In this study, we conduct idealised large-eddy simulations (LES) using the Icosahedral Nonhydrostatic (ICON) model . To enable periodic boundary conditions, the simulations are run on a planar torus grid, which automatically connects the respective boundaries. ICON uses a two-time level predictor-corrector scheme to integrate the dynamical core every dynamical time step, while diffusion, advection and the fast physics parametrisations are computed on a larger basic time step dt. Slow physics parametrisations as the ecRad radiation scheme by are called on a multiple of the basic time step. Sub-grid scale turbulence is modelled using the Smagorinsky-Lilly scheme . Moreover, the two-moment bulk microphysics scheme by without ice physics is employed, with some additions regarding droplet sedimentation as outlined in Sect. . Note that ICON uses a saturation adjustment instead of prognostic supersaturation.

In our study, we run idealised simulations of 10 outbound MAGIC transects, called “A” legs. We simulate one control run (control) and one run with active droplet sedimentation parametrisation (drop_sed) for each leg for 48h in an 8km by 8km domain with 50m horizontal resolution. Hereby, the drop_sed configuration is identical to the control configuration, with the only difference being the activation of cloud droplet sedimentation in the ICON microphysics directly from the start of the simulation. The vertical grid spacing is 9m until 2.8km, after which it is stretched to the model top at 20km, with a total of 400 vertical levels. Here, it should be noted that the model resolution can influence the strength of the sedimentation impact, as shown by the DNS studies of and . However, considering the consistency of the signal also in our sensitivity experiments, we are confident that this impact would be small and only quantitative. The first 6h are disregarded as spinup with the exception of the analysis presented in Sect. , where the spinup period is shortened to 2h.

Our setup closely follows that described in , so we will here only repeat important features or deviations. As the transect covers around 2000km, high-resolution simulations are only feasible in a ship-following configuration, that is, the geographical location of the small domain needs to follow the ship track. The original ICON version lacked this feature, so it was added manually. The simulations are initialised using the first applicable ship-launched sounding and forced using geostrophic winds, ship-following advective tendencies for temperature and humidity and the large-scale vertical velocity. These forcings were adapted for ICON based on the original ones from . Furthermore, the sea surface temperature is prescribed and used to compute the surface fluxes in a version of the parametrisation. On top of that, we employ the same relaxation strategy as . We nudge the horizontal mean wind towards the observed sounding wind every 12 h, whereas we nudge humidity and temperature every 30min, but only from 3km upwards. In addition, prescribed the cloud droplet number concentration Nd based on ship measurements of cloud condensation nuclei (CCN), which is not possible in a two-moment microphysics scheme, as both mass and number concentrations are predicted. Instead, in ICON's two-moment scheme, a uniform background CCN concentration is prescribed below 4km, which decays exponentially above this threshold. We choose the pre-existing intermediate concentration of 250 cm-3 for all legs to simplify the analysis, but conduct a sensitivity experiment addressing this choice in Sect. . It should be noted, that this ship-following setup is not truly Lagrangian. With an average speed of 10ms-1, the ship moves faster than the mean wind speed of 6.9ms-1 identified in Lagrangian SCT trajectories . This was explored in sensitivity experiments (not shown), which used a reduced (halved) update frequency of the large-scale forcing mimicking a slower-moving idealised trajectory. Our results were not qualitatively affected, and our conclusions remain unchanged.

The original ICON two-moment microphysics scheme does not contain the process of sedimenting cloud droplets due to their low sedimentation velocity of a few cms-1, compared to other hydrometeors like rain, snow or graupel that can reach up to 10ms-1 . As is a standard microphysics scheme, we only present a brief overview of the necessary equations for sedimentation and refer to the paper for details.

Hydrometeor masses x are assumed to follow the generalised Γ-distribution 1f(x)=Axνexp⁡(-λxμ), with the hydrometeor-specific shape parameters μ,ν and the coefficients 2A=μM0Γ(ν+1μ)λν+1μandλ=Γ(ν+1μ)M1Γ(ν+2μ)M0-μ. The latter depend on the first two moments Mm of the distribution, which can be obtained by evaluating 3Mm=∫0∞xmf(x)dx for m={0,1}. Since f(x) describes the hydrometeor mass distribution, the m=0 integration over the whole mass spectrum yields the number density N of the respective hydrometeor species, i.e. M0:=N. Analogously, the first moment is written as the mass density L of the respective hydrometeor species, i.e. M1:=L. In a two-moment scheme, both initial moments N and L are predicted. Sedimentation is addressed by solving the partial differential equation 4∂Mm∂t=-∂∂zv¯m⋅Mm with the mean sedimentation velocity v¯m of each moment m={N,L} and species individually. v¯m itself can be obtained by computing the respective velocity-weighted moment 5v¯m=1Mm∫0∞v(x)xmf(x)dx using the sedimentation velocity v(x) of each hydrometeor species. Apart from rain, the latter are assumed to follow a power-law relationship 6v(x)≃αxβρ0ργ, with ρ0=1.225kgm-3, hydrometeor-specific constants α,β,γ and a density correction ∼ρ-1 to account for the change in atmospheric density. For cloud droplets, α=3.75×105ms-1kg-β,β=2/3 and γ=0.2, where the density correction exponent γ is smaller than the original γ=0.4 for the other hydrometeors due to the considerably lower mass.

The present formulation features two key differences from . Firstly, while assume a generalised Γ-distribution for the hydrometeor masses (cf. Eq. ), assume that cloud water follows a lognormal radius (r) distribution. For the terminal fall velocity, both approaches describe it via a Stokes velocity, but also introduce a density correction ∼ρ-γ to account for the change in atmospheric density with height. Secondly, in the study of , cloud droplet number concentration is prescribed at a constant value of Nd=140 cm-3, that fits to their case study. In the two-moment microphysics of the present study, Nd is prognostic, so it varies over the course of the transect.

Transforming the velocity-mass relation from Eq. () to a velocity-radius relation using the diameter D(x)=axb yields the same Stokes terminal velocity as reported by : 7v(r)=4αa2ρ0ργr2≡cr2. Inserting a=0.124mkg-β and b=1/3 for cloud droplets and an air density of ρ=1.110kgm-3 yields c≈1.0×108m-1s-1 in the present study. Comparing this to the value c=1.19×108m-1s-1 from reveals a deviation of about 19%, implying that the fall velocity in the latter is slightly higher than in this setup.

