Clouds and precipitation are an integral part of the atmospheric system relevant for weather and climate. Considerable uncertainty remains in our understanding and modelling of clouds and their interaction with other parts of the climate system. The main issues are an incomplete physical understanding of cloud microphysical processes, a lack of quantitative formulations representing microphysical processes on model grid scales which are typically several orders of magnitude larger than the process scales, and the many non-linear interactions between different components of the system. In recent decades, the modification of cloud properties by aerosols has received particular attention, as anthropogenic aerosol emissions have changed strongly over the historic period.

Many modelling studies have investigated the impacts of an aerosol change on either isolated clouds or larger cloud fields but found different responses of the studied clouds depending on environmental conditions, model formulations, duration of simulations, and domain size recent reviews by. Recent studies have highlighted that it is necessary to simulate entire cloud fields over long periods in order to quantify a climate-relevant aerosol signal e.g. due to interactions between clouds and their thermodynamic environment. These interactions can at least partly compensate for the large changes simulated for individual clouds e.g.. In a case study of tropical deep convection, found that locally invigorated convection in polluted conditions induces stronger large-scale subsidence resulting in an overall suppression of precipitation on a cloud-system scale. demonstrated with simulations extending over three summer seasons that aerosol perturbations can produce large local changes in precipitation, while not significantly changing the mean precipitation.

The highly non-linear nature of convective cloud dynamics and microphysics calls for the use of large ensembles due to a potentially rapid growth of small perturbations to the system e.g.. While the importance of predictability limits has been acknowledged in weather forecasting, its implications for the evaluation of cloud microphysics parameterisations or the quantification of aerosol–cloud interactions has only been acknowledged in a few studies . To our knowledge, the first study to highlight the importance of intrinsic predictability for cloud microphysics evaluation and aerosol–cloud interactions is . Along with changes to various parameters in the cloud microphysics, cloud–radiation interaction, and CCN number concentrations, they applied random perturbations to the large-scale forcing, the surface fluxes, and nudging timescale in their 2-D simulations of deep tropical convection. investigated the sensitivity of convective clouds over the ARM Southern Great Plains site to the choice of cloud microphysical parameterisations and perturbed initial conditions. While they found the mean hydrometeor profile and cloud fraction to be strongly dependent on the chosen cloud microphysical scheme, the variability of cloud fraction, precipitable water, and surface precipitation induced by different microphysical schemes was similar to those resulting from perturbed initial conditions. In a similar modelling framework to , also applied random perturbations to simulations of deep tropical convection based on the Tropical Warm Pool International Cloud Experiment. They found a large variability in top-of-atmosphere radiative fluxes between ensemble members generated by modest perturbations to the boundary-layer temperature structure. In this case, therefore, a large ensemble with 240 members was required to retrieve a robust aerosol-induced signal in the top-of-atmosphere radiative fluxes. In their ensemble, surface precipitation was insensitive to aerosol changes. The simulations in these studies use large-scale forcing time series, which provide realistic time variations in forcing, but do not allow for a two-way interaction of the clouds with the large-scale forcing. While this avoids the even larger complexity of cloud-induced changes to large-scale circulation, it is ultimately necessary to include this interaction in order to quantify the impact of uncertainties in cloud microphysical processes or changes in aerosol concentration on the atmospheric system.

The relative importance of meteorological and aerosol conditions for cloud properties also has implications for obtaining observational evidence of aerosol–cloud interactions. Many observational studies of aerosol-induced changes in cloud properties need to rely on correlations between bulk parameters e.g., which raises the question of co-variability and coincidence e.g.. The importance of cloud dynamics in observational datasets has recently been demonstrated by . The study analysed the correlation of aerosol, cloud dynamics, and a range of cloud properties for shallow warm-phase clouds over the ARM Southern Great Plains site. They showed that the variability of cloud radiative properties was dominated by cloud dynamics rather than cloud microphysical properties.

One approach to investigate the role of intrinsic predictability and the relative importance of aerosol and meteorological variability is the use of convection-permitting ensemble systems. Ensemble forecasting is now an important component of operational forecasting and is increasingly used at convection-permitting or even higher spatial resolutions e.g.. The use of convection-permitting ensemble forecasts provides a means for assessing the magnitude of aerosol-induced changes in the context of variations in the cloud and precipitation evolution due to perturbations in the meteorological conditions, which are consistent with the uncertainty in available meteorological observation. Besides offering insight into the questions of robustness and observability of aerosol-induced changes, the ensemble approach explores whether perturbations of the aerosol environment should be included in future forecasting systems for quantitative precipitation forecasts.

