The measurements reported in J15 took place starting from 16:00 UTC. We match the model time with this period, which mainly affects the radiative budget at cloud top via the solar zenith angle. The initial profiles of potential temperature and the total water mixing ratio are shown in Fig. , where the moisture profile is saturated between the levels of approximately 300 and 650 m. The strength of the potential temperature inversion at the top of the cloud (after condensation of the excess moisture from Fig. ) is approximately 8.5 K. For simplicity, the horizontal wind is initialized to u=-12 ms-1 and v=0 ms-1, following the standard meteorological notation, which corresponds to the observed wind speed in J15. Surface energy fluxes and the large-scale subsidence are prescribed as constants according to based on stratocumulus clouds observed in comparable conditions in a similar regime. The fluxes of latent and sensible heat are set as 93 and 16 Wm-2, respectively, while the subsidence is described by the divergence of horizontal winds set as 3.75×10-6 s-1. The model grid resolution is set to 50 m (10 m in the vertical) and the domain size is 5 km across laterally, extending up to 1400 m in the vertical. A damping layer is applied in the top 100 m of the model grid to prevent unwanted wave propagation. The model time step is 1 s.

The initial aerosol size distribution is described in the model as a sum of lognormal modes. J15 reported the accumulation mode aerosol concentration in the range of 200 to 800 cm-3, with cloud droplet number concentration (CDNC) of approximately 150–200 cm-3. Therefore, we set the initial accumulation mode concentration to 200 cm-3. An additional 400 cm-3 particles were allocated in the Aitken mode, which can be viewed as a typical feature in the marine boundary layer e.g.. However, for the current setup, the Aitken mode particles reside mostly below the critical size for droplet activation – pilot test runs showed little sensitivity in the results for the Aitken mode number concentration. In addition, natural GCCN particles consisting of sea salt, which are virtually omnipresent in marine boundary layers and also seen by J15, were assigned to the background aerosol, with a mode diameter at 1 µm and concentration at 1 cm-3. The lognormal size distribution parameters for the initial model aerosol population are summarized in Table 1.

For the seeding aerosol, we use sea salt as a proxy for the particle composition. We use SALSA’s parallel bin regimes to describe the seeding aerosol initially as externally mixed from the background. The seeding aerosol is then allowed to interact with the background particles through coagulation and cloud collection. We will assume two modes for the seeding particles, with mean diameters at 1.5 and 8 µm, which roughly correspond to the mode mean diameters shown in J15, but they are also more generally representative of the powdered salt size ranges presumed effective in terms of precipitation enhancement .

In the model experiments, the seeding emissions are performed in cloud, near the cloud-top altitude, at approximately 580 m, as in J15. Two methods for the release of the seeding particles are considered: (i) a domain-wide instantaneous injection of the aerosol at the specified layer and (ii) an explicit Lagrangian point source emission. In the former, the particles are assumed to occupy a layer of 50 m in depth. This seeding method does not represent a realistic scenario and serves to provide additional information about the importance of the total emitted mass in terms of the magnitude of the seeding effect. For the latter, the trajectory and speed of the emission source are prescribed for a more realistic seeding scenario. We assume the seeding aerosol plume to immediately occupy a vertical cross section of 50×50 m2. Further dilution of the plume is controlled dominantly by grid-scale mixing. To mimic the airborne emissions, we assume a speed of 60 ms-1 for the source, whose trajectory is illustrated in Fig. . The seeding source propagates towards the positive x direction along a trajectory that covers the entire extent of the domain in the y direction. Since the seeding proceeds against the horizontal wind (in the x direction), the seeding is stopped at the middle of the domain. This is to avoid seeding the same plume twice, because the rear of the plume is advected back into the domain from the right due to the cyclic boundary conditions.

Our experimental strategy is to create two parallel sets of realizations: a control simulation without seeding (referred to as Ctrl) and a set of experiments with seeding particle emissions. This allows us to account for both the direct microphysical effects and the dynamical feedbacks potentially caused by the aerosol perturbation. We must take care that the initial states for the control simulations and seeding experiments are identical. Therefore, a “master” model run is performed, from which the model state is saved to a “restart” file prior to the time of the seeding procedure. The length of the master run is 4 h, to allow the boundary-layer mixing and precipitation process to settle in a quasi-steady state (i.e. spinup). All our model experiments, including both the control and seeding experiments, are initialized from this restart file, which ensures that any differences in the experiments can be attributed directly to the seeding.

