Improving aerosol activation in the double-moment Uniﬁed Model with CLARIFY measurements

, Abstract. Representing the number and mass of cloud and aerosol particles independently in a climate, weather prediction or air quality model is important in order to simulate aerosol direct and indirect effects on radiation balance. Here we introduce the ﬁrst conﬁguration of the UK Met Ofﬁce Uniﬁed Model in which both cloud and aerosol particles have ‘double-moment’ representations with prognostic number and mass. The GLOMAP aerosol microphysics scheme, already used in the HadGEM3 climate conﬁguration, is coupled to the CASIM cloud microphysics scheme. We demonstrate the performance of the new con- 5 ﬁguration in cloud-resolving simulations of a case study deﬁned from the CLARIFY aircraft campaign in 2017 near Ascension Island in the tropical south Atlantic. We improve the physical basis of the activation scheme by representing the effect of existing cloud droplets on the activation of new aerosol, and we also attempt to account for the effect of unresolved vertical velocities. The ﬁrst of these improvements should be applicable to the representation of aerosol activation in other microphysics schemes. While these changes lead only to a modest improvement in model performance, they reinforce our conﬁdence in the 10 ability of the model to simulate aerosol-cloud microphysical interactions. Capturing these interactions accurately is critical to simulating aerosol effects on climate. on these clouds is a priority for climate modelling efforts worldwide. In this paper, we describe cloud-resolving model 15 simulations in a 2 ◦ by 2 ◦ region of the tropical south Atlantic Ocean near Ascension Island. The simulations are performed with the UK Met Ofﬁce Uniﬁed Model (UM), with double-moment aerosol microphysics driving double-moment bulk cloud microphysics at 500 m horizontal resolution. As well as testing the aerosol and chemistry component of the model at a higher resolution than has been attempted before, we study and suggest improvements to the performance of the aerosol activation scheme. We evaluate the second day of a two-day long simulation against CLARIFY (CLouds and Aerosol Radiative Impacts 20 and Forcing) aircraft measurements on 19 August 2017.