In the present study, we investigate the robustness and relative importance of aerosol-induced changes in mixed-phase, sea-breeze-related convective cloud in high-resolution ensemble simulations with perturbed meteorological and aerosol initial and lateral boundary conditions. The case was selected from the COnvective Precipitation Experiment (COPE) that was conducted over the southwestern peninsula of the UK in 2013 . On the selected day (3 August 2013) deep convective clouds with maximum cloud top heights of about 5 km developed in the late morning along converging sea-breeze fronts. The line of convective clouds remained roughly stationary along the main axis of the peninsula until the late afternoon. Generally, new cells formed at the southwestern tip of the peninsula and merged into larger cloud clusters while propagating northeastwards along the line. Simulations of this case were conducted with the Unified Model (UM) at a spatial resolution of 250 m using the newly developed Cloud–AeroSol Interacting Microphysics (CASIM) module . The comparison of the baseline simulation with observational data and the sensitivity of cloud properties to aerosol perturbations was presented in the first part of this study and is briefly summarised here: increasing aerosol concentrations suppress precipitation in the morning. With progressing organisation of the clouds along the sea-breeze fronts, the response transitions into precipitation enhancement. In the early phase, precipitation decreases continuously with aerosol concentration (0.1 to 30 times the observed value), while in the afternoon the largest accumulated precipitation occurs with the observed aerosol profile. Limitations on cloud deepening from a mid-tropospheric stable layer were hypothesised to inhibit a further increase in precipitation for aerosol number concentrations larger than the observed values. Vertical velocities increase in the convective core regions with aerosol concentrations. However, contrary to the convective invigoration hypothesis e.g., changes in latent heat release are dominated by changes in the warm-phase part of the cloud with very small changes above the 0 ∘C line. It was hypothesised that accompanying changes in the cloud field structure (fewer, larger cells with increasing aerosol) were important for the changes in latent heat release from condensation.

In this paper, we extend the analysis of by including simulations with perturbed meteorological conditions in the analysis. With the combined perturbed meteorology and aerosol initial condition ensemble we investigate whether the aerosol-induced changes are (i) robust to and (ii) significant relative to small changes in the meteorological initial conditions. The paper is structured as follows: Sect.  provides details on the model set-up and observational data used in this study. The ensemble simulations are compared to observational data in Sect. . In Sect. , we discuss the variability of cloud properties in the perturbed meteorology-only ensemble, while the impact of aerosol perturbations on clouds and precipitation for individual ensembles members is assessed in Sect. . Finally, the results from the full ensemble, i.e. including perturbations to meteorology and aerosols, are presented in Sect. . The findings are summarised in Sect. .

The initial condition ensemble discussed in this paper is constructed by downscaling selected members from the operational global ensemble system of the Met Office (MOGREPS, ) over the southwestern peninsula of the UK. The global model ensemble is recomputed from the Met Office operational analysis and initial condition perturbation for 18:00 UTC on 2 August 2013. The global model version and set-up used for the operational forecast in 2013 are employed for the rerun (UM, version 8.2, PS31 configuration, N400 resolution, i.e. ≈33 km in mid-latitudes). This includes stochastic physics as described in . The control run (no initial condition perturbations applied) and nine global ensemble members provide the initial and boundary conditions for the higher-resolution regional simulations. The control run is included in the term “ensemble members” if not stated differently. The selection of the ensemble members for dynamical downscaling is based on the time series of moisture convergence and moist static energy convergence computed over the regional model domain from the global model fields (Fig. ). These time series are then used to construct a similarity matrix by summing the Euclidean distances of moisture convergence and moist static energy convergence. Using the algorithm by nine clusters are defined and from each cluster the closest member to the mean cluster time series is chosen for downscaling. Note that, while this procedure provides a sampling of different time series, it does not necessarily retain the statistical properties of the global ensemble. It is known that convection-permitting ensembles constructed by downscaling global ensemble members do not represent the mesoscale error characteristic correctly e.g.. As a result convection-permitting ensemble forecasts are often under-dispersive e.g.. Our high-resolution ensemble will hence represent some unknown fraction of the true meteorological uncertainty for the studied day. Most likely the meteorological uncertainty is underestimated in the current study. Although the ensemble selection and initialisation of the ensemble should be improved in future studies, we do not think that this is a strong caveat to our main conclusions.