The main model experiments performed in this study are summarized in Table 2. The seeding experiments Seed1 and Seed2 use the moving point emission source along the trajectory shown in Fig. . The total seeding rate in the former experiment is set as 1.5×1011s-1 and in the latter as 1.5×1012s-1. With the assumed injection plume cross section and the aircraft speed, this yields initial concentrations of approximately 1 and 10 cm-3, respectively, which will be rather quickly diluted by in-cloud mixing and drizzle formation. These settings were chosen in terms of the seeding particle concentrations in the mixed plume, as it depends strongly on the assumed injection cross section. We set the target concentration after mixing to be similar to the estimated range in J15 (10-4 to 10-2cm-3), as shown in Sect. 4. Please note that while the injection procedure in Seed1 and Seed2 tries to mimic the aircraft emission, we do not consider the possible aerodynamic effects caused by the aircraft. In the experiment Seed3 the seeding particles are injected instantaneously in a domain-wide slab at the same altitude as the point emissions in Seed1 and Seed2. The initial concentration in Seed3 is set as 1cm-3.

In addition to the main experiments, a small ensemble of sensitivity tests are performed based on the Ctrl and Seed2 configurations, where we vary the boundary-layer moisture content and the large-scale divergence settings between the ensemble members randomly within ±10 % of the values used in the corresponding main experiments. The ensemble has 20 members (i.e. pairs of simulations with the Ctrl and Seed2 configurations), whose purpose is to characterize the sensitivity of the seeding results to the model initial conditions. The data are used to investigate process rate statistics as well, which tend to be highly variable in space and time. However, these sensitivity tests obviously do not provide an exhaustive representation of the different sensitivities of the seeding process, which should be tackled with dedicated research.

The precipitation rate in the simulated case is overall rather low in both the model and observations: the observed estimate reported in J15 is about 0.04mmh-1 on average, sampled around the cloud base height. In order to estimate the significance of the seeding effects in UCLALES-SALSA relative to the findings in J15, we want to match the simulated precipitation rate as closely as possible to the measurements. We find that in the current case, the precipitation rate is strongly controlled by three key aspects in the model setup: the background aerosol, the vertical resolution and the prescribed subsidence rate. For the former, we focus here on the role of natural GCCN, due to their overall small concentration but potentially strong impact on drizzle formation. For the middle, the vertical resolution of the model is known to have a substantial influence on the representation of entrainment mixing at cloud top . This is expected to modulate the rate of evaporation of cloud droplets due to the entrained dry air from above the cloud, which affects the mean droplet size and the size distribution width and, therefore, drizzle formation via the collision–coalescence process. Lastly, the subsidence rate is known to impact precipitation formation due to effects on cloud thickness and, thus, droplet growth . Pilot model simulations are performed to test the corresponding choices made in our simulation setup.

First, Fig.  illustrates the effect of GCCN concentration on the simulated precipitation in pilot experiments. With 1cm-3 (used in the experiments), we obtain a precipitation rate much closer to the observed estimate than with a lower concentration (0.1cm-3). Similar concentrations of GCCN were also measured in the field campaign according to J15, and the good agreement with the observed precipitation rate (0.04mmh-1) warrants the use of the background aerosol size distribution detailed in Table 1.

Second, Fig.  shows the effect of vertical resolution on the simulated precipitation rate. It is evident that 20 m spacing in the model vertical grid yields a lower precipitation rate, than the simulations with 5 or 10 m grid spacings. That said, the difference seen between 5 and 10 m grid spacings is minor. Even though 10 m resolution has been shown to be inadequate to fully represent the effects of entrainment mixing , considering this result and the fact that the UCLALES-SALSA is computationally a rather expensive model, we find that the 10 m vertical grid spacing is justified.

Third, Fig.  presents the precipitation rate with the large-scale divergence rate selected for our simulations 3.75×10-6s-1; and a higher value representing stronger subsidence 8.0×10-6s-1, as in. The results indeed indicate that the precipitation rate is quite sensitive to the subsidence, similar to , and that the lower setting yields precipitation rates much closer to the measurements reported in J15.