A series of recent field campaigns  have focused on the tropical south-east Atlantic ocean, which hosts one of the planet's largest stratocumulus decks, and is the destination for much of the biomass burning aerosol that originates from central and southern Africa. The prevailing winds, which are south-easterly in the boundary layer and easterly in the free troposphere, advect smoke over the ocean where slow subsidence causes the smoke to mix with the clouds. The smoke can have large direct, semi-direct and indirect radiative effects on the regional climate (Costantino and Bréon, 2013;Lu et al., 2018;5 Gordon et al., 2018). Here we focus on the indirect effect of the aerosols.
In a previous study, Gordon et al. (2018) evaluated aerosol transport and microphysics in global and convection-permitting simulations of the south-east Atlantic. In this paper, we start from an updated version of the same atmospheric model, and increase the resolution further, to the cloud-resolving scale. We also increase the sophistication of the cloud microphysics scheme from single-moment to double-moment, in order to study aerosol-cloud interactions in more detail. The resulting 10 model is the first configuration of the Unified Model with fully double-moment aerosol and cloud microphysics. Doublemoment microphysics, including prognostic cloud droplet number concentration, is important to enable good representations of processes such as aerosol activation and droplet settling at high spatial and temporal resolution. The coupling to the doublemoment interactive aerosol microphysics scheme enables aerosol-induced variability in the droplet number concentration.
Compared to single-moment cloud microphysics schemes, double-moment schemes have been shown previously to im- 15 prove the representation of stratiform rain in NWP simulations (Morrison et al., 2009) and to reduce a range of biases in high-resolution climate models (Seiki et al., 2015). The CASIM (Cloud AeroSol Interacting Microphysics) double-moment microphysics scheme we use here is that previously published by Shipway and Hill (2012); Grosvenor et al. (2017); Miltenberger et al. (2018); Stevens et al. (2018) and Furtado et al. (2018). In the last of these manuscripts, Furtado et al. (2018) evaluate CASIM for deep convective clouds and compare it to a reduced, single-moment version of the same scheme, and 20 to the different single-moment cloud microphysics scheme (Wilson and Ballard, 1999) used in the operational version of the model. For the case they study, the CASIM double-moment microphysics initially performed better than the single-moment schemes, although these gave comparable performance to the double-moment scheme when tuned.
In climate simulations with resolutions coarser than around 0.5 degrees, updraft velocities in shallow clouds are almost entirely unresolved and convection is parameterized. The activation of aerosols to form cloud droplets requires the supersaturation 25 of water vapor relative to aerosols and hydrometeors to be diagnosed or parameterized. Typically, supersaturation is calculated by imposing an updraft speed (or a distribution of updraft speeds) derived from diagnostics of the sub-grid turbulence rather than the grid-box mean updraft speed, which is close to zero. A single cloud droplet number concentration per grid box is thus produced and used in the prediction of rain rates (via an autoconversion parameterization) and cloud albedo.
simulations (Grosvenor et al., 2017;Miltenberger et al., 2018;Furtado et al., 2018) have also used grid-box mean updraft speeds to activate aerosols at horizontal resolutions ranging from 250 m to 1 km, and a similar approach has been taken in Regional Atmospheric Modeling System (RAMS) and some Weather Research Forecasting (WRF) simulations (Saleeby and Cotton, 2004;Thompson, 2016). The scale invariance of activation schemes has been tested before down to horizontal resolutions of 1 km (Possner et al., 2016). However, these resolutions are still much coarser than typical LES resolution, and therefore the 5 full variability in updraft speeds will not be resolved. By comparing cloud-resolving and LES simulations, Malavelle et al. (2014) developed a bootstrapping parameterization which enables the estimation of the fraction of the variance in updraft that is resolved.
In existing clouds, activation of new droplets will often be negligible, but not always, for example if the updraft strengthens towards the top of the cloud. In a detailed model, Pinsky and Khain (2002) suggested that in-cloud activation leads to a 10 bimodal cloud droplet size spectrum, and is an important factor in accelerating rain formation by broadening the droplet spectrum (Segal et al., 2003;Heymsfield et al., 2009). In a deep cloud case study, the large eddy simulations of Fridlind et al. (2004) suggested that aerosol concentrations in the boundary layer were too low to explain observed droplet number concentrations, and therefore aerosols must be entrained from the mid-and upper troposphere and activated inside the clouds.
More recent detailed modeling studies have continued to investigate secondary activation Khain et al. (2012); Fan et al. (2018). 15 To capture fully effects of in-cloud activation on the droplet size distribution, a detailed microphysics scheme is needed, such as a size-bin-resolving scheme or a super-droplet model, and to accurately simulate the full dynamical response of deep clouds to aerosols, very high spatial resolution may be needed, which in turn requires relatively short timesteps. If the model timestep is shorter than the 'relaxation timescale', supersaturation production is balanced by condensation onto existing droplets, a bias will occur unless supersaturation is represented as a prognostic variable (Khain and Lynn, 2009;Fan et al., 2012;Lebo et al., In this study, we follow the suggestion by Korolev (1995); Ghan et al. (2011), and others to improve on this procedure by accounting for existing cloud droplets when new droplets are activated, assuming that there exists an equilibrium between supersaturation production by updraft and condensational growth of existing droplets. This assumption can be seen as a natural extension of the saturation adjustment assumption, and should apply in the same conditions. We emphasise that we seek here to improve the accuracy of our existing model, but our improvements will not enable it to compete with detailed studies of 5 aerosol-cloud interactions that employ spectral bin microphysics or prognostic supersaturation.
We attempt to improve the activation scheme further by accounting for unresolved sub-grid-scale updraft velocities, as a first step towards implementing the parameterization of Malavelle et al. (2014). We show, unsurprisingly, that accounting for existing cloud droplets in the activation scheme reduces the cloud droplet number while accounting for sub-grid-scale updrafts increases it. This may explain why previous studies with CASIM (Grosvenor et al., 2017) have successfully produced realistic 10 droplet concentrations with realistic CCN, despite underestimating the updraft and ignoring existing droplets. We examine the implications of our improvements for the cloud droplet spatial distribution and size distribution and for rain formation.
We evaluate our simulations against CLARIFY aircraft measurements in 2017 to confirm they are realistic and to identify directions for future developments.
2 Case study and aircraft measurements 15 The CLARIFY aircraft campaign took place from 16 August to 7 September 2017. The BAE-146 aircraft of the Facility for Airborne Atmospheric Measurements (FAAM) was based at Ascension Island during this period. Extensive sampling of biomass burning aerosol interacting with clouds was achieved during 24 flights usually of around 3.5-4 hours' duration. The aircraft flew in all directions around Ascension Island, according to where aerosol and cloud transitions could be identified or in order to pass under satellite tracks. 20 The research aircraft was fitted with a comprehensive suite of thermodynamic, radiometric, cloud physics and aerosol instrumentation for the CLARIFY field campaign. Ambient air temperature was measured using a non-deiced Rosemount/Goodrich type-102 total air temperature sensor. Atmospheric water vapour was measured using a WVSS-II near-infrared tunable diode laser absorption spectrometer fed from a standard flush mounted inlet (Vance et al., 2015). The temperature and humidity measurements are used to calculate relative humidity in cloud-free air. The temperature measurement in cloud was subject 25 to significant wetting effects that led to a cold bias, as illustrated by Heymsfield et al. (1979). The derived in-cloud relative humidity is therefore set to 100% in this work. Zonal, meridional and vertical wind components were derived from the five-port turbulence probe located on the aircraft radome (Petersen and Renfrew, 2009;Barrett et al., 2019). On the transit at 5180 m altitude from Ascension Island to the cloud, the mean vertical velocity was −0.010 ms −1 . The small magnitude of this mean velocity compared to the in-cloud vertical velocities we discuss later suggests the probe is sufficiently well calibrated for our 30 analysis so we do not subtract any baseline offset from the observed updrafts in the evaluation we present in Section 5.
The size distribution of aerosol particles was measured using a Passive Cavity Aerosol Spectrometer Probe (PCASP, Droplet Measurement Technologies) for nominal diameters between about 0.1 and 3 µm. We applied a complex refractive index of r i = 1.54 − 0.027i, appropriate for biomass burning aerosol during the CLARIFY time period (Peers et al., 2019) and recomputed the bin boundaries for the PCASP instrument. This resulted in changes to the locations of bin centres, compared to the nominal values from the manufacturer, of usually around 5% but sometimes up to 20% in the diameter range below 1 µm. For smaller particles with diameters between 0.03 and 0.3 microns, we also used a Scanning Mobility Particle Sizer (SMPS). The total number concentration of aerosols with diameter larger than about 2.5 nm were measured with a TSI 3786 Condensation 5 Particle Counter (CPC). Aerosol data were only used when in cloud-and precipitation-free air. We determined this using the standard deviation of raw power on the Nevzorov total water content probe (Korolev et al., 2013), where a power greater than 3.0 mW (∼ 1.5 × 10 −4 gm −3 ) indicates cloud conditions, following Barrett et al. (2019). An additional safety window of 5 s (∼ 500 m) either side of positively identified cloud was applied to account for diffuse cloud edges and imperfect temporal and spatial synchronisation between probes and data recording systems. The cloud droplet size distribution (between 2 and 10 52 µm diameter) was measured with a Cloud Droplet Probe (CDP) that was calibrated with a ten point bead calibration (Rosenberg et al., 2012). Precipitation-sized particles were measured using a 2D-Stereo (2DS) probe (10 to 1280 µm diameter) and a Cloud Imaging Probe (CIP-100) probe (100 µm to 6.4 mm diameter). Data from the CDP, 2DS and CIP-100 are combined to produce a composite PSD at a 1 Hz sampling frequency following the method of Abel and Boutle (2012). Elsewhere in this paper, the cloud drop number concentration (CDNC) and liquid water content (LWC) are calculated using the CDP data only. 15 5 https://doi.org/10.5194/acp-2020-68 Preprint. Discussion started: 21 February 2020 c Author(s) 2020. CC BY 4.0 License.
For cloud measurements, in-cloud conditions were determined using a liquid water content threshold of 0.01 g kg −1 calculated by integrating the cloud drop number size distribution from the CDP.
The most comprehensive sampling of a cloud feature took place on 19 August. The aircraft flew south of the island to sample a large precipitating cloud structure around 1.5 • in size. Biomass burning aerosol was detected both within and just above the boundary layer. Cloud top height peaked at around 2.5 km altitude. The cloud deck was sampled as shown in Figure 1, in a 5 series of five straight-and-level aircraft trajectories along a line of strong radar echoes seen on the aircraft weather radar.
Taken together, the aircraft observations described later in the paper suggest that the boundary layer is decoupled or cumuluslike, with a stratocumulus cap above large precipitating cumulus clouds beneath. The observed stratocumulus clouds could also be detrained remnants of cumulus. In the simulations, the cumulus sometimes seems to extend up to the top of the boundary layer. However, the size of the cloud feature is larger than average for stratocumulus-to-cumulus transition clouds, and the 10 deepest cumulus appeared to be organized linearly. Based on this and on geostationary satellite imagery (not shown) we would describe it as the beginnings of a fish rather than sugar, flowers or gravel (Stevens et al., 2019).
In order to validate our simulations, we are also able to draw on surface measurements from the ARM site at Ascension Island, and satellite observations of cloud droplet concentration and liquid water path. To obtain these, the same procedure as used by Gordon et al. (2018) is followed. 15

Model setup
We use the RA1 (Bush et al., 2019) configuration of the UK Unified Model (UM) with some settings borrowed from the GA7.1 configuration, which is the global climate configuration submitted to CMIP6. Following Gordon et al. (2018), who built on idealized simulations by Planche et al. (2017), we use the United Kingdom Chemistry and Aerosols (UKCA) module from the climate model, which has prognostic two-moment aerosol microphysics (GLOMAP-mode, Mann et al. (2010)). GLOMAP 20 stands for Global Model of Aerosol Processes. As explained in the Introduction, we also use the CASIM two-moment bulk cloud microphysics module (Shipway and Hill, 2012).
In order to simulate the region of interest at 500 m resolution, we start with a global model setup similar to that used by Gordon et al. (2018) and identical to that used in the intercomparison study of Shinozuka et al. (2019). The horizontal resolution is 0.8 • × 0.55 • (N216) and there are 70 vertical levels from the surface to 85 km altitude. The horizontal winds are 25 nudged to ERA-interim above the boundary layer. Anthropogenic aerosol emissions from the CMIP5 database are combined with biomass burning emissions from the Fire Energetics and Emissions Research (FEER) inventory for August 2017. While the configuration used by Gordon et al. (2018) was based on GA6.1 and UM version 10.3 we now use GA7.1 (Walters et al., 2019) and UM version 11.2. The offline-oxidants configuration of United Kingdom Chemistry and Aerosols (UKCA) chemistry is used and GLOMAP dust is switched off. The global model is initialized from the model for August 2016 used by Gordon  The 500 m-resolution simulation has 450 grid-boxes by 450 grid-boxes in latitude and longitude, and the same 140 vertical levels as the 7 km-resolution simulation. It is centred on −11 • latitude, −14.5 • longitude. A more recent UM version, 11.3 is used, as this has the latest configuration of the CASIM microphysics. Other differences compared to version 10.8 are expected to have only minor effects. As in the 7 km and global models, the offline-oxidants configuration of UKCA chemistry is used.