The ICON two-moment microphysics offers two options to calculate hydrometeor sedimentation, a semi-implicit approach and an explicit approach. Apart from the different numerical implementations, which we will not discuss here, the main physical difference between them stems from the calculation of the sedimentation flux. In the semi-implicit scheme, the sedimentation flux is calculated by taking into account the updated inflow from all overlying levels within the current time step. By contrast, the explicit scheme only considers the state from the previous time step and does not account for the inflow from above (A. Seifert, personal communication, 2024). In the present study, we opted for the explicit approach, as the impact of including inflow from the current time step is very limited. Even for heavy rainfall, which is not likely to occur in marine stratocumulus, a terminal velocity of vmax=10ms-1 would lead to a Courant number of 8C=vmax⋅dtΔz≈0.56 with our settings dt=0.5s and Δz=9m, implying that even fast settling rain would not be able to reach the next grid box.

For more technical details on the numerical implementation of the explicit scheme, we refer to or .

In order to keep the simulated inversion height close to the observed one over the course of multiple days, employed a weak temperature gradient (WTG) correction based on . In the WTG framework, it is assumed that horizontal temperature gradients in the free troposphere are small. Thus, temperature perturbations can be connected directly to vertical motion in the atmospheric column. achieved this through a damped gravity wave approach. Treating the observed temperature as the reference profile, it is possible to calculate a correction ω′ to the vertical velocity ω in pressure coordinates using the partial differential equation: 9∂∂pf2+am2am∂ω′∂p=k2RdTv′p. Here, Tv′ is the deviation of the virtual temperature from the reference profile (analogously ω′), Rd is the dry gas constant, k=2.4×10-6m-1 is the wavenumber of the gravity wave, f is the Coriolis parameter and am=1d-1p(1000hPa)-1 is the momentum damping rate. The reference virtual temperature is computed from the large-scale forcings. Furthermore, it is assumed that ω′ vanishes at the surface and the tropopause . This yields a correction term that acts to lower (raise) the LES inversion through increased (decreased) subsidence, in case it starts to drift upwards (downwards).

In the setup of , this correction was calculated during the simulations to adjust the vertical velocity dynamically. We cannot adopt this procedure in our study, since we want to compare the outcome of control and drop_sed targeting the cloud droplet sedimentation mechanism. Applying a dynamical correction would distort the sedimentation effect, as in both cases the simulations would be drawn to the reference profiles. To nevertheless obtain results, that qualitatively fit to the observations, we opt for an offline WTG correction. Before performing the main runs that are presented in this study, we conduct control runs no_wtg for each leg with the original large-scale forcings based on (called lsf_no_wtg), but without an application of the WTG correction during the runs. We do this in a low resolution setup on a 4km by 4km domain with around 132m horizontal resolution. Moreover, we only use 200 vertical levels with a layer thickness of at most 25m below 3km and stretched above. Lastly, we strictly nudge the simulation state to the reference temperature and humidity above 3km on a time scale of 1min to ensure that reference and simulation are correctly synced above the boundary layer. Note that this coarser setup produces results that are qualitatively similar to those obtained at finer resolution.

Using the no_wtg outputs, we compute the WTG correction offline for all time steps based on Eq. (), add it to the original vertical velocity from the large-scale forcings and obtain new large-scale forcings lsf_wtg_1. Using the latter, we perform first iteration control runs wtg_1, completely identical to before, but with the adapted vertical velocity. Clearly, this approach will not work flawlessly, as changes from previous time steps are not taken into account this way and thus, overcorrections can occur in the later stages. To account for this, we repeat our procedure and compute the offline WTG correction for the wtg_1 runs, thus obtaining lsf_wtg_2. Using this, we perform second iteration runs wtg_2, compare them to wtg_1 and choose the best fit iteration for the forcings (i.e. lsf_wtg_1 or lsf_wtg_2) for each leg based on the development of the inversion height. This (leg-dependent) forcing configuration is fixed and serves as input for the main runs of both control and drop_sed, respectively. The individual choices for the iterations can be found in Table . This approach yields a consistent outcome for all cases, exhibiting the characteristic deepening and the sub-cloud layer cumulus evolution, which is the main point of interest in our study (cf. Fig. ).

Before we present the results, we provide a short overview of the individual legs, collected in Table . As aforementioned, our study contains cases from all seasons including a variety of meteorological conditions. The broad majority of transects was executed in warmer months, where the large lower tropospheric stability leads to a stable situation, in which stratocumulus decks can readily form under a strong inversion . The third column demonstrates that while most of the cases begin close to the North American coast, three start further offshore than 126°W (or 800km). Note that the distance in km is the great-circle distance from Los Angeles (LA), which was computed based on the ship's geographical position, and is a solid approximation of the ship's path .

In the subsequent analysis, if not stated otherwise, we focus on the stratiform stages where a domain-averaged cloud fraction fc of at least 40% exists. We chose this particular threshold to eliminate periods of non-existing stratocumulus decks as well as to cut legs that have already completed the transition and have broken up irreversibly. On the grid-scale, fc is binary with either 100% or 0%, which is determined by a cloud water mixing ratio threshold of 10-8kgkg-1. Note that the cloud water hydrometeors and the rain water hydrometeors in ICON are separated by a mass threshold of x*=2.6×10-10kg. In this study, liquid water content qc, liquid water path (LWP) and the subscript c refer to cloud water, whereas rain water path (RWP) and the subscript r refer to rain water, unless stated otherwise. The final location of the stratocumulus deck in the control runs can be found in the fourth column of Table , where legs that transitioned before the end of the simulation are highlighted in bold font. As the fc threshold is applied for each leg individually, this can yield small time periods where one run is still in a stratiform stage, while the other is not. To make the analysis more comparable, we use the more conservative outcome for both runs, as these events occur only infrequently.

