol-cloud interactions.
The atmospheric research station at Mace Head has been a research platform for studying trace gases, aerosols and 50 meteorological variables since 1958 [O'Connor et al., 2008]. The station is uniquely exposed to a variety of air masses, such as clean marine air and polluted European air. Over the long history of observations and numerous fieldcampaigns held at the Mace Head research station, few airborne field experiments have been conducted. During the PARFORCE campaign in September 1998, aerosol and trace gas measurements were made to map coastal aerosol formation [C. D. O'Dowd et al., 2001]. During the second PARFORCE campaign in June 1999, measurements of sea 55 spray plumes were made on an aircraft installed with a Lidar . In the NAMBLEX campaign in August 2002, flights were conducted to measure aerosol chemical and physical properties in the vicinity of Mace Head Heard et al., 2006;Norton et al., 2006]. None of the research flights thus far have studied aerosolcloud interactions and cloud radiative properties at Mace Head. 60 For ground-based observations, it is often assumed that measured species are well-mixed throughout the boundary layer. Often this assumption is valid and many observational studies have shown that models which use ground-based measurements can accurately simulated cloud droplet number concentrations (CDNC) [Conant et al., 2004;Fountoukis et al., 2007;Russell and Seinfeld, 1998], making bottom-up closure a viable method for predicting cloud properties. Closure is defined here as the agreement between observations and model simulations of CDNC and cloud-65 top radiative flux. This well-mixed boundary layer simplification, however, has been shown to be inaccurate in many field experiments (e.g., the Atlantic Stratocumulus Transition Experiment (ASTEX) [Albrecht et al., 1995]; and the Aerosol Characterization Experiments, ACE1 [Bates et al., 1998] and ACE2 [Raes et al., 2000]. Previous studies at Mace Head have shown that decoupled boundary layers were observed with scanning backscatter lidar measurements Milroy et al., 2012]. Such decoupled layers often contain two distinct cloud layers, distinguished 70 as a lower layer within the well-mixed surface layer and a higher decoupled residual layer between the free troposphere 3 and surface layer Milroy et al., 2012;Stull, 1988]. General characteristics associated with decoupled boundary layers are a weak inversion, a decrease in aerosol concentration relative to the surface layer, and more commonly occurring in relatively deep marine boundary layers ( > 1400 m) [Jones et al., 2011]. Dall'Osto et al [2010] showed the average height of the surface mixed layer, over Mace Head, varies from 500 m to 2000 m, and the 75 decoupled layers have heights ranging from 1500 m to 2500 m. Marine boundary layer decoupling is often seen in the tropics and has been attributed to processes that involve cloud heating and surface cooling as cloud warming can result from cloud-top entrainment, leading to decoupling of the boundary layer [Albrecht et al., 1995;Bates et al., 1998;Bretherton et al., 1997]. In addition, Bretherton and Wyant [1997] have suggested that the decoupling structure is mainly driven by an increasing ratio of the surface latent heat flux, (i.e., evaporative cooling at the surface) to the net 80 radiative cooling within the cloud, while other factors, such as drizzle, the vertical distribution of radiative cooling in the cloud, and sensible heat fluxes, play less important roles. Turton and Nicholls [1987] used a two-layer model to show that decoupling can also result from solar heating of the cloud layer. Nicholls and Leighton [1986] suggested decoupling results from cloud-top radiative cooling and the resulting eddies do not mix down to the surface. Zhou et al. [2015] showed that the entrainment of the dry warm air above the inversion could also be the cause. Marine 85 boundary layer decoupling is often seen in the tropics and has been attributed to easterlies bringing air over increasing SST, which increases latent cooling and adds negative buoyancy below the cloud layer [Albrecht et al., 1995].  and Sollazzo et al. [2000] showed that, in a decoupled atmosphere the two distinct layers have similar characteristics (e.g., aerosol and trace gases composition), but different aerosol concentrations and gradually mix with each other, entraining air from the surface layer into the decoupled residual layer and vice versa. These previous 90 studies show that aerosol concentrations in the upper residual layer are lower than those in the well-mixed surface layer implying an overestimation in cloud radiative flux when using ground-based aerosol measurements.
Satellite measurements of microphysical properties, such as CDNC, have the potential to be independent of groundbased measurements, and therefore be reliable for studying decoupled clouds. Satellite estimates of CDNC have only 95 become possible recently due to the increased resolution in measurements [Painemal and Zuidema, 2011;Rosenfeld et al., 2014;Rosenfeld et al., 2012;Rosenfeld et al., 2016]. Therefore, current measurements still require ground-based validation until the method is further developed.
The focus of this manuscript is on the top-down closure between satellite retrievals and airborne measurements of 100 cloud microphysical properties, as well as, traditional bottom-up closure coupling below and in-cloud measurements of cloud condensation nuclei (CCN), updraft, and cloud microphysical properties. In-situ measurements of CDNC are not available so bottom-up closure is expressed in terms of cloud-top radiative flux rather than CDNC and top-down closure of satellite CDNC is compared to ACPM simulated CDNC. The methods section describes how observations were collected, as well as the methods for estimating CDNC with satellite measurements and calculating radiative 105 flux with the ACPM. The results section summarizes the bottom-up and top-down closure for coupled and decoupled clouds and quantifies the differences in cloud radiative flux for cases that were affected by cloud-top entrainment.