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This simulation is initialized from the global model on 18 August at 0000UTC. By 19 August, all of the air masses that advect into the domain from the boundaries will have been simulated by the 7 km-resolution model rather than the global model for at least two days, and therefore the resolved wet scavenging processes evident in Figure 2 and in the 4 km simulation of Gordon et al. (2018) will have affected the aerosol concentrations, and the higher resolution will have had time to affect the winds.
In the domain averages we present, we exclude the 20 grid-boxes nearest to the domain boundaries to remove the transition region between the 7 km and 500 m resolution simulations. The number 20 is arbitrary and chosen by eye, and corresponds 5 to around 30 minutes of advection time for a wind speed of 5 ms −1 : enough time to produce some more resolved turbulence but not enough time for full mixing of the boundary layer. We are able to run 500 m simulations driven by the 65 km global model without the intermediate-resolution nest, but then we would need to exclude more grid boxes at the boundaries of the innermost simulation to allow the high resolution structure to spin up.
The boundary layer scheme we use in the 500 m-resolution model is based on that of Lock et al. (2000), blended with the 10 Smagorinsky-type scheme from the Met Office Large Eddy Model (Brown, 1999) as described by Boutle et al. (2014). The scheme is expected to be dominated by the Lock et al. (2000) scheme rather than the Smagorinksy-type scheme at this spatial resolution, while their contributions would be approximately equal at 250 m resolution.
As the 500 m-resolution model configuration is different to that published by Gordon et al. (2018) (for example, most aerosol-related settings are upgraded to GA7.1 from GA6.1), many of the tunings used in our previous simulations are no 15 longer required. In the wet scavenging code, Gordon et al. (2018) changed a parameter designed to represent the fraction of the area of a grid box over which rain occurs from 30% to 100%. We reverse this change because while it is still more likely that entire 500 m grid-boxes are raining than entire global model grid boxes, we do not account for the evaporation of rain returning scavenged aerosols to the atmosphere. The 30% parameter can therefore be thought of as the fraction of rain which does not evaporate. We have not verified the accuracy of this assumption, which will clearly depend on the regime studied and should 20 be revisited in future. We no longer tune the dry deposition velocity. The biomass burning emissions diameter (specifically, the number geometric mean diameter) is still 120 nm instead of the default for UKCA of 150 nm. This diameter is shown by Shinozuka et al. (2019) to give aerosol dry diameters in reasonable agreement (within 40%) with measurements from the parallel NASA ORACLES campaign (ObseRvations of Aerosols above CLouds and their intEractionS), although the diameter is still slightly overestimated compared to ORACLES. For example, in the lower free troposphere most affected by smoke, the 25 simulated dry diameters are biased 37% high. The mass of organic carbon in the same location, which dominates the overall aerosol mass, is biased high by 8%.
The model is fully coupled to the standard radiative transfer scheme in the UM, via the RADAER module for the aerosols (Bellouin et al., 2013). Direct and semi-direct effects of the absorbing aerosols on the cloud are therefore included in the simulations but will be fairly small in this period due to the relatively low aerosol concentrations, and are not the focus of this work. 30

Activation, microphysics and coupling
In the global and 7 km models, the UKCA diagnostic activation scheme, based on the parameterization of Abdul-Razzak and Ghan (2000), is used to calculate the droplet number concentration (West et al., 2014). On each timestep, the scheme calculates 8 https://doi.org/10.5194/acp-2020-68 Preprint. Discussion started: 21 February 2020 c Author(s) 2020. CC BY 4.0 License. the droplet concentration at cloud base, and imposes it on grid boxes that are above cloud base and still in the same cloud. The droplet concentration does not depend on the concentration on previous timesteps. These diagnostic droplet concentrations are used to calculate autoconversion rates in the single-moment cloud microphysics scheme of Wilson and Ballard (1999). This activation scheme is referred to as the 'UKCA activation scheme' later in the paper.
In our 500 m-resolution simulations, aerosols activate in the CASIM code to form cloud droplets, also using the 'ARG' 5 parameterization of Abdul-Razzak and Ghan (2000). This parameterization is called once per timestep in grid-boxes when a non-zero mass of water is condensing from the vapor phase. The treatment is subsequently referred to as the 'CASIM activation scheme'. The updraft speed used in the ARG scheme is set equal to the grid-box mean updraft speed or 0.001 ms −1 , whichever is higher. We reduce this threshold from the original 0.1 ms −1 in this paper, which avoids an unphysical spike in the distribution of droplets (Supplementary Figure S1) and an underestimation of the frequency of low droplet concentrations. Instead of the 10 tuned values used by Gordon et al. (2018), the hygroscopicities used are now those recommended by Petters and Kreidenweis (2007) including a kappa value for organic carbon of 0.2. If the number of droplets activated in a timestep exceeds the number of droplets already existing in that grid cell the droplet concentration used in the microphysics and radiation schemes is updated to the new value. If, on the other hand, the cloud fraction in the grid box goes down, the droplet concentration is altered in proportion, as discussed later. Cloud droplet number concentrations in our 500 m-resolution simulation are also calculated 15 diagnostically on each timestep by the UKCA scheme (West et al., 2014), using the same procedure as in the global model, described above. These number concentrations are not used by the model's microphysics or radiation scheme, and so in future simulations this parameterization could be switched off. However, for this study we leave it switched on in order to examine its scale invariance and to compare the predicted droplet concentrations with those from CASIM.
In the CASIM microphysics, condensation of water vapor onto cloud droplets is treated with 'saturation adjustment' so 20 supersaturation is not prognostic and is assumed to be zero at the end of each model timestep. Autoconversion and accretion are handled by the parameterization of Khairoutdinov and Kogan (2000). In our simulations the clouds are entirely warm phase; for a description of the representation of cold clouds in CASIM see Miltenberger et al. (2018). In addition to our reduction of the activation updraft minimum, we also change the cloud droplet size distribution assumed by the bulk scheme from an exponential distribution to a gamma distribution. This change is explained further in the context of the evaluation in Section 5.7.