We divide all 10 cases into two categories: optically thick (or simply thick) and optically thin (or simply thin), respectively. This classification is based on the amount of liquid water in the cloud deck and targets the blackbody behaviour of a cloud regarding its longwave emissivity. It is well-known that a cloud's longwave emissivity (and thus, its integrated radiative cooling) is approximately constant at LWP≳ 30–50 gm-2 e.g.. However, at lower values, this emissivity increases with LWP and so does the radiative cooling that drives stratocumulus development. In the following, LWP denotes the in-cloud liquid water path, which is computed by weighting the domain-averaged liquid water path by the corresponding area cloud fraction based on fc. As summarised in the last two columns of Table , eight legs fall in the thick category, while two belong to thin with maximum liquid water paths well below 50gm-2 in the first 6h. Note also, that rain water contributes to longwave emissivity in principle, however, its impact is negligible during the early stages of the thin legs (e.g. Fig. ). For consistency, Table  therefore reports LWP without RWP, as including rain water would not affect the outcome.

Before we focus on the impact of cloud droplet sedimentation, we will briefly evaluate the quality of our simulations. In doing so, we first compare control runs of two representative legs of each category to MAGIC ship observations regarding inversion height and cloud-base height, and assess the overall development of the SCT. The simulated inversion height zinv in this study is determined by the height of maximum gradient of liquid water potential temperature θl in the boundary layer. It is computed at each time step and each grid cell and averaged over the domain afterwards. The observed inversion height is computed using profiles of potential temperature θ instead of θl, as no condensate was measured in the regular ship radiosonde launches.

Figure depicts the evolution of the domain-mean fc of the thick Leg 16A as well as the thin Leg 11A, excluding the 6h spinup window. The expected course of the SCT is nicely visible for the thick leg in panel (a). Starting with a low-lying thick stratocumulus deck of high fc, zinv increases continuously, until cloud breakup occurs in the very end. During this process, the stratocumulus deck decouples from the surface and cumulus clouds form below the main deck, indicated by a low fc below the stratiform cloud deck. This behaviour is consistent with the initial stages of the deepening-warming mechanism , where the rise in sea surface temperature drives decoupling from the surface. Analogous simulation results for the initial stages of the SCT in MAGIC transects could be obtained by and . The influence of the diurnal cycle is also identifiable, with episodes of continuous cloud thickening and inversion rise during night-times in contrast to cloud thinning and inhibited growth during day-times during solar insolation. The LES inversion tracks the observed inversion quite well, apart from a bias during day-times, where the inversion seems to decline in the observations. Moreover, the observed first cloud-base from the ship ceilometer (hereafter cloud-base) follows the stratocumulus base relatively steadily in the beginning. Afterwards, it starts oscillating between the stratocumulus base and the underlying cumuli, depending on whether the ship passes under a cumulus cloud or only the stratocumulus deck. Overall, the vertical extension and location of the cloudy layer as a whole is captured well.

In panel (b), the thin Leg 11A is depicted. It is noticeable that the cloud deck is absent at first, forming during the first night. The simulated transect begins more than 1000km off the coast, leading to an immediately (semi-) decoupled stratocumulus deck with underlying cumuli. The second obvious difference to Leg 16A is the thickness of the deck accompanied by a brief day-time breakup in the middle of the transect. Apart from that, both the deepening process and the diurnal cycle are similar. Furthermore, the observed inversion as well as the observed cloud-base exhibit the same features as in panel (a). They are tracked quite well by the simulated cloud, apart from the day-time bias of the inversion. The cloud-base also shows brief disruption episodes, pointing at the structure of a thinner, more broken-up stratocumulus deck. At the end of the second night, the observed cloud-base drops abruptly to around 200m, which is not reproduced by the LES. In total, our simulations successfully capture the initial SCT development regarding the deepening of the boundary layer as well as the decoupling from the surface together with the formation of underlying cumuli.

Secondly, we want to evaluate the simulations by comparing them to satellite observations. Figure depicts the domain albedo for the same two representative legs, 16A for thick and 11A for thin. The background plot shows a midday snapshot of the broadband shortwave albedo from the Fifteenth Geostationary Operational Environmental Satellite (GOES 15), obtained using the techniques described in at a pixel resolution of 4km. The image during Leg 16A in panel (a) represents a prime example of a subtropical SCT. It is by an extensive, contiguous stratocumulus deck of high albedo, that starts to break up at around 134°W and transitions into free ocean cumuli. In contrast, the cloud deck during Leg 11A in panel (b) is more fragmented, has lower albedo and breaks up earlier. The small embedded rectangle shows the LES pseudo-albedo A of the 8km by 8km domain at the time of satellite snapshot, which serves as a proxy for the real albedo. We adopt the approach outlined in based on to include the solar zenith angle. Note that while Fig.  only displays a snapshot, we will briefly address the albedo susceptibility in the discussion, where we excluded angles >80° when the sun is located near the horizon. A is computed as 10A=(1-fc)αsfc+fcAc, with the ocean albedo αsfc=0.06 and the cloudy albedo Ac. The latter is computed using the individual albedo of a cloudy layer αcld : 11Ac=αcld+αsfc(1-αcld)21-αsfcαcld. Furthermore, we calculate the optical depth τ for αcld using the approach of : 12τ=∑i=c,r32∫qi(z)ρ(z)reff,i(z)ρwdz, summing over the individual contributions of cloud and rain water. ρ represents the local air density, ρw=1000kgm-3 represents the density of water, reff and q denote the effective radius and the mixing ratio of the respective liquid hydrometeor. reff is obtained directly from the ICON output (parametrised after Eq. (32) of ). For the sake of brevity, we refer to Appendix A of for the details of the computation of αcld.

The magnitude of the pseudo-albedo largely matches the satellite in both cases. Similarly, both simulation domains capture the qualitative differences in cloud morphology between the two cases described above. The thick Leg 16A case exhibits a broad cloud deck covering most of the LES domain, whereas Leg 11A is far less extensive and features more isolated cumuli, consistent with conditions in the breakup region. In both cases peak albedos inside individual cumuli exceed observed albedo ranges. Furthermore, the simulated cloud deck during Leg 16A seems to be a little more broken than observed. However, it is important to be aware of the scales. The LES domain corresponds to only two by two pixels in the satellite image, which thus (by design) cannot capture any scales of mesoscale organisation. Overall, it is encouraging that the individual simulations exhibit analogous differences to those shown in the satellite images.