Regional simulations with a grid spacing of 1 km (500 by 500 grid points) are started at 00:00 UTC on 3 August 2013 from the 10 selected global model runs. These simulations provide the initial and boundary conditions for simulations in a second set of nested simulations with a horizontal grid spacing of 250 m (900 by 600 grid points). For the regional simulations, we use the UM version 10.3 (GA6 configuration, ) with the CASIM module. In contrast, to the global ensemble, we do not use the stochastic physics module for the regional ensemble, as we aim to investigate the role of initial condition uncertainty. The model set-up for the regional simulations is identical to the set-up described in . The control simulations are identical to the simulations used in , with the only difference being that the simulations discussed here use the cloud droplet number predicted by CASIM instead of a prescribed value for the computation of the radiative fluxes. Note that the aerosol direct effect is not included in the simulations. In all regional simulations, moisture conservation is enforced according to . All simulations are run for 24 h. If not stated otherwise, the analysis presented in this paper focusses on the time period between 09:00 and 19:00 UTC, i.e. the time period of main convective activity. Also note that ensemble members have been sorted according to the large-scale moisture convergence computed from the fluxes at the domain boundary: ensemble member 1 has the largest large-scale moisture convergence and ensemble member 9 the smallest.

Cloud microphysical processes are parameterised within the CASIM module which in this study is configured as a double-moment microphysics scheme with five different hydrometeor categories. The CASIM module can represent the interactions between aerosol fields and cloud microphysical properties. For the ensemble simulations, we use the so-called “passive-aerosols” mode: aerosol fields are used for droplet activation and ice nucleation, but are not altered by cloud microphysical processes. The impact of this choice on the representation of aerosol–cloud interactions is discussed in . Aerosol initial and lateral boundary conditions are derived from aircraft data as described in . In the following, simulations with the aerosol profile derived from observations are referred to as “standard-aerosol” simulations. Additional simulations of each ensemble member are performed with perturbed aerosol profiles, for which aerosol number densities and mass mixing ratio are multiplied at all altitudes by a factor of 10 (“high aerosol”) and 0.1 (“low aerosol”), respectively. Hence, the mean aerosol radius is retained in the perturbed profiles. Accordingly, the entire ensemble with perturbed meteorological and aerosol initial conditions has 30 members in total.

For the evaluation of the ensemble with the standard-aerosol profile, we use the same set of observations as in the first part of this study. These include radiosonde and aircraft data from the COPE field campaign and data from the operational radar network. Details about these datasets can be found in .

Given the overall similar meteorological situation in the ensemble members, i.e. a line of convective clouds forming along sea-breeze convergence zones, the main impact of the perturbed meteorological initial conditions should be (i) perturbations to vertical lifting and hence condensation and (ii) the vertical cloud structure by modifications to the vertical wind shear and the thermodynamic profiles. The discussion in this section focusses on the meteorological ensemble with the standard-aerosol profile. Differences in the large-scale moisture convergence, upstream thermodynamic profiles, and sea-breeze strength are discussed in Sect. . The resulting variation in cloud properties is described in Sect. .

The simulation of each meteorological ensemble member was conducted with three different aerosol profiles: a so-called standard-aerosol scenario, which was derived from aircraft observations; and low- and high-aerosol scenarios, which have a factor of 10 lower and higher aerosol number concentration, respectively. The impact of the perturbed aerosol profiles on cloud and cloud field properties as well as precipitation formation in the control simulation has been discussed in the first part of this study. In this section, we compare the aerosol signal in the different meteorological ensemble members, i.e. the difference in realisations with different aerosol scenarios but identical meteorological initial and boundary conditions. Therefore, we test the robustness of aerosol-induced changes to small perturbations in the meteorological conditions. To quantify the significance of aerosol-induced changes we use a two-sided t test for ensemble members paired according to meteorological conditions (Table 1). Using paired ensemble members reflects the interdependence of cloud properties in realisations with different aerosol but identical meteorological initial and boundary conditions. Significance is tested at the 5 % level.