2 Methods
The August 2015 campaign at the Mace Head research station (Galway,Ireland;53.33ºN,9.90ºW) focused on aerosolcloud interactions at the north eastern Atlantic Ocean by coupling ground-based in-situ and remote sensing 110 observations with airborne and satellite observations. This section summarizes the measurements used for this study and the model used to simulate the observations.

Ground-based measurements
At the Mace Head research site, aerosol instruments are located in the laboratory at about 100 m from the coastline.
They are connected to the laminar flow community air sampling system, which is constructed from a 100 mm diameter 115 stainless-steel pipe with the main inlet at 10 m above ground level, so that samples are not impacted by immediate coastal aerosol production mechanisms, such as wave breaking and biological activity Norton et al., 2006;C O'Dowd et al., 2014;C. D. O'Dowd et al., 2004;Rinaldi et al., 2009]. The performance of this inlet is described in Kleefeld et al.[2002]. Back trajectories during the period of the experiment show that the origin of air masses is predominantly from the North Atlantic; therefore, the air masses sampled at Mace Head generally represent 120 clean open ocean marine aerosol. Mace Head contains a variety of aerosol sampling instrumentation, spanning particle diameter range of 0.02 µm and 20 µm. Size spectral measurements are performed at a relative humidity < 40% using Naphion driers. Supermicron particle size distributions were measured using an Aerodynamic Particle Sizer (APS, TSI model 3321, 0.5 < Dp < 20 µm). The remaining submicron aerosol size range was retrieved from a scanning mobility particle sizer (SMPS, 0.02 < Dp <0.5 µm), comprised of a differential mobility analyzer (DMA, TSI model 125 3071), a condensation particle counter (TSI model 3010, Dp > 10 nm), and a Kr-85 aerosol neutralizer (TSI 3077).
Cloud condensation nuclei (CCN) measurements were performed with a miniature Continuous Flow Stream-wise Thermal Gradient Chamber, which measures the concentration of activated CCN over a range of supersaturations [Roberts and Nenes, 2005]. During this study, the supersaturation range spanned 0.2% to 0.82%. Aerosol hygroscopicity was calculated using -Köhler theory [Petters and Kreidenweis, 2007] with the sampled CCN 130 concentrations at a particular supersaturation and corresponding integrated aerosol number concentration at a critical diameter [Roberts et al., 2001]. Figure 1 shows time series of CCN spectra and aerosol number size distributions throughout the campaign. The ground-based remote sensing measurements utilized in this study are the MIRA36, 35.5 GHz Ka-band Doppler cloud radar [Goersdorf et al., 2015;Melchionna et al., 2008] to obtain vertical velocity distributions at cloud-base and the Jenoptik CHM15K ceilometer [Heese et al., 2010;Martucci et al., 2010] to obtain 135 cloud base height.