A common measure for analysing boundary layer growth is the entrainment velocity 13we=dzinvdt-wsub,inv, originally introduced by . The calculation involves the change in zinv and the subsidence velocity wsub at the inversion. In the following, we decide against the usage of we in illustrating plots and instead discuss zinv directly. The reason is that we oscillates considerably due to the temporal derivative, requiring substantial smoothing to become interpretable, whereas zinv itself is smooth. However, we continue to use the exact we when comparing changes with values reported in the literature, in order to enable a quantitative evaluation. Qualitatively, variations in zinv mirror those in we, as deviations in the subsidence velocity at the inversion are small between drop_sed and control for the majority of the time, and thus 14we,drop_sed-we,control=Δwe≈Δdzinvdt holds. In the following, all differences Δ are computed as drop_sed - control.

To enable a more compact analysis, we distribute the legs in the two categories as in Table . While the optically thin category only consists of two legs, the optically thick one contains eight legs, complicating an individual assessment. Due to their similar behaviour, we opt for a composite analysis in the latter. We use the great-circle distance to Los Angeles for each leg, bin the data in 25km intervals and then average over all legs in the category in order to acquire one distance-binned dataset. Obviously, the physical interpretation has changed in this setup, as this results in average quantities of all respective transects. However, for our purpose, this is the preferred outcome, since we aim to compare drop_sed and control, which consist of the same transects. Thus, in the subsequent analysis, we deal with averaged quantities in the thick category, while we stick to the two thin legs individually, as also their distance overlap is small.

The top panels of Fig.  show the development of zinv in both categories. In panel (a), the averaged inversion of the eight thick legs follows the expected continuous increase in the direction of the free ocean. However, there are two sharp drops, one in the beginning and another at around 2000km. Both can be explained by the number of legs contributing to these intervals. The former originates from Leg 07A, being the only leg this close to the coast, but having a relatively high stratocumulus deck, while the latter comes from Leg 12A, which starts very late compared to all other thick legs and has a strong low-lying deck (see Fig. ). Δzinv is becoming more negative, apart from the very beginning and a considerable period around 2300km, indicating reduced entrainment in the drop_sed runs. While the initial increase is an artifact of the averaging procedure, when new legs are added (cf. the distribution above panel (a)), the sharp increase in the later stage is a distinct feature of Leg 12A, which will be discussed in Sect. . The increasing negative divergence in the core region between 550 and 1900km (indicated by the blue shading) corresponds to a mean reduction in we of around 9%, which is in good agreement with previous studies. The non-precipitating LES studies of and yielded a reduction in we of around 7%, while reported a decrease of up to 25% in their precipitating case. and found even stronger reductions of 20% to 50% in their DNS, as these simulations generally observe more pronounced effects through their fine resolutions. It is important to acknowledge that the present value of 9% is an average over different transects and also includes diurnal cycle effects, while the other LES studies consist of one specific case in nocturnal conditions. Here, we observe individual periods of reduced entrainment that can be as large as 20% in precipitating cases, consistent with .

In contrast, the thin cases in panel (b) show a different behaviour. While the development of the deepening boundary layer is the same for both Leg 04A (solid) and Leg 11A (dashed), the behaviour of control compared to drop_sed differs crucially. For Leg 04A, Δzinv is constantly increasing after 1000km, implying that entrainment is enhanced in the drop_sed run. In this case, this even leads to a 60m deeper boundary layer at the end of the simulation. In this period, a mean entrainment amplification of 10% is observed, which is of comparable magnitude to the previously reported reductions in LES studies. For Leg 11A, this effect is not as pronounced, but still noticeable. The inversion in the drop_sed run starts roughly 10m below the control one after the delayed cloud formation (cf. Fig. b). After a brief increase of this deviation, the trend is a slow, but steady decrease, which can be quantified to a mean entrainment amplification of 2% in the drop_sed case. As soon as Δzinv reaches 0m, an abrupt drop occurs, that can be attributed to the sudden formation of drizzle (cf. panel (d), details in Sect. ). To our knowledge, enhancement of entrainment in stratocumulus due to cloud droplet sedimentation has not been reported before.

The bottom panels of Fig.  depict the corresponding precipitation rates in both categories. The thick cases in panel (c) develop relatively strong precipitation throughout the majority of the transects, which is comparable to the heavy drizzle rates of 1mmd-1 in and . The reason for the seemingly lower values and the oscillatory behaviour is the averaging over multiple legs, leading to a mix of day-time and night-time. It is evident that the precipitation rates are considerably increased in the presence of droplet sedimentation, in accordance with . In contrast, the precipitation rates of the thin cases in panel (d) are very small. Leg 04A develops almost no surface precipitation at all, independent of the type of simulation. Leg 11A also shows very limited precipitation, apart from the final stage of the simulation, where a sharp enhancement can be observed. This increase is greatly reinforced in the drop_sed case, directly affecting zinv in panel (b). From that, we can conclude that precipitation is a strong factor in the boundary layer development of the present cases.

The observations from the previous section raise two main questions. First, how can droplet sedimentation lead to enhanced entrainment and second, why does this predominantly occur in the thin legs. In this section we aim to disentangle the primary process chain by examining the temporal evolution of the sedimentation effect in two stages: the short-term effect in the initial hours and the long-term effect afterwards.

Sedimentation acts to remove cloud water from the cloud-top layer and thereby reduces evaporation. This reduction in evaporation impedes entrainment and directly leads to an increase in LWP . The initial reduction in entrainment is visible in all our simulations, not only the thick ones, but also the thin ones. To quantify this, we computed the mean Δzinv in the hours 2 to 5 for each leg, except Leg 11A, where we used the hours 13 to 16 due to the delayed cloud formation. This way, we discard only the two initial hours as spinup, after which the simulations have mostly stabilised. For Leg 04A, the reduction occurs mainly in the first 4h, which is not displayed in Fig.  due to the discarded spinup window of 6h. To verify that the observed effect is not an artifact of model spinup, we conduct another simulation for this leg. In doing so, we start with the control settings, but activate droplet sedimentation after 15h and let the simulation evolve until the end. We chose this particular activation time step, as the cloud deck's properties such as thickness or LWP, are comparable to the initial hours. A plot for the resulting zinv for Leg 04A can be found in the appendix Fig. .