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The coupling from the UKCA aerosol microphysics code to the CASIM cloud microphysics proceeds simply by passing the aerosol mass and number in the soluble Aitken, accumulation and coarse modes, and the volume-weighted hygroscopicity of these modes, to the activation scheme in CASIM. The CASIM microphysical process rates are coupled to UKCA following the procedure used in the default configuration of the UM with single-moment microphysics from Wilson and Ballard (1999).
The autoconversion and accretion rates are summed and passed back to the aerosol microphysics code to determine the rate 30 of removal of aerosols in droplets by rain, while the rain and snow rates are used to determine the rate of impaction scavenging of aerosol by precipitation. These processes also reduce the prognostic droplet number concentration. The liquid water content is used in the calculation of the rate of conversion of sulfur dioxide to aerosol-phase sulfate inside cloud droplets in the UKCA module of the code. The CASIM microphysics code has the capability to simulate aerosol microphysical processing , for example the reduction of aerosol number concentration when cloud droplets collide and coalesce, or the increase in aerosol number concentration when rain evaporates. However, there is no capability to track the composition of the aerosol inside hydrometeors during processing, nor to perform aqueous chemistry in the CASIM module.
For simplicity and to save on computational expense, therefore, we do not keep track of aerosols in hydrometeors separately to aerosols outside them, and keep the aqueous chemistry in the UKCA code. Aerosols that activate to form cloud droplets are only removed if they are wet scavenged (i.e. they form rain) and if this happens it is irreversible: the evaporation of rain does not 5 return aerosols to the atmosphere. A coupled GLOMAP-CASIM double-moment model that includes aerosol microphysical and chemical processing is deferred to future work.   cloud top height and optical depth is described by Gordon et al. (2018) and follows Boers et al. (2006) and Grosvenor and Wood (2014). The cloud feature is reproduced by the model, but it is substantially smaller than that observed by the satellite and it is displaced to the south-east. The south-easterly displacement suggests the wind speed in the boundary layer in the 7 km model is likely a little slower than in reality. The liquid water path seems to match the satellite well in the 7 km simulation. In the 500 m simulation, the in-cloud liquid water path is also realistic, but the relative frequency of intermediate liquid water paths between 5 100 and 300 gm −2 is underestimated compared to the satellite. The retrieval of cloud droplet number does not yield data in all cloudy pixels due to confusion with overlying cirrus cloud which prevents the retrieval of cloud top temperature. However, from the valid pixels, the cloud droplet concentration in the 7 km simulation is realistic. In the 500 m simulation, a large number of isolated high peaks in the droplet concentration are seen, while there are no such high peaks in the measurements. In the simulation, these peaks correspond to high updraft speeds at some point in the history of the cloud. In practice, this variability 10 may not bias the area average: Supplementary Figure S2 shows the same figure, except with the central subfigures replaced by the droplet concentration and water path in the 500 m simulation regridded to 5 km resolution, which is not dissimilar to the apparent resolution of the relatively sparsely sampled MODIS cloud droplet number concentration. The simulations in these subfigures show better agreement with the observations.

Temperature and humidity
15 Figure 4 shows the aircraft measurements of temperature and relative humidity compared to the global and 7 km-resolution simulations in the left and central sub-figures. These measurements are supported by Supplementary Figure S3, which shows the corresponding data from radiosondes at Ascension Island compared to the regional and global simulations. The simulations boundary layer height at Ascension Island is lower than in the simulation domain, by approximately 500 m in the observations and 300 m in the 7 km-resolution model. As well as the error in the boundary layer height, the temperature is generally underestimated by the simulations by around 1.5 • C above the boundary layer, although the simulations do reproduce the hint of a secondary inversion at around 3.5 km altitude reasonably well. The relative humidity is slightly underestimated in most of the boundary layer compared to the aircraft data. Unlike the humidity derived from the aircraft, the radiosondes record lower 10 humidities than the model. This discrepancy may be due to imperfect matching between the clouds in the model grid boxes and the observations as we also saw in Figure 3, or due to effects from Ascension Island, which is not included in the model.
Above cloud, all simulations produce an elevated relative humidity in the moderately polluted aerosol layer, in good agreement with the aircraft measurements in Figure 4. 15 The simulated vertical profiles of aerosol number concentration are compared to observations on the right of Figure 4. The observed accumulation-mode aerosol number concentration in the boundary layer varies from 350 to 700 cm −3 below 1000 m altitude, and 200 to 400 cm −3 between 1000 and 2000 m. The domain mean in the simulation, around 700 cm −3 below 1000 m and 600 cm −3 above, is biased high compared to the observations. The Aitken mode number concentration above the boundary layer is over-predicted by the model by a larger amount, more than a factor of two, suggesting that new particle formation 20 in the free and upper troposphere may be overestimated. The overestimate could be in one or both of the regional models, or the global model, as these particles may advect in through the boundaries of the regions. Aitken mode particles are likely to originate from new particle formation rather than biomass burning since the geometric mean diameter of the smoke emissions is 120 nm, which is already in the accumulation mode, and there is no mechanism in the model for the smoke particles to shrink.

Aerosol number concentration and size distribution
As this study is focused on the boundary layer, and the concentrations in the Aitken mode there seem realistically similar to the 25 difference between the PCASP concentration and the CPC concentration, we do not investigate this further. However, it will be important to study the scale invariance of nucleation-mode microphysics in this model in future work.
The observed aerosol size distribution is shown in Figure 5. As suggested by the number concentrations in Figure 4, the Aitken mode concentration is consistently overestimated, but the accumulation mode dry diameter is simulated well, generally within 30% of observations, though it appears to be overestimated by a larger amount at the 1900 m level, the altitude of the of the Aitken mode number concentration is unlikely to lead to substantial biases in the cloud droplet number because, while too high, the concentrations are still much lower than those of the accumulation mode in the boundary layer.

Liquid water content
The aircraft targeted areas of strong radar reflectivity, and so its sampling of liquid water content is biased towards thicker clouds. This bias must be addressed as we compare the observations with the whole range of model grid cells in our domain, 5 as discussed by Field and Furtado (2016). The distribution of liquid water content at the five altitudes sampled by the aircraft is compared to the distribution at the same altitudes of the cloudy grid-boxes of the 500 mresolution model in Figure 6. than the difference over the full range of liquid water content ( Figure 6). In some of the subsequent evaluation, we focus on observations and simulation data made at liquid water contents above 0.15 gkg −1 , as this is where most of the observations lie. The histograms of vertical velocities in two bins of liquid water content shown in Supplementary Figure S5 show that, as expected, high liquid water content is associated with updrafts while low liquid water content is more likely in downdrafts.

5
We compare simulated grid-box mean updraft speeds in our 7 km and 500 m-resolutions models to observations in Figure 7.
We include all grid boxes where the overall cloud liquid water content is greater than 0.01 gkg −1 irrespective of the cloud fraction. Clearly the width of the distribution is underestimated substantially, even in the 500 m simulation. An underestimate is expected, because the 500 m model grid boxes does not resolve all the updrafts. On the other hand, the aircraft records vertical velocity at 32 Hz, corresponding to approximately one measurement for every 4 m it traverses, and therefore it should represent 10 all of the turbulence that would be captured by a large eddy simulation. In our model, we therefore rely on parameterized boundary layer mixing. In the 7 km simulations, almost no variability in updraft speed in these clouds is resolved.  Table S2. When split by liquid water content, the width of the vertical velocity distributions in the model matches observations better, although it is still underestimated. Before splitting by liquid water content, the mean vertical velocity at each altitude was generally within 0.1 ms −1 of zero, but after the split this is no longer the case, as indicated in Supplementary   Table S2. We note that the two variables are not independent: large positive liquid water contents are correlated to large positive speed. The residual bias may be a sampling artefact we did not successfully remove, or it may indicate that there is not enough simulated convection.