In the previous two sections, the response of cloud properties to perturbations of the aerosol or meteorological initial and boundary conditions has been discussed separately. The 10 meteorological ensemble members vary in the large-scale moisture convergence, thermodynamic profile, and wind shear. The variation in the large-scale moisture convergence is most important for the cloud field properties, e.g. cloud fraction, cell number, condensate generation, and accumulated precipitation (Sect. ). The mean cloud top height varies between ensemble members according to the different thermodynamic profiles. Aerosol-induced changes follow a similar pattern for each meteorological ensemble member (Sect. ). An increase in aerosol number concentration translates to a larger CDNC, mean cell area, and outgoing shortwave radiation, while the cell number and precipitation efficiency decrease with increasing aerosol concentrations. The mean cloud top height, condensate generation, and outgoing longwave radiation display only very small changes in response to altered aerosol concentrations. To detect aerosol-induced changes in cloud properties or precipitation formation with observational datasets, it is important to separate changes resulting from different meteorological conditions from changes resulting from different aerosol concentrations. This is necessitated by the co-variability of aerosol and meteorological conditions in the real atmosphere. The question of the relative importance of meteorological and aerosol initial and boundary conditions for the cloud field structure and precipitation formation is also important for operational numerical weather prediction and the future design of ensemble prediction systems. Here, we use the combined meteorological and aerosol initial condition ensemble, i.e. combining the discussion of the two previous sections, to address the question of the relative importance of aerosol and meteorological variability for the COPE case. The discussion will focus on changes in the 10 h mean properties of the cloud field between 09:00 and 19:00 UTC. The mean value of the considered variable is displayed along with its spread from the meteorological ensemble members on the right side of Figs. – for each aerosol scenario (different colours). If instantaneous realisations of the different (domain-averaged) variables were to be considered (box plots on left side of the figures), the variability would be much larger than suggested by the domain-mean time-averaged plots (right side of the plots). For a quantitative assessment we use the p values from two-sided t tests for the full ensemble, i.e. not pairing ensemble members according to the meteorological initial conditions as in Sect. .

The cloud droplet number concentration at either cloud base or cloud top is strongly influenced by the assumed aerosol scenario but varies little between the different meteorological members (Figs. , S9a). As a result, a clear aerosol signal remains present even when the meteorological variability is taken into account. The aerosol-induced CDNC change remains highly significant at the 5 % level in the unpaired tests (Table 1).

Although there is a stronger meteorology-induced variability in the cell number and mean cell size (Fig. ) and the predicted range of values overlap for different aerosol scenarios, the aerosol signal is clearly detectable in these variables and aerosol effects remain significant also in the unpaired test (Table 1). However, if the cloud fraction, the mean cloud top height, or the distribution in different cloud top height classes is considered, the meteorological variability dominates (Figs. , ). Hence, changes in cloud fraction, mean cloud top height, and deep cloud fraction are not significant at the 5 % level, if ensemble members are not paired according to meteorological conditions (Table 1). Considering previous arguments on convective invigoration, it is interesting to note that the cloud top height varies only very little with aerosol scenario but is sensitive to relatively small changes in meteorological conditions. Consistent with the small changes in cloud top height, no significant differences in outgoing longwave radiation exist between the aerosol scenarios (Fig. b, Table 1). For the outgoing shortwave radiation a stronger aerosol signal is retained above the meteorological variability due to the large impact of aerosol concentrations on CDNC (Fig. a). However, this signal is not statistically significant for an aerosol increase beyond the standard-aerosol scenario (Table 1).

Precipitation formation is known to be strongly influenced by dynamical and microphysical processes. used an analysis of the water budget to separate the contributions from cloud dynamics and microphysics to aerosol-induced changes. As expected, condensation ratio CR and condensate gain G vary strongly between different meteorological ensemble members, but show little sensitivity to the aerosol scenario (Figs. a, S14a and b). The small dependency of the condensate gain on the aerosol number concentration may be a result of using a saturation adjustment scheme for the condensation in our model. Previous studies using a prognostic supersaturation found the condensation rates to be dependent on the CDNC number concentration e.g.. However, due to the thermodynamic constraints on integrated condensation, we do not expect this will have a strong impact on the overall behaviour of the condensate gain. In contrast to CR, the precipitation efficiency displays a relatively small systematic dependency on the large-scale moisture convergence and a large dependency on the aerosol scenario (Fig. a). However, the condensate loss L varies strongly across meteorological ensemble members due to its close relation with the condensation gain (Fig. S15). This co-variability is discounted for in PE. However, still only the aerosol-induced PE change between the standard- and high-aerosol scenario is significant at the 5 % level for unpaired ensemble members.