The results for all legs are summarised in Table  with the sensitivity result for Leg 04A in brackets. The first two rows present the difference of two measures for the stratocumulus top: zinv and the mean cloud-top height zct. The latter is calculated from the maximum height of the cloud water mixing ratio >0.01gkg-1 in each column and is averaged over the domain afterwards. It serves as an additional tool to check if zinv behaves as expected in the initial hours of the simulation. Note that Δzct evidently leads to larger differences than Δzinv, as it is directly driven by the sedimenting droplets. Both approaches yield an overall negative difference for all legs, apart from Leg 12A (marked in bold), confirming the reduced entrainment in the initial hours. For Leg 12A, only zct confirms the reduced entrainment, whereas zinv disagrees. However, in this case, the thermodynamic inversion clearly does not fit to the top of the cloud in the early hours of the simulation (cf. Fig. ), which is further indicated by its actual high sedimentation velocity. Considering this, we conclude that also in this case, entrainment is indeed reduced in the initial hours. Regarding the sedimentation velocity, it is clear that legs with a low initial LWP also have substantially lower sedimentation velocities due to their smaller effective radii. Comparing LWP_control to the LWP in Table , it is noticeable that some of the optically thick legs (especially Leg 05A and Leg 15A) would be categorised as optically thin. However, this is simply an artifact of the initial cloud formation, that vanishes shortly. The expected increase in LWP in the drop_sed runs (i.e. positive ΔLWP values in the fourth row) is not observed uniformly for all legs. Instead, a decrease is observed for the legs 07A, 12A, 16A and 17A. However, taking into account the change in RWP in the sixth row, this deviation can be readily explained by the considerable amplification of rain water in these cases. The excess is at least 2.7gm-2, while the other legs have a maximum excess of 1.5gm-2. The rain water depletes the cloud by collecting droplets and removes them through precipitation, which is enhanced in drop_sed by the sedimenting cloud droplets . In the other cases, this enhancement does not (yet) dominate and thus, the reduction in entrainment yields an increase in LWP.

So far, we have seen that the initial stages indeed yield the expected reduction in entrainment accompanied by an increase in LWP, if the simultaneous increase in RWP is not too strong. Rain formation in general is obviously crucial, as drizzle in stratocumulus can have a substantial effect on boundary layer dynamics by, among other things, depleting the cloud of liquid water or reducing turbulent kinetic energy (TKE) e.g.,. For now, we will restrict our analysis to the general cases, but we will treat the impact of precipitation in a sensitivity experiment in Sect. .

Next, we focus on the impact of sedimentation after the initial period, continuing with the amount of liquid water in the cloud. Figure shows the mean relative qc profile, as well as the mean relative radiative heating rate profile, split up into the two categories. These profiles (and all subsequent ones) were obtained as follows: For each leg at each time step after the 6h of spinup, the height coordinate was normalised by the corresponding zinv. After that, the corresponding legs were merged and a normalised mean profile over all time steps was computed in both categories. Starting with the thick legs, the decline in LWP, which was already foreshadowed in Table , is also visible in the overall mean in panel (a). The stratocumulus region around the maximum of the profile shows a clear decrease, while there is a slight increase in the sub-cloud areas in the drop_sed runs. Moreover, the maximum also dropped considerably due to the sedimenting droplets. In contrast, the thin legs retain and even amplify their initial liquid water increase throughout the entire cloud layer. One reason behind that is the lack of drizzle in the thin cases, which only only forms towards the end of the simulation in both legs (cf. Fig. d), and thus, does not drain the cloud of liquid water.

This behaviour is also reflected in the radiative heating rate in panel (b). The peaks in both drop_sed curves have shifted to lower relative heights. In the thick cases, the peak cooling rate declined substantially. However, most of it was simply transferred to lower heights, where a comparable strengthening can be observed. In contrast, the thin cases show an amplification in longwave cooling across the full cloud layer, consistent with the qc profile in panel (a). The reason for the overall increase, instead of a shift as for the thick legs, is the LWP dependence of the longwave cooling, which was the mean criterion for our categorisation in Sect. . For the thin legs, an enhancement in LWP still leads to an enhancement in integrated longwave cooling, which is why the cooling rate is amplified across the entire layer .

Figure presents analogous profiles of selected turbulence quantities. In the thin case, the overall increased qc, combined with enhanced longwave cooling, is expected to amplify turbulent circulations in the boundary layer e.g.. Panel (a) shows the buoyancy flux, which is indeed enhanced in the drop_sed case throughout the cloud layer, while it remains relatively unchanged below. In contrast, the thick legs exhibit the opposite behaviour. Buoyancy production is considerably decreased in the upper cloud layer and relatively constant elsewhere, apart from an increase near the surface. The former decrease can be attributed to several stabilising factors. The removal of liquid water from the top due to the rain yields not only a decrease in longwave cooling, but also in latent heat release and less cloud-top evaporation overall. Both categories consistently display a minimum buoyancy of around 0.5cm2s-3 in the sub-cloud layer, which is characteristic of the decoupling process, that occurs during the course of the SCT. Note that while no full buoyancy flux reversal is visible, this is a mean profile of eight cases over a period of 42h. Full individual decoupling represented by negative buoyancy fluxes does in fact occur in the later stages of the simulation of each leg.

The corresponding minimum is also apparent in the vertical wind variance w′2 in panel (b), although less distinctive in the thick category. The same overall observations can be made here. While the thin legs show an increase in w′2 across nearly the entire boundary layer, the thick legs display a consistent decline in w′2, indicating that turbulence is increased in the former and reduced in the latter. Comparing the profiles of w′2 and qc in Fig. , they follow the same trend. In the thin cases, both quantities increase, while in the thick cases, both quantities decrease in the stratiform cloud layer. This correlation between qc and w′2 in the presence of cloud water sedimentation was also found in other studies. and simulated a non-precipitating, low-LWP case and observed an enhancement of both qc as well as w′2, aligning with the results of our thin cases. On the other hand, found a qc profile similar to that of our thick cases, along with a reduction in w′2 in their drizzling, high-LWP simulation. This resulted in an overall increased LWP, in contrast to the LWP reduction in our thick cases. However, this apparent contradiction can be resolved by the respective amounts of precipitation. In the case of , surface precipitation was around 0.2mmd-1, while almost all of our thick legs reach precipitation rates of ≳1mmd-1, consistent with the magnitude of and . This much stronger precipitation quickly overwhelms the initial LWP increase, resulting in both reduced LWP and w′2.