Droplet concentrations
The simulated in-cloud droplet number concentration is calculated by first dividing the grid-box mean droplet number concentration by the cloud fraction, then removing any grid cells where the in-cloud mean liquid water content is below 0.01 gkg −1 10 or where the cloud fraction is below 0.05.
With the CASIM activation scheme, Table 1 shows that the mean droplet concentration is overestimated by a factor of two to three depending on altitude in the clouds with higher liquid water content, and by a larger factor in clouds with low liquid water content. The overestimate is likely to be due in part to the substantial overestimate in aerosol concentrations in the accumulation mode, and in part due to the activation scheme and warm rain representation (discussed later). variability (the width of the distribution) is also overestimated, although the frequency of very low droplet concentrations is underestimated. Table 1 shows the overestimate in mean droplet concentration is more severe than the figure suggests, because the aircraft targeted areas of strong radar reflectivity and therefore preferentially sampled high liquid water contents and high droplet concentrations.
The UKCA activation scheme in the same simulation also overestimates the variability in droplet concentration, but the 5 mean is closer to observations. Most likely, UKCA produces fewer droplets than CASIM because the CASIM droplet number depends on the highest updraft in the history of the cloud while the UKCA droplet number depends on the updraft at the particular instant the droplet number is diagnosed. This mechanism is explained further in Section 6. In UKCA at 7 km resolution, by contrast, the variability is underestimated and the mean droplet concentration is also underestimated, more severely, by up to a factor three. This UKCA activation scheme (so far only used at convection-permitting resolution by Gordon et al.

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(2018)), also produces a spike in the very lowest bin. This spike is the result of a lack of scale-awareness in the scheme as it is currently coded. It corresponds to the minimum droplet concentration being assigned, 5 cm −3 , because the characteristic updraft speed is out of the range allowed in the code (a more detailed discussion is given in the supplement). Grid-boxes with updrafts out-of-range are seen in the 7 km-resolution simulations as well as the 500 m simulations.
As well as the bias mentioned above, the UKCA diagnostic activation scheme suffers from a lack of scale invariance at 15 high resolution in the sense that the 7 km simulation does not yield the same distribution of cloud droplet concentrations as the 500 m simulation. This is unsurprising as at 500 m the updraft PDF can often have a substantially non-zero mean in any  conclusion here is that the UKCA activation scheme should not be used as-is in cloud-resolving simulations, even though the domain mean droplet numbers it produces are realistic in this case study. Indeed, this UKCA activation scheme must be used with care even at the relatively coarse 7 km resolution (perhaps with an increased minimum width for the updraft distribution).
Because the diagnostic droplet concentrations in the 7 km model do not feed through the lateral boundaries of the 500 m 10 simulations, biased droplet concentrations in our 7 km model should not substantially affect the 500 m model.

Cloud and rain particle size distributions
We compare the cloud and rain size distributions between the model and the observations in Figure 9. We find the model represents large cloud droplets well, but overestimates the number of small droplets and underestimates the number of large rain drops. The cloud droplet size distributions are broadly similar for cloud liquid water contents below and above 0.15 gkg −1 , as shown in the Supplement as Figure S8. The simulated surface rainfall amount is compared to observations from the GPM 5 satellite dataset (Huffman et al., 2014) in Supplementary Figure S9. Despite the poor representation of the rain size distribution observed by the aircraft, the total surface rainfall rate simulated by the model is in generally good agreement with the satellite data. Simulated vertical profiles of rain mass and number concentration are evaluated in Figure 12, which is shown later as it includes model developments discussed in the following sections. This evaluation confirms that, compared to the aircraft data, the rain mass is generally well simulated but the number concentration of small drops is overestimated and that of very large 10 drops underestimated. We note that the autoconversion and accretion parameterizations from Khairoutdinov and Kogan (2000) could in principle be tuned to attempt to address this bias, but we did not attempt to do so.
In the simulations shown in Figure 9, we have used a gamma size distribution instead of the default exponential cloud droplet size distribution assumed by CASIM and published by Grosvenor et al. (2017); Miltenberger et al. (2018) and others. We find (not shown) that once both the moments for droplet mass and number concentration are predicted by the model, adjusting the 15 prescribed size distribution shape (e.g. changing from an exponential to a gamma distribution) without changing these moments does not strongly affect the important results of the microphysics parameterization, such as rain formation rates. However, in the next section we wish to calculate the number mean droplet radius in order to determine supersaturation, and this is sensitive to the shape. For example, an exponential size distribution has a number mean radius equal to one-third of the effective radius and 0.55 times the volume mean radius, while the more realistic gamma size distribution with µ = 5 has a number mean radius 20 equal to 75% of the effective radius and the effective radius is larger than the volume mean radius by 15%. This 15% is still larger than the 8% found in observations (Freud et al., 2011), but in much better agreement than the 66% factor by which the effective radius of the exponential distribution is greater than its volume mean radius. The gamma size distribution is given by for drop diameter D, shape parameter λ, and droplet concentration N d . The size distributions shown in Figure 9 and used in our  Supplementary Table S3. The gamma size distribution we use overestimates the number of small droplets compared to 30 observations, but it captures the number of larger cloud droplets very well.
Simulations by Pinsky and Khain (2002) and others showed that in principle a bimodal droplet spectrum could arise as a result of secondary droplet nucleation. We have some indications, from Figure 7, that updrafts may accelerate in our clouds, leading to secondary activation, as strong updrafts, above 4 ms −1 , are more frequently observed at higher altitudes. It is then . tempting to claim the droplet spectrum in Figure 9 is a bimodal distribution with peaks at 7 µm and about 20 µm. When we filter the observed size distribution to exclude low liquid water contents in which secondary activation is not expected we find (on the right of Supplementary Figure S8) that at high altitudes in the cloud the slightly bimodal distribution remains.
However, it could easily be an instrument artefact, and it could probably also arise from different aerosol types, entrainment, or collision-coalescence processes. Thus it is very speculative to suggest secondary activation is actually taking place. In our 5 simulations, by contrast, there is no mechanism for secondary activation to lead to a bimodal size spectrum: the new droplets must fit into the existing size spectrum definition.

Developments to the activation scheme I: in-cloud activation
The procedure for aerosol activation adopted in both CASIM and UKCA activation schemes is to activate aerosols on each timestep as if no cloud were present whenever there is a tendency for water mass to condense. In UKCA, the number of droplets 10 that exist in the box before the activation scheme is run is not stored, so the new value of the droplet concentration is used regardless of the previous concentrations. In CASIM, the number of droplets already in the grid-box is stored, and if the new number exceeds the old, the number of droplets is increased to the new value. The overwriting of old droplet concentrations by new droplet concentrations if they exceed the old is the procedure of Stevens et al. (1996);Lohmann (2002), and others, but Lohmann (2002) only activated aerosols at cloud base, and assumed cloud droplet concentrations were uniform in columns within a cloud, a procedure since followed by the UKCA activation scheme (West et al., 2014). The procedure in CASIM, as in most models that employ the more widely used Morrison and Gettelman (2008) activation scheme and its successors, is to do activation at all vertical levels within the cloud, with a maximum supersaturation that is diagnosed assuming no hydrometeors 5 are present on each timestep. In CAM5.0 however, a fixed supersaturation of 0.3% above cloud base is assumed . The use of the grid-scale mean updraft in the CASIM activation scheme, as in RAMs (Saleeby and Cotton, 2004;Thompson, 2016), differs from the scheme of Morrison and Gettelman (2008), which was written with climate model resolution in mind and therefore uses a turbulent sub-grid-scale updraft (Morrison et al., 2005) instead of the grid-scale mean, which is mostly unresolved at low resolution.