The aerosol-induced change in accumulated precipitation is the combined result of the changes in condensation ratio and precipitation efficiency. While the accumulated surface precipitation in most meteorological ensemble members decreases with increasing aerosol scenario, these differences are much smaller than the variability of accumulated surface precipitation between meteorological ensemble members (Fig. S11b). The meteorological variability is due to large differences in the condensate gain, which is directly related to the variability in large-scale moisture convergence. The aerosol signal is much larger for an increase in the aerosol concentrations beyond the standard-aerosol scenario due to a significantly larger change in the precipitation efficiency. The mean precipitation rate behaves qualitatively very similarly to the accumulated precipitation (Fig. a). Consistently, neither changes in mean precipitation rate nor accumulated precipitation are statistically significant (Table 1).

The ensemble-mean condensed water path increases with increasing aerosol concentrations, if all hydrometeor types are considered (Fig. b). However, the liquid water path (condensate in the cloud and rain category) shows relatively little sensitivity in its median value, while the mean liquid water path generally decreases with increasing aerosol concentrations (Fig. S13a). The frozen water path increases with increasing aerosol concentrations for most ensemble members (Fig. S13b), which is consistent with a longer timescale for precipitation formation. The aerosol-induced changes in both variables are much smaller than the variability induced by different meteorological initial and boundary conditions and are hence not significant at the 5 % level (Table 1).

High-resolution ensemble simulations (Δx=250 m) with perturbed aerosol and meteorological initial and boundary conditions were performed for convection forming along sea-breeze convergence zones over the southwestern peninsula of the UK. The relative importance of perturbations in meteorological (10 members) and aerosol initial conditions (three for each member) for various cloud properties and precipitation formation is analysed over a forecast lead time of 10–20 h. The 10 different meteorological ensemble members develop similar mesoscale flow patterns with a sea-breeze convergence zone establishing over the centre of the peninsula. As a result of the different lateral boundary conditions, the large-scale boundary-layer moisture convergence and the accumulated condensate gain vary by a factor of 2 and the accumulated surface precipitation by a factor of 2.5 between ensemble members. The average cloud fraction differs by up to 0.1 between the meteorological ensemble members. This meteorological variability is compared to changes in cloud properties induced by a factor of 10 increase and decrease in aerosol number concentrations relative to the standard scenario. While the perturbations to the meteorological initial conditions reflect at best the uncertainty for the investigated case, changes in aerosol number concentration by a factor of 100 are probably even larger than what could be expected for the climatological variability.

Changes in aerosol concentrations can potentially modify cloud field properties, e.g. cell number and size, cloud depth, cloud fraction, and the domain-wide condensate budget (condensate gain and loss, precipitation rate). Aerosol-induced changes are consistent across the ensemble, suggesting that the physical mechanism discussed by is robust against small changes in meteorological initial conditions. The variability of cloud field properties across the ensemble is summarised in Fig. . The possibility of discerning aerosol-induced differences in various cloud metrics relative to realistic meteorological variability is assessed in the following. First, the idealised situation where the meteorological initial conditions are identical for different aerosol perturbations is assessed by pairing ensemble members according to the meteorological initial conditions. This is equivalent to testing the statistical significance of the differences between realisations with different aerosol scenarios and identical meteorological initial and boundary conditions. For the paired ensemble members, a factor of 10 increase or decrease in aerosol concentrations introduces statistically significant changes (at the 5 % level) in CDNC, cloud fraction, cell number and size, outgoing shortwave radiation, instantaneous and mean precipitation rates, and precipitation efficiency (Table ). Note that the statistical analysis is based on a very small sample, which affects the validity of several assumptions. However, since the statistical results agree qualitatively with the physical analysis, we use the significance values as a helpful diagnostic for summarising the results. Aerosol-induced changes in accumulated precipitation are only significant for an increase in aerosol concentrations beyond the standard scenario. An analysis of the condensed water budget suggests that for a decrease in aerosol concentrations, a smaller condensation ratio is balanced by an increasing precipitation efficiency. In contrast, for higher aerosol concentrations than in the standard scenario, the precipitation response is dominated by a strong decrease in precipitation efficiency with little change in the condensation ratio due to the thermodynamic constraints on cloud top height.