In panel (c), the third moment of the vertical velocity w′3 is depicted. While the second moment of the vertical wind characterises the strength of turbulent fluctuations, the third moment describes the asymmetry between upward and downward motions. Positive (negative) w′3 indicates strong and narrow updrafts (downdrafts), in the presence of generally weak and broad downdrafts (updrafts). For both categories, w′3 is consistently positive throughout the boundary layer, implying that there is an overall weak subsidence disrupted by narrow updrafts. In the thin cases, it increases in the presence of cloud droplet sedimentation across the cloud layer, pointing at even stronger, more concentrated updrafts. Together with w′2, we can confidently say that in drop_sed, stronger updrafts drive vertical motions in the cloud. In contrast, w′3 is only slightly enhanced in the thick cases, and even unaffected in the upper levels of the cloud.

The full resolved TKE profile is presented in panel (d). The sub-grid scale contribution is small and exhibits the same behaviour, which is why it is omitted here. All profiles show the characteristic peaks near the inversion and at the surface, where the impact of shear is the strongest. Overall, it reinforces all our observations regarding control and drop_sed from before. In the thin cases, the TKE is considerably increased in the entire boundary layer. In contrast, it is decreased in the cloud layer in the thick cases and slightly enhanced towards the surface.

Based on these previous findings, we can construct the following process chain to explain the differences in entrainment outcomes among the two categories in the presence of sedimentation. In the initial stages, cloud droplet sedimentation leads to the expected and often observed result in all cases: entrainment is lowered, as droplets are removed from the inversion layer, reducing the potential for evaporative cooling. Accordingly, this is accompanied by an increase in LWP. After this initial period of a few hours, the individual cases split.

In the heavily precipitating optically thick cases, the trend of reduced boundary layer growth continues, as droplet sedimentation enhances rain formation. Rain acts to lower convective intensity, as latent heat release near the top and latent heat consumption below cloud-base impede turbulent circulations. Furthermore, it drains the cloud of liquid water, which overwhelms the initial increase in the present cases. Thus, the initial weaker boundary layer growth is amplified and continues until the end of the simulation (or the breakup of the cloud deck).

In the optically thin cases without strong precipitation, neither the TKE reduction nor the liquid water depletion occurs. Rather, the initial LWP increase induces additional longwave cooling, which is not yet saturated due to the small overall LWP. This leads to more potent turbulent circulations in the boundary layer, especially stronger and narrower updrafts, that can redistribute moisture from the ocean surface and thereby enable more liquid water production. This turns into a feedback loop of more liquid water leading to more cooling leading to more turbulence leading to more liquid water, that counteracts the weak stabilising effect of rain. Since the sedimentation velocities in the thin legs are low due to their small effective radii, the additional turbulence is able to transport liquid water all the way to cloud-top. This re-enables stronger evaporative cooling, which, in combination with the longwave cooling, adds to the total cooling. As long as rain formation remains limited and the LWP is small enough for the radiative cooling to be unsaturated, this turbulence intensification prevails. Altogether, the enhanced convective intensity, supported by the evaporative cooling, promotes stronger entrainment and allows it to persist over an extended period of time.

The previous investigations involving the averaged profiles evidently resemble overall behaviour, however, certain periods of individual deviations can be shadowed. Since we simulate two full days, the effect of the diurnal cycle is included in our runs. Especially the day-time thinning of the cloud deck in the thick legs can have a profound impact on the LWP, and also potentially shift the leg from the thick to the thin category. One example, which is even visible in panel (a) of Fig. , is the period between 2200 and 2400km. Here, the continuous decline of Δzinv is interrupted by a period of strong increase, indicating enhanced entrainment. As evident from Table , only Leg 12A contributes this far off the coast, implying this is an individual feature of this leg, that we can analyse.

For clarification, we displayed zinv of Leg 12A in this time period in panel (a) of Fig. . The vertical dashed lines mark the interval of increased entrainment in the drop_sed run, that we analyse in the following. We decided to extend this interval a little further than the extremes to also capture the initial and final stages more accurately. The steady increase between the two extremes of Δzinv corresponds to a mean acceleration of we of 18 % over the course of 7h. This acceleration is not only substantially larger than the previous amplification of around 10% in the case of Leg 04A, but also in the vicinity of the strongest individual reduction of an individual leg of around 20%. In panel (b), both LWP and RWP in this period are depicted. The overall amount of LWP is well within the range, where longwave cooling is not saturated, until the beginning of the second night. The low values are the result of the day-time thinning through solar insolation. The RWP declines simultaneously and arrives at almost no rain at the start of the chosen interval. While the LWP was larger in the control run before, this flips and reaches values more than twice as high in the drop_sed run. At the end of the day, the overall magnitude of the LWP increases again, supporting the rain formation in drop_sed. As soon as the RWP is substantially increased in drop_sed, the corresponding LWP declines and becomes once again lower than in control, marking the end of the interval.

Following the analysis in Sect. , Fig.  shows the different relative profiles. The solid lines represent the relative profiles for Leg 12A in the selected period marked by the dashed vertical lines in Fig. . Furthermore, we added the full thin profiles from Figs.  and in fainter dashed lines as a reference. Without repeating the details regarding individual profiles, it is evident that all six Leg 12A profiles behave analogously to the thin cases. During this period, qc, longwave cooling as well as the turbulence quantities are considerably increased. Especially the former two show an even stronger amplification for Leg 12A than for the thin legs, which is possible thanks to the absence of rain. This leads to a pronounced increase in TKE throughout the entire boundary layer, promoting entrainment in the drop_sed run. These results firmly support the proposed feedback loop from Sect. , confirming that enhanced longwave cooling is a main driver in regions of low LWP. Furthermore, this demonstrates that the categorisation into optically thick and optically thin is not rigid. Especially initially thick legs can become thin over the course of one diurnal cycle, when solar insolation dries out the cloud deck during the day (as we saw here for Leg 12A), highlighting the importance of the diurnal cycle in the context of the SCT.