Figure  shows the flux of precipitating water sampled at an altitude of 300 m, which is close to the cloud base height (around 250 m after the seeding). In the control case, the precipitation rate is approximately 0.03–0.05 mmh-1, which agrees well with the corresponding measured precipitation rate in J15. It is evident that the seeding emission rate and seeding strategy have a strong influence on the seeding efficiency. The experiment Seed1 (with a low emission rate) yields a positive but rather weak signal in terms of the precipitation flux. Instead, Seed2 (with high emission rate) approximately doubles the precipitation flux within an hour after the start of the seeding, compared to the control run. Likewise, an even stronger (by a factor of 3) increase in precipitation is shown by Seed3, where the initial seeding concentration is the same as in Seed1, but the total injected mass is much larger because it is applied to all grid points across the target layer. Therefore, it is important to consider the impact of the seeding strategy on the mixed plume concentration.

Figure  shows the estimated domain mean profiles of the seeding particle concentration. Since the seeding takes place in cloud, practically all the particles are activated very quickly. Therefore, the concentration is analysed using the number of cloud droplets activated by the seeding particles, 15 min after the seeding. This gives the plumes some time to mix; with further delay, the plume concentration starts to be more and more affected by precipitation, after which it is difficult to robustly distinguish the particles associated with seeding in our modelling setup. Moreover, taking the profile as domain average is justified because the trajectory of the source in Seed1 and Seed2 is set to cover the entire width of the domain in the y direction, as depicted in Fig. , and it takes approximately 10–15 min after the seeding injection for the turbulent diffusion to spread the seeding particles across the domain area. As indicated in Fig. , clearly the highest average concentration is seen for Seed3 and the lowest for Seed1, which indeed emphasizes the connection between the plume concentration and the seeding effects. The mean of the Seed2 profile in Fig.  suggests that in order to produce an approximately 2-fold precipitation yield, the concentration of seeding particles mixed in the cloud layer should be on the order of 0.01cm-3.

As briefly discussed in Sect. 3.4, modelling precipitation is sensitive to various aspects of the model setup and the initial conditions, which yield uncertainties in the simulations. These uncertainties are thus part of the estimated seeding effects as well, which we test based on the ensemble simulations performed using the Ctrl and Seed2 configurations, varying the input boundary-layer moisture content and the large-scale subsidence rate. Figure  shows the absolute and relative precipitation enhancements between the two model configurations for each ensemble member. The seeding effects are somewhat sensitive to the boundary-layer moisture content, with the absolute precipitation enhancement increasing with increasing moisture (and the overall precipitation rate). In terms of the relative enhancement, the conclusion is nearly opposite, with the largest relative enhancement seen with the driest boundary layer (associated with low precipitation rates). Considerably less sensitivity is found to varying subsidence within the ±10% range, although the precipitation rate did show sensitivity to larger changes in subsidence (Fig. ).

The model simulations tend to overestimate the liquid water content (LWC) compared to the observed values: as indicated in Fig. , the simulated LWC is around the 0.14–0.15 gm-3 range near the cloud base, while the corresponding estimate in J15 is 0.09 gm-3. However, both our simulations and the reports in J15 indicate quite substantial variability in these values, and the result varies strongly depending on how deep into the cloud layer the sampling is performed. The layer at 300 m is chosen for sampling, which is close to cloud base but remains consistently in cloud. Figure  suggests an increasing reduction in LWC with increasing seeding emission, which is qualitatively in agreement with the findings in J15. Further, the simulated CDNC shown in Fig.  is within the range, albeit slightly above the mean, reported by J15 around the time of the seeding (simulated mean approximately 180 cm-3 vs. the observed mean 162 cm-3), although again the variability is substantial in both estimates. The model CDNC shows a decreasing slope, which we attribute mainly to cloud processing and the gradual scavenging of the CCN particles (there is no replenishment of aerosol in our simulations). The seeding experiments show a clear decrease in CDNC compared to the Ctrl configuration. However, in the model the effect is not as strong as the decrease reported in J15 (i.e. from 162 to 77 cm-3 near cloud base).

The main hypothesized pathways to precipitation enhancement via hygroscopic seeding in warm low-level clouds include (1) the reduction of CDNC due to increased competition for water vapour induced by the large seeding particles and (2) enhanced collision–coalescence . Thus, to better understand the reasons for the simulated precipitation enhancement shown in Fig. , we will analyse more closely the cloud microphysical effects induced by the seeding.