UAV vertical profiles
The UAV operations were conducted directly on the coast about 200 meters from the Mace Head research station.
UAVs were used to collect vertical profiles of standard meteorological variables, temperature (IST, Model P1K0.161.6W.Y.010), pressure (Bs rep Gmbh, Model 15PSI-A-HGRADE-SMINI), and relative humidity (IST, P14 140 Rapid-W), as well as aerosol size distributions with an optical particle counter (OPC, Met One Model 212-2), cloud droplet extinction [Harrison and Nicoll, 2014], updraft velocity at cloud base with a 5-hole probe. A list of the various Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2017-201, 2017 Manuscript under review for journal Atmos. Chem. Phys. Discussion started: 21 March 2017 c Author(s) 2017. CC-BY 3.0 License. Table 1. Measurement errors for the relative humidity and temperature sensors are ± 5% and ± 0.5 ºC respectively. As RH sensors are not accurate at high RH ( > 90%), the measured values have been scaled such that RH measurements are 100% in a cloud. At altitudes where the UAV is 145 known to be in-cloud (based on in-situ cloud extinction measurements) the air mass is considered saturated (RH ~ 100%). The temperature and relative humidity sensors are protected from solar radiative heating by a thin-walled aluminum shroud positioned outside of the surface layer of the UAV. A helical cone, mounted in front of the sensors, ejects droplets to protect the sensors. The temperature measurements for both cases in which cloud-top entrainment is explored (see section 3.2) are verified to remain in stratocumulus clouds throughout the ascents and descents, and 150 are not affected by evaporative cooling. The temperature and relative humidity measurements were used to initialize the ACPM below cloud. The UAVs were flown individually in separate missions up to 1.5 hours and each UAV was instrumented to perform a specific science mission (referred to here as aerosol, cloud, 3D winds).

UAV flights and their instrumentation is given in
The OPC measured aerosol number size distributions in eight size bins between 0.3 and 10 µm diameter. A erosols 155 were sampled via a quasi-isokinetic shrouded inlet mounted on the nose of the UAV. Aerosols samples were heated upon entering the UAV (ΔT > 5 K due to internal heating by the electronics), reducing the relative humidity of the sampled air to less than 60% and decreased with height ( < 50% above 150 m) before aerosol size was measured.

160
In-cloud extinction was measured in-situ using a disposable optical cloud droplet sensor developed at the University of Reading [Harrison and Nicoll, 2014]. The sensor operates by a backscatter principle using modulated LED light which is backscattered into a central photodiode. Comparison of the sensor with a DMT Cloud Droplet Probe demonstrate good agreement for cloud droplet diameters >5µm [Nicoll et al., 2016].

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Finally, a 5-hole probe for measuring 3-dimentional wind vectors was mounted on a third UAV. The 3D wind vectors are determined by subtracting the UAV motion given by an inertial measurement unit (IMU) from the total measured flow obtained by differential pressures in the 5-hole probe [Calmer et al., 2017;Lenschow and Spyers-Duran, 1989;Wildmann et al., 2014]. UAV 5-hole probe measurements were collected along 6 km long straight and level legs at

Satellite measurements
Research flights with the UAV were conducted in conjunction with satellite overpasses to compare retrieved CDNC and maximum supersaturation (Smax) with ACPM simulated values using the Suomi NASA Polar-orbiting Partnership 6 satellite. The satellite estimations of CDNC and Smax are based on methods described by Rosenfeld et al.[2014;2012; 180 2016], which are briefly summarized in the following paragraph. The case selection criteria for satellite observations required the overpass to occur at a zenith angle between 0º and 45º to the east of the ground track, to have convective development that spans at least 6 K of cloud temperature from base to top (~1 km thick), and to not precipitate significantly. In-situ observations were often of thin clouds (< 1 km thick), and the satellite observations consist primarily of the more developed clouds in the same system.

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To obtain CDNC, cloud droplet effective radius profiles were extracted from the Suomi NASA Polar-orbiting Partnership satellite. Figure 4 shows an image from the Suomi visible infrared imaging radiometer suite on 21 August overlapped on a map of western Ireland. The vertical profile in figure 4 shows satellite retrieved and ACPM simulated effective radius. To estimate the CDNC, the satellite effective radius (Figure 4) is first converted to mean volume 190 radius (rv) using a linear relationship [Freud et al., 2011]. Next, it is assumed that any mixing that occurred between the cloud and cloud-free air was inhomogeneous; this implies that the actual rv is equal to the adiabatic rv. CDNC can be calculated by dividing the adiabatic water content in the cloud by rv [Beals et al., 2015;Rosenfeld et al., 2012].
The cloud base height and pressure was used to calculate the adiabatic water content. Cloud base height and pressure were obtained from the height of the NCEP reanalysis of the cloud base temperature, as retrieved from satellite. The 195 cloud base height was validated against the ceilometer. Freud et al. [2011] showed that the inhomogeneous assumption resulted in an average over-estimate in CDNC of 30%, so the CDNC is reduced by 30% to account for the bias with the assumption. Finally, to calculate Smax the cloud base updraft velocity, from the UAV or cloud radar, is needed and when paired with the CDNC, it can be used to empirically calculate Smax [Pinsky et al., 2012;Rosenfeld et al., 2012].
The methodology was validated by Rosenfeld et al. [2016].