10
There are two possible mechanisms by which this double-moment scheme may overestimate the impact of in-cloud activation, leading to overestimated cloud droplet concentration. First, the effect of existing cloud droplets on supersaturation is neglected by default, but activation is still repeated every timestep at all levels in the cloud. Second, provided a cloud does not evaporate, the cloud droplet number produced depends on the maximum updraft speed over the cloud's lifetime rather than the mean updraft speed, though it is not clear that this mechanism leads to an overestimate, or is correct. 15 Existing cloud droplets certainly affect the supersaturation of water vapor in the cloud. In models like ours with saturation adjustment, there is an assumption that the concentrations of water vapor and liquid water reach equilibrium over one model timestep, which in our case is 20 s. In pre-existing clouds with sufficiently high liquid water content and droplet number, we may assume the sink of water vapor to unactivated aerosols will be negligible, and therefore we may write, after Squires (1952) and others, for example Politovich and Cooper (1988); Korolev and Mazin (2003), an equation for the time evolution of the 20 supersaturation s, using the notation of Ghan et al. (2011): Here w is updraft velocity, α(T ) is a thermodynamic term that relates the updraft to the tendency for water vapor to condense as it cools, N is the droplet number,r the number mean droplet radius, γ * is another term which follows from the thermodynamics of rising moist air with assumptions detailed in Chapter 12 of Pruppacher and Klett (1997), and G is the growth coefficient, 25 which depends on the diffusivity of water vapor in air and on the thermal conductivity of the air. Our prescription here is valid only for warm-phase clouds; Korolev and Mazin (2003) describe a more general approach for mixed phase clouds. We correct the diffusivity following the size-independent formulation of Fountoukis and Nenes (2005) except with an accommodation coefficient of 1 as recommended by Laaksonen et al. (2005). If (hypothetically) the system were not in equilibrium and w, T , N andr were constant in time, the supersaturation s(t) could then be approximated by (e.g. Grabowski and Wang, 2013) 30 where s = s 0 at t = t 0 . In this equation, (γ * GNr) −1 may be interpreted as τ , the relaxation timescale for the supersaturation, and, in liquid clouds with sufficiently high water content, the supersaturation relevant to aerosol activation is given by the 20 https://doi.org/10.5194/acp-2020-68 Preprint. Discussion started: 21 February 2020 c Author(s) 2020. CC BY 4.0 License. equilibrium or 'quasi-steady' value (Politovich and Cooper, 1988) s eq = αwτ.
Therefore the concentration of newly activated aerosol in each aerosol mode i, N d,i,new , is related to the concentration of aerosol in that mode N a,i in the same way as in the activation parameterizations, by where σ i is the mode width and is the critical supersaturation. The coefficient A is a function of temperature and B i of the particle hygroscopicity, r a,i is the geometric mean radius of the i th aerosol mode, and the equation assumes the aerosols are internally mixed (Pruppacher and Klett, 1997). The effect on the supersaturation of the condensation or evaporation of rain is currently neglected in these 10 simulations. While the rain water mass is non-negligible compared to the cloud liquid water mass, above cloud base (where it matters) the product of the rain number and the radius is less than 1% of the product of the cloud number and cloud radius at least in the clouds we study here, so the effect on the relaxation time is negligible. At cloud base, the rain mass concentration can exceed the cloud droplet mass, but the small number of rain droplets still means the effect of rain on the relaxation time is negligible.

15
In well-established clouds with high liquid water content, Korolev (1995); Ming et al. (2007); Ghan et al. (2011) suggested that using Equation 4 should be a better approximation for the supersaturation than the maximum supersaturation s max generated by activation parameterizations such as ARG. Dearden (2009) tested this approximation in large eddy simulations, and found the maximum supersaturation s eq calculated assuming equilibrium with existing droplets to be a much better approximation than that derived using a precursor to the ARG parameterization (Twomey, 1959), which is valid in the approximately 20 same conditions as ARG: at cloud base. We use the quasi-steady state equation only when it produces a lower supersaturation than the ARG parameterization. The more detailed microphysics scheme of Phillips et al. (2007) also uses a diagnostic parameterization similar to that of ARG at cloud base and a different approach above. However, inside clouds Phillips et al. (2007) represent supersaturation prognostically, without saturation adjustment, in contrast to our cruder quasi-steady approximation.
In a general circulation or mesoscale model with a sub-grid cloud fraction scheme, partially cloudy grid boxes must be 25 accounted for. By default in CASIM, the grid-box mean change in cloud droplet number concentration on each timestep is where ∆t is the model timestep, 20 s in our tests,Ñ d,t+1 denotes the newly calculated in-cloud (denoted by tilde) cloud droplet number concentration,Ñ d,t that calculated on the previous timestep,N d,t+1 denotes the newly calculated grid-box mean (denoted by overbar) cloud droplet number concentration, and F t+1 is the current cloud fraction. TheÑ d is calculated by running the ARG parameterization over the whole grid box on the assumption that it is completely cloudy so the real grid-box mean cloud droplet number concentration is this value multiplied by the cloud fraction. In some models ∆t is set to an activation timescale rather than the model timestep (20 minutes in the case of Morrison and Gettelman (2008)). The multiplication by cloud fraction is done after taking the maximum rather than before to handle the case where the cloud fraction increases but the 5 cloud droplet number decreases. The activation scheme is not run when the cloud fraction decreases. When a cloud evaporates, there is a homogeneous mixing assumption: the cloud is assumed to evaporate uniformly across the grid box so that all of the cloud droplets get smaller as the liquid water content decreases, and they are only removed when the cloud fraction or mass of liquid water reach thresholds close to zero (10 −10 kg kg −1 for liquid water content and 10 −12 for cloud fraction).
In our improved activation scheme, we assume that in each partially cloudy grid box, the total number of droplets that will 10 either be activated, or remain activated, on a new timestep, denoted by t + 1, is the sum of those activated inside the old cloud and those activated in any new cloud that forms. Therefore we replaceÑ d,t+1 in Equation 7 bỹ The first term in this Equation 8 represents aerosols that will be activated at equilibrium in the existing cloud. This term comprises both aerosols that are already contained in large cloud droplets and aerosols that may be newly activated in the 15 existing cloud due to increasing updraft speeds and supersaturations ('secondary activation'). The second term in Equation 8 represents aerosols that will be activated in any additional new cloud that forms in the grid box. We thus obtain where F t is the cloud fraction calculated at the end of the previous timestep and then advected,Ñ d,cloud,t+1 is the in-cloud droplet number calculated using Eq. 4 for the supersaturation andÑ d,ARG is the result of the ARG parameterization (or a 20 similar treatment such as that of Twomey (1959) or Nenes and Seinfeld (2003). In our model, F t is available even when the sub-grid cloud scheme is diagnostic rather than prognostic, and the equation is not used if F t+1 − F t < 0: if this is the case we use instead If the cloud fraction is below 5% or the in-cloud supersaturation calculated from the cloud droplets via Eq. 4 is higher than that 25 calculated with the ARG parameterization, we revert to Equation 7, using only the ARG scheme. The equations for the various conditions are summarised in Table 2.
With all of the double-moment approaches we are aware of, over the lifetime of a cloud, the in-cloud droplet number is more likely to increase than it is to decrease, because the droplet number in each gridbox is overwritten if the new droplet number exceeds the old. Therefore, the fraction of activated aerosol will end up corresponding to the highest updraft speed seen during 30 that lifetime. Morrison et al. (2005) divided the number of additional new droplets activated by 2 to help compensate for this. Table 2. Equations for activation to apply in different possible situations as described in the text