To start with, our model shows very little change in the in-cloud supersaturation between the experiments, as shown in Fig. , sampled 15 min after seeding. As most of the ambient aerosol is activated close to the cloud base at the level of the peak supersaturation, Fig.  gives the first indication that the seeding effect through water vapour competition is likely of minor importance in our simulations. In order to find proof for this, we analyse the microphysical process rates. The process rates exhibit substantial spatial and temporal variability, so they are analysed using the ensemble simulations, taking the mean across the ensemble members. Figure  shows the ensemble mean relative changes between the Ctrl and Seed2 configurations for the rates of cloud activation, autoconversion and accretion. Note that the latter two are calculated directly by the coagulation scheme of UCLALES-SALSA and therefore the rates are diagnosed during model runtime as the water mass transferred from cloud droplet bins to drizzle/precipitation bins and as the mass collected by the drizzle and raindrops from other liquid droplet size classes. Consequently, since these processes are not described by dedicated parameterizations in our model, the corresponding rates are most likely not directly comparable with results from other microphysics schemes that do employ dedicated parameterizations. Nevertheless, Fig.  generally corroborates the interpretation suggested by the supersaturation profiles: the cloud activation rate shows only a modest decrease (by up to 6 %), which is gradually enhanced over the course of 2–3 h (almost until the end of the simulation). The gradual change hints that instead of a direct seeding effect via the water vapour competition, the difference is most likely caused by the enhanced scavenging of CCN particles between the Ctrl and Seed2 configurations. In contrast, the autoconversion rate shows a substantial and sharp increase at the time of the seeding (up to 30 %), which lasts for about half an hour. Afterwards, the accretion rate shows an increase in comparable magnitude, which indicates that after the peaked autoconversion rate, the effect of seeding is shifted from the collision–coalescence mode between cloud droplets to more of a droplet collection type of growth mode controlled by the existing drizzle-sized droplets and rain. The latter also shows a prolonged effect seen until the end of the simulation. Therefore, enhanced collision rate between droplets is most likely the main pathway for the seeding-induced precipitation enhancement according to the model results.

More details on the effects of seeding on the cloud microphysical properties are obtained by plotting the hydrometeor size distributions in the seeding experiments before and after the time of the seeding emission in Fig. . The size distributions are sampled in cloud at 300 m altitude, close to the cloud base height. While the size distributions show negligible changes in the experiment Seed1, in Seed2 and Seed3 there is clearly an increase in the concentration of droplets around the 100–200 µm size range after seeding. After 1 h, there is also a definite increase in the concentration of larger hydrometeors (>500 µm), pointing out the time needed for the seeding-induced drizzle drops to grow to raindrop sizes by collection processes. These features are similar to the corresponding observed size distributions presented in J15: similar to Fig. , the observed size distributions showed a clear increase in concentrations around the 100–200 µm range as well as in the sub-millimetre diameters after the seeding. The former corresponds to the expected size range for the transition between cloud droplets and drizzle. This is accompanied by a shoulder in the decreasing slope of the distribution both in the model and in the observations in J15. Here we find slight differences between the model and observations: in UCLALES-SALSA the transition range is found just below 100 µm whereas in J15 it appears to be closer to 200 µm. This also yields a difference in the magnitude of the seeding effect, which seems to be larger in J15. In addition, looking at the distribution slope for cloud droplets, UCLALES-SALSA indicates a slightly more peaked distribution shape than the observations in J15. The more peaked shape is speculated to arise from the strategy for the cloud droplet bin representation chosen in UCLALES-SALSA (described in Sect. 2). Nevertheless, the marked qualitative similarity between the model seeding effects and the results in J15 is a very encouraging result and provides strong support for UCLALES-SALSA being able to capture the primary microphysical pathway for the hygroscopic seeding effects on precipitation in the case examined.

To close the connection between the microphysical effects and precipitation, Fig.  shows the contribution to the overall precipitation flux as a function of size. The data in Fig.  are obtained from the same height level as in Fig. . As expected, enhanced precipitation due to seeding first takes place by the drizzle size ranges (about 100 µm) and later by the growth of the larger raindrops. The latter is strongly associated with the peak precipitation flux seen 1–1.5 h after the seeding emission in Fig. , especially in the experiment Seed3.