In order to further evaluate the proposed mechanism, we conduct three more sensitivity experiments, the first one targeting precipitation. Precipitation in stratocumuli has a profound impact on boundary layer dynamics. showed that heavy drizzle substantially reduces entrainment through a reduction in turbulent kinetic energy. As drizzle forms, latent heat is released in the cloud through condensation, warming the cloud layer. When the rain drops sediment out of the cloud, evaporation leads to cooling in the sub-cloud layer. This combination restrains deep circulations and supports the formation of cumuli below the original stratocumulus deck. These results were largely confirmed in the large-domain LES study by , where also a reduction in TKE as well as boundary layer growth was observed in the presence of strong drizzle.

In our simulations, all optically thick cases are strongly drizzling for a certain period of time, whereas only very limited drizzle forms in the optically thin ones. This can be directly attributed to the differences in the amount of liquid water in the clouds. The surface precipitation rates for the representative legs can be found in panels (a) and (b) of Fig. , respectively. Leg 16A features substantial drizzle rates from the beginning, with a considerable drop during the first day due to the day-time thinning of the cloud deck. Moreover, in the drop_sed runs, precipitation formation is generally enhanced because of the sedimenting droplets, which was also observed by . In contrast, Leg 11A only develops a sizeable amount at the end of the second night, which is again substantially larger in the drop_sed run. This strong increase is also responsible for the abrupt drop in the drop_sed inversion shown in panel (d), since the rain drops not only reduce the available TKE, but also simply deplete the cloud of liquid water .

To rule out the possibility that the absence of drizzle alone is responsible for the observed behaviour in the thin cases, we performed two non-precipitating sensitivity runs for the representative legs. The resulting zinv together with the precipitating runs can be found in the bottom panels (c) and (d) of Fig. . Comparing the impact during Leg 16A, there is a clear difference after the first night. While the precipitating case shows only a weakened divergence in Δzinv during the first day, the non-precipitating case actually shows a weak, but continuous, enhanced boundary layer growth in the drop_sed case. After this period of faster growth, it roughly stabilises until the end, leading to an overall lower boundary layer in the non-precipitating drop_sed run. So after the strong initial decrease in entrainment, Δzinv in the non-precipitating runs remains similar, with periods of slightly increased or reduced boundary layer growth. This reflects the counteracting effect of the sedimenting droplets and the enhanced turbulence, where the latter is now not affected by precipitation. During the stronger entrainment phase, there is a lot more liquid water near cloud-top (cf. Fig. b, green line) leading to enhanced evaporative cooling and thus, stronger turbulence in the entrainment zone. Furthermore, during the day, the LWP drops substantially into the regime of unsaturated longwave cooling, while still being considerably enhanced in drop_sed (cf. Fig. ). This way, the overall cooling is not only redistributed, but also magnified and the amplified turbulence can work against the sedimenting droplets. After that period, the sedimentation balances out the increased turbulence, as the cloud enters the thick regime during the second night again and cloud water is not longer enhanced in the cloud-top region. This situation can be seen as an unstable equilibrium of the sedimenting droplets reducing entrainment and the enhanced LWP counteracting it by amplifying turbulent circulations.

For Leg 11A, the situation is different. Both runs commence around the same zinv, followed by two episodes of strongly increasing Δzinv, with an intermission of decreasing Δzinv. So even though almost no drizzle drops are present in the beginning, the inclusion of rain processes alters the base state of the stratocumulus deck. Furthermore, the lack of rain enables even faster entrainment in the drop_sed case until the middle of the first day, after which solar insolation dries out the deck. The fact that the control inversion grows faster in this period might by a consequence of the almost vanishing cloud. After the reformation is complete, drop_sed entrains faster again, resulting in a net raised cloud-top height after the full 48h.

In summary, the overall impact of precipitation can mask and overwhelm the enhanced entrainment effect of sedimentation in the thin cases, if substantial amounts of drizzle form. However, we can infer from the analysis of Leg 16A, that even though drizzle plays a large role in reducing entrainment, it is not solely responsible for reduced entrainment in simulations with activated cloud droplet sedimentation. Rather, sedimentation reinforces drizzle that decreases entrainment, while the non-precipitating thick case shows that the additional liquid water can balance out the original sedimentation-entrainment feedback after the initial period. In contrast to the consistent entrainment increase in Leg 04A, this outcome is unstable, since it lacks the amplification of longwave cooling as an additional driver of turbulence.

The second sensitivity experiment examines the influence of the CCN background in the individual transects. CNN are among the important factors regulating precipitation onset, as the amount of cloud droplets is directly dependent on the number of CCN. In general, higher CCN concentrations yield more and smaller cloud droplets and thus, thicker clouds e.g.,. In the Northeast Pacific, the CCN concentration declines towards the open ocean, as the influence of continental pollution diminishes. This westward decrease has also been observed during the MAGIC campaign . As mentioned in Sect. , we used a background CCN concentration of 250 cm-3 for all legs, which is a solid approximation for the thick legs in our 48h window . Apart from Leg 12A, these simulations either terminate or the stratocumulus deck breaks up no later than 138.2°W (cf. Table ). However, for parts of Leg 04A and especially for Leg 11A, this value exceeds the acceptable range. The latter leg starts outside the continental influence and is further a low CCN leg . To address this issue, we repeated the Leg 11A runs with the ICON maritime setting of a background CCN concentration of 100 cm-3. We did this both in the precipitating and the non-precipitating setup to observe possible changes in both cases. Before discussing the results, it is worth noting that CCN concentrations are not the primary driver behind the observed thick and thin categories. The likely more important drivers are large-scale synoptic conditions impacting temperature and humidity. Most of the thick legs form under a strong inversion with cold and moist inflow from the North. In contrast, this inflow is considerably attenuated in the thin legs, yielding thinner cloud decks with weaker inversions.