Condition Equation Application
Ft+1 − Ft > 0, Ft+1 > 0.05, and Eq. 9 Activation inside existing clouds This 'ratcheting' mechanism is not necessarily unrealistic, since turbulence-induced upward fluctuations in updraft speed in clouds may well activate more droplets, while downward fluctuations around a positive mean updraft are unlikely to lead to large existing droplets completely evaporating. However, the ratcheting means the double-moment scheme should produce more droplets on average than a single-moment scheme, for example if the diagnostic UKCA activation scheme were fed by the same updraft speeds and the same aerosol. The droplet concentrations shown in Figure 8 suggest that indeed the CASIM 5 scheme does produce more droplets, but the comparison is complicated by the UKCA procedure of setting vertically constant droplet concentrations above cloud base.
In the version of CASIM we are using, aerosol processing is not included, so aerosols are not removed from the gas phase or tracked separately in the cloud phase. Therefore, in our improved scheme, once a cloud forms and the supersaturation used in the activation scheme is reduced due to the existing droplets, the number of aerosols activated on subsequent timesteps 10 within the cloud will be smaller than the number activated the first time the cloud formed. Because the droplet number is only updated if it is higher than the previous droplet number, this will not generally cause the droplet number to decrease, but it will artificially hinder secondary activation from increasing the droplet number. In other words, while our improvements are designed to reduce secondary activation, because of the lack of processing we may have reduced it too much. This potential bias could be avoided in future work when aerosol processing is re-introduced to the model. 15 7 Developments to the activation scheme II: sub-grid vertical velocity for cloud-resolving resolutions An overestimate in droplet number must be balanced to some extent by underestimates, since it has been shown that the default activation scheme performs realistically (Grosvenor et al., 2017;Miltenberger et al., 2018;Stevens et al., 2018). The likely explanation is an underestimate of the turbulence by cloud-resolving simulations which still have much lower resolution than large eddy simulations. The updraft speed distribution is compared to CLARIFY measurements in Figure 7. It is clear that the 20 width of the distribution is significantly lower in the model, even when the bias introduced by the aircraft sampling high radar reflectivity is approximately accounted for.
The result of the study of Malavelle et al. (2014) is that the ratio of the variance of simulated updrafts to the variance of real updrafts is given by for grid resolution ∆x, a parameter Z ml proportional to the boundary layer height as described in Supplementary Table S4, and fitted constants E1 = 2.59, E2 = 1.34, a = 7.95,b = 8.00 and c = 1.05. An additional correction factor f is required to 5 account for the difference between effective and actual grid resolution. This factor varies from model to model but for the Unified Model it is a factor four correction to the variance (Malavelle et al., 2014). The constant of proportionality between Z ml and the boundary layer height depends on the cloud regime. The updraft velocity in the activation scheme can then be set to correct for unresolved fluctuations in the velocity distribution, following Equation 21 in Malavelle et al. (2014).
In the cloudy part of the model domain, the mixed layer height is around 2000 m, so the formulation, accounting for effective grid resolution, suggests a scaling factor of approximately 3 (see Supplementary Table S4). The comparison of the PDF between the model and observations suggests a factor that varies from 1.5 to 4.2 depending on altitude and liquid water content. We give more weight to results at cloud base and to the data binned by liquid water content in Supplementary Figure S4, so we 15 use a factor of 2. We do not implement the Malavelle et al. (2014) scheme in full as it appears to exaggerate the scaling factor required for the model resolutions and boundary layer we are studying. Moreover, we note that scaling all our updrafts up by a factor two doubles the mean updraft speed used in the activation scheme as well as the standard deviation. For the cloud we simulate, at cloud base and at cloud top this leads to poorer agreement of the mean updraft speed with observations, while in the middle of the cloud the agreement improves. The potential for such a scaling to introduce bias requires further study. 20 We also ran simulations with 1.5 km and 3 km resolution, where the Malavelle et al. (2014) scheme would suggest a scaling factor of about 8 is needed, and we find similarly that for most altitudes this would increase the width of the updraft PDF substantially beyond that which is observed (Supplementary Figure S10). Further work is needed to understand the reasons for this overestimated correction factor fully, but the underlying premise that the updraft may be scaled up to account for its unresolved fraction may still be appropriate.

25
8 Results of improvements to activation scheme For our 500 m simulations, Figure 10 shows that when we correct the activation scheme in two places, we obtain relatively similar cloud droplet numbers to those we started with, with a slight improvement to the agreement of the model with observations. Overall, it looks like a factor 2 correction to the updraft (as suggested by observations at cloud base) produces cloud droplet number in good agreement with the default model for this resolution. However, as well as being resolution-dependent, 30 this finding may be specific to the type of cloud we study, and will likely be influenced by other sources of bias -for example, the assumption that the aerosols are internally mixed, the assumptions about hygroscopicity, or errors in simulating the aerosol size distribution.
The mean maximum supersaturation from the ARG parameterization is around 0.25% at cloud base in the default simulation and around 0.35% when the updraft speed is multiplied by two, in line with expectations (Ghan et al., 2011). The maximum 5 diagnosed supersaturations in new clouds, calculated by the ARG parameterization, and in existing clouds calculated with the quasi-steady-state assumption, are shown as in-cloud domain mean vertical profiles in Figure 10 and as in-cloud histograms in Supplementary Figure S11. They demonstrate that in-cloud activation is clearly not negligible even in this relatively shallow cloud: the mean in-cloud maximum supersaturation can exceed 0.1%. However, in the cloud we study, it is lower than the 0.3% prescribed for convective clouds above cloud base by Wang et al. (2013). The standard deviation of the maximum 10 supersaturations (not shown, for clarity) is also around 0.1% for the case when the updraft speed is multiplied by two, and 0.05% when the updraft is not corrected. The mean in-cloud value is similar to the 0.1% found in a smaller cumulus cloud by Politovich and Cooper (1988). Very occasionally, the relaxation time can exceed the model timestep of 20 s, as shown in the histograms in Supplementary Figure S11, and in this case a bias will result, but the number of grid boxes in which this happens is not significant. 15 When we account for the effect of existing cloud droplets on supersaturation in the activation scheme, the instantaneous concentration of new droplets activated is always lower above cloud base than when we do not. Increasing the updraft speed increases the activation at cloud base, leading to more activation at cloud base, but, for a factor of two increase in updraft, the number of droplets activated inside the cloud remains lower than in the original model. This difference in vertical profile propagates to the prognostic concentration of cloud droplets, and the consequence is a lower cloud droplet concentration where 20 it is most important for radiative transfer -where the domain-mean liquid water content is highest close to cloud top-compared to the droplet concentration at cloud base.
The PDFs of cloud droplet number concentration shown in Figure 11 match the aircraft slightly better after the constraint, as the PDF narrows slightly. However, the width of the PDF is still biased to be too wide and sometimes too concentrated at low droplet number concentrations.
25 Table 4. Mean in-cloud cloud droplet number concentration in the three simulations in Figures 10 and 11 (original, supersaturation corrected in clouds, and supersaturation corrected and updraft speed increased) and in the observations from the FAAM aircraft cloud droplet probe.
Model grid-boxes and CDP observations where the liquid water content exceeds 0.15 gkg −1 are shown above the horizontal line, those with lower liquid water contents below.
Altitude ( The new scheme gives a modest improvement to model performance in the cloud we chose, but we have not demonstrated it would work in any cloud. In a thin cloud with high cloud fraction but low liquid water content, the relaxation time might reach values comparable to the model timestep, which will most likely lead to biases. To avoid unphysical results, the quasi-steady state scheme could be switched off if the relaxation time is equal to, or exceeds, the timestep, and the ARG scheme used by itself instead. In our simulation, the relaxation time is either well below the timestep, or the quasi-steady-state supersaturation 5 is higher than the ARG supersaturation, and in this case the quasi-steady state supersaturation is not used. However, there is no guarantee that these conditions would always be satisfied with different timestep lengths or in different cloud types.
The effect on cloud microphysics of the changes to the activation scheme is detailed in Figure 12. Reducing the cloud droplet number concentration by accounting for the effect of existing clouds on supersaturation increases rain number and mass concentration, unsurprisingly, and increasing the updraft speed in the activation scheme reduces rain formation in the 10 very highest clouds. However, the impact of the results on microphysics is small: in particular, there is no substantial impact on cloud liquid water content in these simulations, and no effect on the altitude at which rain forms.