Aerosol-cloud parcel model simulations
A detailed description of the aerosol-cloud parcel model (ACPM) is presented in Russell and Seinfeld [1998] and Russell et al. [1999]. The ACPM is based on a fixed-sectional approach to represent the (dry) particle size domain, with internally mixed chemical components and externally mixed types of particles. Aerosols are generally internally mixed at Mace Head owing to lack of aerosol sources. The model employs a dual moment (number and mass) 205 algorithm to calculate particle growth from one size section to the next for non-evaporating compounds (namely, all components other than water) using an accommodation coefficient of 1.0 [Raatikainen et al., 2013]. The dual moment method is based on Tzivion et al. [1987] to allow accurate accounting of both aerosol number and mass, and incorporates independent calculations of the change in particle number and mass for all processes other than growth.
The model includes a dynamic scheme for activation of particles to cloud droplets. Liquid water is treated in a moving 210 section representation, similar to the approach of Jacobson et al. [1994], to account for evaporation and condensation of water in conditions of varying humidity. In sub-saturated conditions, aerosol particles below the cloud base are considered to be in local equilibrium with water vapor pressure (i.e., relatively humidity < 100%).
Coagulation, scavenging, and deposition of the aerosol were included in the model but their effects are negligible 215 given the relatively short simulations used here (<2 h) and low marine total aerosol particle concentrations (<500 cm 3 ; Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2017-201, 2017 Manuscript under review for journal Atmos. Chem. Phys. Discussion started: 21 March 2017 c Author(s) 2017. CC-BY 3.0 License. Dp > 10 nm). Aerosol hygroscopicity as a function of size (and supersaturation) is determined from CCN spectra and aerosol size distributions as mentioned in Section 3.1, and is used as model input. The ACPM is also constrained by measured temperature profiles, cloud base height, and updraft velocity distribution (Figure 3). The in-cloud lapse rate is assumed to be adiabatic, unless specified otherwise, so simulation results represent an upper bound on CDNC and 220 liquid water content that is unaffected by entrainment. To account for release of latent heat in the cloud, the vertical temperature gradient is calculated as = ( + ) ⁄ , where dT is change in temperature for the vertical displacement of an air parcel, g is acceleration due to gravity, w is updraft velocity at cloud base, dt is time step, L is latent heat of water condensation, ql is liquid water mixing ratio, and cp is specific heat of water [Bahadur et al., 2012].
A weighted ensemble of positive updraft velocities measured with the cloud radar and UAV 5-hole probe were applied 225 to the ACPM [Sanchez et al. 2016].
The simulated cloud droplet size distribution is used to calculate the shortwave cloud extinction. Cloud extinction is proportional to the total droplet surface area [Hansen and Travis, 1974;Stephens, 1978] and is calculated from, where r is the radius of the cloud droplet, ( ) is the number of cloud droplets with a radius of r, and ( ) is the Mie efficiency factor, which asymptotically approaches 2 for water droplets at large sizes (r > 2 um).
Finally, the radiative flux (RF) is calculated as RF = αQ, where Q is the daily-average insolation at Mace Head and α is the cloud albedo. α is estimated using the following equation [Bohren and Battan, 1980;Geresdi et al., 2006] where is the cloud optical depth defined as and H is the cloud height or thickness and g, the asymmetric scattering parameter, is approximated as 0.85 based on Mie scattering calculations for supermicron cloud drops. RF is calculated for both, simulated cloud extinction and 240 measured UAV extinction. 8 occasionally influenced by anthropogenic sources, however, the cases shown consist of aerosol of marine origin with concentrations under 1000 cm -3 (Figure 1).