The resulting zinv can be found in Fig. . The precipitating case shown in panel (a) exhibits a similar evolution in the low CCN scenario with a weaker growing zinv in the drop_sed case. However, on closer inspection, the period of continuously stronger entrainment during the first day in the drop_sed case of the standard CCN scenario is not distinctly present in the low CCN one. Rather, an overall weaker growing boundary layer with brief intermittent bursts of stronger entrainment is observed, resulting in a decreasing trend of Δzinv. It can also be seen from the disappearance of the dashed line in the second night, that the cloud fraction of the stratocumulus deck drops below 40% and does not recover until the end. This development can be explained by the altered precipitation behaviour. The maximum drop_sed surface precipitation rate of below 1mmd-1 is reached at the end of the second night in the standard CCN scenario (cf. Fig. b). In the new experiment, this value is surpassed at the beginning of the second night and increases up to almost 1.5mmd-1 in both control and drop_sed (not shown). The lower CCN concentrations facilitate rain formation due to the larger droplets, which is in accordance with earlier findings from e.g. . The resulting strengthened decoupling leads to the observed reduced boundary layer growth in the low CCN scenario. Additionally, the continuous negative divergence of Δzinv can be explained by the overall enhanced rain formation in the drop_sed case. As for the thick legs, the reinforcement of rain in combination with the sedimenting droplets is stronger than the amplified turbulence and we observe overall less entrainment. It should be noted that this effect is less pronounced than during the thick legs, because drizzle formation is still suppressed in the beginning due to the low overall LWP. Thus, the latter is still periodically enhanced in drop_sed and the resulting stronger circulations can (partially) balance out the slow sedimentation velocity combined with the weak drizzle.

In the non-precipitating scenario of the different CCN cases in panel (b), the dashed blue and orange lines remain close to the solid ones, in contrast to panel (a). This is because rain is absent and cannot interfere with the cloud dynamics, which leads to a very similar development of the dashed and the solid curves. Comparing Δzinv, the evolution of the dashed and the solid line is slightly different. Instead of the exchanging periods of increased and decreased entrainment, there is an initial decline in entrainment in the drop_sed run, followed by a continuous amplification and a final decline. While less CCN clearly influence the quantitative cloud development, the overall stronger entrainment in the drop_sed run, even leading to a deeper boundary layer, remains unchanged.

In general, we can conclude that the low CCN scenario does not yield structurally different outcomes. It slightly modified the course in the non-precipitating setup and reinforced drizzle formation in the precipitating one. This does produce a considerably different outcome in the latter, but this is not in conflict with our proposed process chain. It rather shifts this leg into the regime, where precipitation-induced stabilisation additionally works against the enhanced turbulence feedback loop and takes over earlier.

The last sensitivity experiment targets the magnitude of the sedimentation velocity. As sedimentation reduces entrainment, higher sedimentation velocities should evidently lead to a stronger reduction . Table  summarises the mean cloud droplet sedimentation velocities in the top 75m of the representative legs. For Leg 11A, vsed,75 is about two thirds of Leg 16A in the precipitating case, and half of it in the non-precipitating case. As the cloud in the non-precipitating Leg 16A run contains much more liquid water (cf. Fig. ), the effective radii are larger and the sedimentation velocities are higher compared to the precipitating case. In contrast, Leg 11A lacks this feature, as there is almost no precipitation anyway. In general, the thin cases have substantially smaller sedimentation velocities due to their lower effective radii.

To emulate the impact of the sedimentation strength of an thin leg on a thick leg, we conducted two sensitivity runs (precipitating and non-precipitating) for Leg 16A. In these simulations, we artificially halved the sedimentation velocity in the ICON microphysics. The resulting mean sedimentation velocity can be found in the respective third columns of Table . Clearly, the manual scaling by a factor of 0.5 does not yield a precise halving of the individual sedimentation velocities, as this introduces additional feedbacks. However, on average, the overall mean reduction is around 50%, which is similar or even smaller than vsed,75 of Leg 11A.

Panel (a) of Fig.  shows the corresponding Δzinv, that are each calculated with the respective control run (i.e. either precipitating or non-precipitating). Comparing the precipitating cases, the reduced sedimentation difference (orange) follows the same course as the original one (blue). On closer inspection, it is noticeable that this remarkably occurs at almost exactly half the value for the entire transect. Similarly, the precipitation rate differences (dashed) are also roughly halved, confirming the direct impact of vsed on drizzle production . This further implies that, even in the case of lower sedimentation speeds, drizzle dominates boundary layer deepening in the thick cases and yields a constantly slower boundary layer growth rate. However, the amount of drizzle production seems to be directly determined by the sedimentation velocity. The drizzle dominance is also visible, when comparing the precipitation curves to Δqc,75 in panel (b). All four main periods, where blue is clearly above orange in the former, largely coincide with an inverse behaviour of the latter. This is the direct effect of strong drizzle depleting cloud-top of liquid water.

For both non-precipitating cases (green, magenta), the only consistent decrease of Δzinv occurs during the initial period until the end of the first night. Analogously to the precipitating cases, this is weakened in the halved vsed case (magenta), which roughly stabilises afterwards, implying that both runs entrain similarly. At the end of the second night, the stable period is interrupted by a period of increased entrainment in the drop_sed run, that even briefly yields a higher net cloud-top height. Taking into account panel (b), the latter can be explained by a sudden excess in Δqc,75 during the second night, enabling stronger entrainment in the drop_sed run through evaporation. Furthermore, we can disentangle the other individual differences in the non-precipitating simulations. Interestingly, until the end of the first day, the simulation with the halved sedimentation speed ends up at lower amounts of liquid water near cloud-top (magenta below green) and also less LWP overall (cf. Fig. , dashed green vs. dashed orange). We can infer from this that the second-order liquid water reinforcement effect of the sedimenting droplets seems to be more powerful than the net loss of liquid water near cloud-top directly through sedimentation. In other words, even if vsed is higher and should deplete cloud-top more efficiently, the increased qc through the turbulent moisture redistribution can overcome this in the present thick case and yield a higher amount of liquid water near the top, strengthening the potential for evaporative cooling. These differences between green and magenta in panel (b) account for the steady rise of the green curve and the relatively stable magenta curve in panel (a). We can conclude that the initial decrease in Δzinv is evidently driven by vsed. After the initial stages, its major impact on precipitation continues, which drives the evolution in the drizzling simulations. In contrast, in the non-precipitating runs, it seems that after the initial period an unstable equilibrium is reached. This equilibrium appears to be largely unaffected by the magnitude of the sedimentation velocity in a direct way. It is, however, dependent on the base states of cloud liquid water near the top, which critically depend on the initial sedimentation speeds.