Discussion and conclusions
We have coupled the UKCA and CASIM two-moment aerosol and two-moment cloud microphysics components within the Unified Model and tested the resulting model at cloud-resolving resolution against CLARIFY campaign data. The model emits While far from perfect, the model performs well. Further detailed evaluation in different cloud regimes is needed to stresstest the aerosol microphysics at high space and time resolution, as we observed some substantial deviations from observed Aitken-mode number concentrations in the free troposphere, and a high bias in cloud droplet number concentration. The model developments we have made are summarised in Table 5.
The case study we focused on, 19 August 2017, has proved a useful test-bed for model evaluation. The five level in-cloud 5 aircraft flight segments allowed large data samples to be obtained with state-of-the-art instrumentation. Additional profiles and saw-tooth segments are also available for analysis. The cloud deck, which is just under 200 km across, is substantial but self-contained, allowing plenty of data to be obtained both in and out of cloud. The case can be simulated reasonably well with our numerical weather prediction model. While other cloud cases have been measured in more detail, this is one of the best cases from the south-east Atlantic stratocumulus-to-cumulus transition zone and would be suitable for future detailed studies 10 of aerosol-cloud interactions.
Our evaluation of meteorology and of aerosol and cloud microphysics highlighted some areas where the model performs well but also some shortcomings. The model simulates the boundary layer clouds realistically, although the top of the boundary layer is low and the cloud we focus on is not quite simulated in the right place. Unfortunately, the low boundary layer top means the matching of the simulated cloud to observations at the same altitudes leads to an imperfect comparison of other cloud properties 15 such as droplet concentration and updraft speed. However, aerosol, cloud and rain number concentrations are all realistic, but overestimated compared to aircraft observations. Cloud liquid water content and rain mass compare reasonably well to satellite measurements. We found the aerosol activation in UKCA without CASIM microphysics breaks down once high fractions of updraft speed are resolved, and for now CASIM is preferred to activate aerosols in simulations with convection-permitting resolutions of 7 km or finer. However, in the climate model, the same activation scheme has no such problems. 20 We tested two improvements to the aerosol activation scheme in CASIM: the correction to the supersaturation for existing while the grey shading shows the region where 95% of the domain mean liquid water content resides. The last plot shows the domain mean rain mass mixing ratio with no liquid water content threshold applied. µ = 5 was found to be needed for the first of these improvements to work, instead of the exponential distribution usually used for the CASIM cloud droplet size distribution, and so all of our results are presented with the gamma distribution. Further work is needed to ensure the Malavelle et al. (2014) correction scales with resolution correctly before it can be implemented online.
Conversely, the CASIM activation scheme will break at coarser model resolution, as it is not possible to apply the Malavelle et al. (2014) correction unless some fraction of the updrafts are resolved. To get around this a sub-grid vertical velocity of the 5 form suggested by Morrison and Gettelman (2008), or a PDF as in UKCA, could be implemented into CASIM and switched on for low grid resolutions (probably coarser than around 3 km, depending on the cloud type) so that aerosols will still activate when the grid-box mean updraft speed is zero. We also recommend reducing the minimum updraft speed in the CASIM activation scheme from 0.1 ms −1 to 0.001 ms −1 to avoid unphysical spikes in the distribution of cloud droplet number. We have now made the model more physically sound, by reducing incorrect in-cloud activation and using vertical velocities to activate aerosol that are closer to the real vertical velocities observed, and without introducing any new tuning parameters or computational expense. For high-resolution simulations, we believe the approach to secondary activation we adopted following Korolev (1995); Ming et al. (2007); Ghan et al. (2011) is relatively generalizable and could readily be applied to other models, for example WRF-chem with Morrison and Gettelman (2008) or Gettelman and Morrison (2015) microphysics, and 5 other activation schemes such as that of Nenes and Seinfeld (2003). We note that the Morrison and Gettelman (2008) microphysics uses an updraft speed that is already adjusted for sub-grid turbulence and so has no need of the Malavelle et al. (2014) correction. Implementing only the correction to the supersaturation, and no correction to the updrafts, would lead to lower simulated droplet concentrations.
There remain arguments for either switching off droplet nucleation above cloud base altogether, assuming the cloud droplet 10 concentration is uniform in vertical columns above cloud base, or assuming the supersaturation is constant above cloud base as done in convective clouds in CAM5 by Wang et al. (2013). In-cloud activation leads to a broadening of the cloud droplet size distribution above cloud base, but with our approach, any new droplets activated above cloud base must follow the same size distribution as existing droplets (Khain et al., 2015). However, we have still improved on the original method where the importance of activation above cloud base was substantially exaggerated. 15 The improvements to the CASIM scheme may lead to more reliable simulations of aerosol activation and aerosol-cloud interactions that depend more on the concentration of fresh aerosols at cloud base and less on the more processed aerosols found higher in the cloud than previous simulations using similar models, while still allowing activation above cloud base. However, we emphasise that we have not tested the improved model in deep or cold clouds, and we do not suggest it could replace more sophisticated activation parameterizations, some of which already calculate in-cloud supersaturation prognostically (e.g. Fan 20 et al., 2018). In particular, the explicit, prognostic calculation is likely to be needed for calculations of convective invigoration since it is likely that latent heat release and cloud evaporation rates will be erroneous in bulk models with saturation adjustment (e.g. Grabowski, 2007;Hill et al., 2008;Lebo et al., 2012). However, more approximate calculations, used in many if not most convection-permitting studies, may benefit from the improvements to the procedure for aerosol activation we tested, with no additional computational cost.