Ground-based measurement closure
The columns in Table 2 represent the different cases for both clouds that were (a) coupled with and (b) decoupled 255 from the surface BL ("C" and "D" in case acronym, respectively). The first row in Table 2 includes the state of atmospheric mixing, the date, the type of cloud present, and the acronym used for each case. The top portion of Table   2 consists of in-situ airborne measurements, the bottom portion presents ACPM simulation results and their relation to in-situ cloud extinction and satellite-retrieved observations. The ground-based in-situ measurements in Table 2 include the Hoppel minimum diameter 2 (Dmin), as well as the aerosol concentration of aerosol with diameters greater 260 than the Hoppel Dmin and the inferred in-cloud critical supersaturation (Sc) [Hoppel 1979]. The aerosol particles with diameters greater than the Hoppel Dmin have undergone cloud processing and are used here to estimate the CDNC. For each of the case study days, Figure 5 demonstrates the aerosol size distribution measurements, from the SMPS and APS, that are used to find the Hoppel Dmin, Hoppel CDNC and used to initialize the ACPM. Figure 6 shows  The amount of sampling within individual clouds varied from case to case, but the UAVs were generally able to make 290 multiple measurements of the same cloud during each vertical profile. C11Sc was unique in that it involved stratocumulus clouds with a large horizontal extent, allowing the UAV to remain entirely in-cloud during the upward and downward vertical profiles around a fixed waypoint. Figure 8f shows how the difference between simulated and observed extinction (ext) is calculated throughout the cloud based on a discrete sampling of in-cloud measurements.
It is not certain that the UAV measured the cloud core for cumulus cases so ext is an upper limit (Table 2).

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All ACPM simulation results, including those in Table 2, use the cloud radar updraft velocity as input and not the 5hole probe updraft velocity because 5-hole probe updraft velocities are not available for all cases. Nonetheless, the differences in ACPM simulated radiative flux between using the 5-hole probe and cloud radar updraft velocities ( Figure 3) is less than 3 W m -2 for the four cases that had both measurements.

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The integrated effect of ext leads to a difference in cloud observed and simulated radiative flux (RF) for both clouds that were coupled with and decoupled from the surface boundary layer (Table 2). Figure 9, presents a vertical profile of NOPC and equivalent potential temperature. OPC measurements within a thin cloud layer at ~2000 m are removed.
NOPC and equivalent potential temperature (θe) clearly illustrate this decoupling as shown in an example vertical profile 305 ( Figure 9) at 900 and 2200 m.asl, with the latter representing the inversion between the boundary layer top and free troposphere. NOPC decreases from an average of 31 cm -3 to 19 cm -3 at the same altitude as the weak inversion (700-1000 m). In this study, decoupled boundary layers are often observed and aerosol number concentrations (Dp > 0.3 µm) in the decoupled layer were 44% ±14% of those measured at the ground. While NOPC are not directly representative of CCN concentrations, a reduction in aerosol number with height (and potential differences in 310 hygroscopicity) will nonetheless affect aerosol-cloud closures, and ultimately, the cloud radiative properties.
Similarly, Norton et al. [2006] showed results from the European Centre for Medium-Range Weather Forecasts (ECMWF) model re-analysis in which surface winds at Mace Head are often decoupled from synoptic flow and, therefore, the air masses in each layer have different origins and most likely different aerosol properties.
Consequently, the CCN number concentrations measured at the surface do not represent those in the higher decoupled 315 cloud layer, which ultimately dictates cloud radiative flux in the region and RF in Table 2. While aerosol profiles were not collected by UAVs for the decoupled cases presented in concentrations show only slight differences RF of 3 Wm -2 and decreases in CDNC of 10%. The decrease in aerosol concentration resulted in increased supersaturation due to the low water uptake from fewer activating droplets. The increased supersaturation caused smaller aerosols to activate [Raatikainen et al., 2013] and therefore, little change in CDNC. The D06Cu was not influenced as much by low water uptake because the CDNC was much higher at 171 cm -325 3 compared to 86 cm -3 for D05Sc. The D06Cu the CDNC decreased by 42% and RF decreased by 18 Wm -2 . Both decoupled cases still have a RF greater than the coupled cases.

Satellite measurements closure
The satellite and simulated CDNC and Smax measurements are presented in the bottom of Table 2. The method for satellite retrieval of cloud properties could not be used for cases when cloud layers were too thinwhich, unfortunately 330 was the situation during the flights with the decoupled cloud layers. Nonetheless, Figure 4 shows the satellite image used to identify the clouds to calculate CDNC for C11Sc. Satellite retrieved cloud-base height and temperature are verified by ground-based ceilometer and temperature measurements. Figure 6 shows the top-down closures demonstrate that satellite-estimated CDNC and simulated CDNC are within a ± 30% expected concentrations, which is limited by the retrieval of effective radius [Rosenfeld et al., 2016]. The stratocumulus deck at the top of a well-335 mixed boundary layer (C11Sc) shows evidence of cloud-top inhomogeneous entrainment (see section 3.2). Freud et al. [2011] found that the inhomogeneous mixing assumption used to derive CDNC from satellite measurements resulted in an average over-estimate in CDNC of 30% (considering an adiabatic cloud droplet profile). Consequently, satellite-retrieved CDNC is reduced by 30% to account for the inhomogeneous entrainment assumption, which does not necessarily reflect the actual magnitude of entrainment in the clouds. For example, in the C11Sc case, in-situ 340 observations do indeed show cloud-top inhomogeneous entrainment; consequently, the usual 30% reduction in CDNC does not need to be applied (Table 2). Both stratocumulus cases (C11Sc, D05Sc) with cloud-top entrainment (Table   2) are similar to a case studied by Burnet and Brenguier [2007], in which cloud-top entrainment resulted in inhomogeneous mixing. In the following section, C11Sc and D05Sc are reanalyzed to include the effect of cloud-top entrainment on simulated cloud properties using the inhomogeneous mixing assumption.

Entrainment
Based on the ground-based and UAV measurements, ACPM simulations over-estimate cloud radiative flux significantly for three cases (C11Sc, D05Sc, D06Cu). Section 3.1.2 identified that clouds in decoupled layers (D05Sc, D06Cu) have smaller radiative effects than predicted based on ground-based observations as aerosol (and CCN) number concentrations in the decoupled layer are often smaller than in the surface layer. In this section, cloud-top 350 entrainment is also shown to influence the radiative properties of two sub-adiabatic stratocumulus clouds, C11Sc and D05Sc.
The UAV observations show that both C11Sc and D05Sc have sub-adiabatic lapse rate measurements, compared to simulated moist-adiabatic lapse rates within the cloud ( Table 2). The difference between the observed and simulated 355 lapse rates therefore suggests a source of heating in the cloud. The sub-adiabatic lapse rate is attributed to cloud-top entrainment by downward mixing of warmer air at cloud-top (e.g., Figure 7a).  [Burnet and Brenguier, 2007;Neggers et al., 2002;Paluch, 1979]. Paluch [1979] first observed a linear relationship of conservative properties (total water content, qt and liquid water potential temperature, θl) between cumulus cloud cores and cloud edge, to show the cloud-free source of entrained air. Paluch [1979], Burnet and Brenguier [2007], Roberts et al. [2008], Lehmann et al. [2009] observed decreases in CDNC and liquid water content in cumulus clouds as a function of distance from the cloud cores that 365 indicate inhomogeneous mixing at the cloud edge. Burnet and Brenguier [2007] also show that qt is linearly proportional to liquid water potential temperature specifically for a stratocumulus cloud with cloud-top entrainment and inhomogeneous mixing. Direct observations of CDNC and liquid water content were not measured at Mace Head, so direct comparisons of CDNC and qt with Paluch [1979] and Burnet and Brenguier [2007] cannot be investigated here. However, UAV measurements of cloud extinction (Eq. 1), which are related to CDNC ( = ∫ ( ) , is liquid water density), were measured and are found to be systematically lower than the adiabatic simulated cloud extinction (Figure 8).
To apply the cloud-top mixing, a fraction of air at cloud-base and a fraction of air above cloud-top are mixed, conserving qt and θe. The fraction of air from cloud-base and cloud-top is determined with the measured equivalent 375 potential temperature, where , ( ) is the equivalent potential temperature in cloud as a function of height, , is the equivalent potential temperature of the cloud-top entrained air, , is the equivalent potential temperature of air at cloud base, and ( ) is the fraction of cloud-top entrained air as a function of height (referred to as the entrainment fraction). ,  Figure 10a and b present the relationships between two conservative variables measured by the UAV (water vapor content, qv, and θe) for C11Sc and D05Sc. The qv is derived from relative humidity measurements and is equivalent to the qt for sub-saturated, cloud-free air (i.e., < 100% RH). 390 Figure 11 shows the relative humidity and profiles used in Figure 10. cloud-top (e.g. cloud lifetime >> mixing time) . The observed in-cloud qv in Figure 10a and b is less than the conservative variable qt, however, the figure also includes qt based on simulated adiabatic and cloud-top entrainment 395 conditions. Eq. (4) is used to derive the simulated cloud-top entrainment conditions (Figure 10a and b), where the fraction entrained is used to calculate qt and shows a linear relationship between qt and . Measurements above cloudtop (RH < 95%) with qv > 5.1 g kg -1 and qv > 6.5 g kg -1 are used to represent the properties of the entrained air for C11Sc and D05Sc, respectively ( Figure 10). 400 Figure 12 shows the sensitivity of the simulated cloud extinction profile, for the 11 August case, based on measurement uncertainties related to the entrained qv and θ. The key variable for identifying the entrained fraction (Eq. 5), , , is a function of qv and θ, so a decrease in either parameter results in a proportional decrease in , . Eq. (5) shows that entrainment fraction becomes more sensitive to the uncertainty related to the measurement of as the difference between , and , approaches zero.
405 Table 3 shows ext, RF, and CDNC for two cases with cloud-top entrainment (C11Sc and D05Sc) using two methods of accounting for the cloud top entrainment. One method applyies the entrainment fraction calculated in Eq. (5) and the other an entrainment parameterization, presented by Sanchez et al. [2016]. The entrainment parameterization constrains the ACPM simulation to use the observed in-cloud lapse rate instead of assuming an adiabatic lapse rate.

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This is labeled the 'measured lapse rate' entrainment method in Table 3. In the sub-adiabatic cloud cases (C11Sc and D05Sc), the measured in-cloud lapse rate is lower than the adiabatic lapse rate, which leads to the condensation of less water vapor and subsequent activation of fewer droplets in the ACPM simulation. Similarly, the dryer and warmer entrained air (from above cloud-top) leads to evaporation of liquid water in the cloud. Previous observations of stratocumulus cloud-top mixing suggest the entrainment is inhomogeneous [Beals et al., 2015;Burnet and Brenguier, 415 2007], which implies that time scales of evaporation are much less than the time scales of mixing, such that a fraction of the droplets are evaporated completely and the remaining droplets are unaffected by the entrainment. The net decrease in CDNC subsequently results in less extinction of solar radiation compared to the purely adiabatic simulation.

420
The inclusion of inhomogeneous cloud-top entrainment improved the ACPM accuracy for both C11Sc and D05Sc using the measured lapse-rate and entrainment fraction methods ( Figure 8, Table 3). After accounting for inhomogeneous entrainment, RF decreased from 88 Wm -2 to 47 Wm -2 and 45 Wm -2 to 14 Wm -2 for D05Sc and D11Sc, respectively, using the entrainment fraction method. D05Sc simulations still yields significant RF even after accounting for inhomogeneous entrainment, likely because the cloud is in a decoupled BL, as noted in Section 3.1.2 425 to exhibit lower aerosol concentrations than those measured at the surface. The CDNC presented in Table 3 represents the CDNC at cloud base and did not change after applying the entrainment fraction method, however, the CDNC decreases with height for the entrainment fraction method rather than remain constant with height. Finally, the measured lapse rate entrainment method [Sanchez et al., 2016] does improve ACPM accuracy between in-situ and satellite-retrieved cloud optical properties relative to the adiabatic simulations, but has greater ext throughout the 430 Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2017-201, 2017 Manuscript under review for journal Atmos. Chem. Phys. Wm -2 to 14 Wm -2 after accounting for cloud top entrainment with the entrainment fraction.
Based on airborne observations with UAVs, cloud-top entrainment is only observed on 2 out of the 13 flight days and 470 decoupling of the boundary layer occurs on 4 of the 13 flight days. These cases illustrate the need for in-situ observations to quantify entrainment mixing and cloud base CCN concentrations particularly when the mixing state of the atmosphere is not known. Even greater discrepancies between the surface and decoupled layer CCN concentrations will occur in the presence marine biogenic sources such as tidal regions and local anthropogenic [Colin D. O'Dowd, 2002]. Using ground-based observations to model clouds in decoupled boundary layers and not including 475 cloud top entrainment are shown to cause significant differences between observations and simulation radiative forcing and therefore, should be included in large scale modeling studies to accurately predict future climate forcing.
UAV measurements were coordinated with 13 days of satellite overpasses and cloud microphysical properties were retrieved for four of the cases. When accounting for entrainment, the differences between simulated and satellite-480 retrieved CDNC are within the expected 30% accuracy of the satellite retrievals [Rosenfeld et al., 2016]. However, in-situ measurements are necessary to refine satellite retrievals to allow cloud properties to be studied on larger spatial scales.