Secondly, we can use the simulations to assess our ability to discern aerosol–cloud effects for the situation where meteorological initial and boundary conditions are similar but subject to observational uncertainty. This would represent a “perfect” observational campaign where the meteorological conditions each day are only slightly different (convergence within a factor of 2) and large perturbations to aerosol concentrations occur (factor of 10–100). This scenario is replicated by analysing aerosol-induced changes in the full ensemble without pairing ensemble members according to meteorological initial conditions. For the unpaired ensemble, only aerosol-induced changes in CDNC, cell number and size, outgoing shortwave radiation, and precipitation efficiency are statistically significant (Table ). For some of these variables, the changes are significant only for a decrease or an increase in aerosol number concentration relative to the standard scenario. For all other investigated variables (cloud fraction, cloud top height, condensation ratio, domain-average precipitation rate, condensed water path, and liquid water path) the variability resulting from different meteorological initial and boundary conditions is equal to or larger than the aerosol-induced changes.

The ensemble data can be used for a rough estimate of the number of observations that are required for retrieving a robust aerosol signal from observational data for sea-breeze convection. For this analysis we assume (i) the aerosol scenario and meteorology are independent, (ii) the ensemble is representative of the meteorological variability, (iii) the meteorological variability can be described by a Gaussian distribution, and (iv) observational data are perfect. While it is difficult to a priori estimate the impact of these assumptions on the analysis, we expect the analysis to provide a lower limit of the required number of observations due to the following reasons: in contrast to assumption (i), aerosol and meteorological conditions are likely to be correlated e.g., reducing the observed section of the phase space. Secondly, the meteorological variability in the ensemble simulations is not representative of the climatological variability of meteorological conditions for sea-breeze convection over the southwestern peninsula of the UK, which can be assumed to be much larger . Lastly, observational data will not be perfect due to measurement errors and spatial and temporal sampling issues e.g.. All these issues will likely increase the number of required samples compared to the values suggested by our analysis.

With the assumptions listed above, a Gaussian distributions representing the meteorological variability is defined for the low- and the high-aerosol scenario. For each variable, the mean value across all ensemble members with the same aerosol scenario is used as the mean of the Gaussian distribution. The standard deviation σ of the Gaussian distribution is defined by assuming the value range (minimum and maximum) across the ensemble members equals 4σ (3σ and 5σ are tested as well). Then 104 realisations with n samples are drawn from the Gaussian distributions for the low- and high-aerosol scenario separately. The number of samples n can be interpreted as the number of times the same day is observed, as the statistical analysis presented here uses either daily average or accumulated variables. However, it may be possible to interpret the necessary number of observations also as number of individual observations, e.g. from satellite overpasses, if subsequent observations are not autocorrelated, i.e. are from different cloud lifecycles. If snapshots are used, it may be necessary to take into account the possibly different life cycle stages of the observed cloud field e.g.. However, given the limited number of ensemble members in our analysis, an assessment of this effect is beyond the scope of our study. For each of the 104 realisations, we test the hypothesis that the low- and high-aerosol scenarios are not equal with a two-sided t test. The resulting distribution of p values gives the probability that a significant aerosol-signal can be retrieved from a sample of n observations with low- and high-aerosol conditions each (Fig. S16). The number of days required to have a 95 % chance of observing a significant aerosol-induced change in various cloud properties is listed in Table . This required number of observations only gives an approximate indication, as the exact number is sensitive to the assumptions made regarding the presentation of the meteorological variability in the ensemble, e.g. whether the ensemble spread corresponds to 3σ, 4σ, or 5σ. It is important to note that the statistical analysis has the strong caveat of being based on a rather small ensemble. To obtain robust statistics a much larger ensemble with several hundreds of ensemble members would be required, which is currently beyond the computational resources available. However, we think the analysis provided here gives some general indication of the scale of observations required as the statistics confirm the impressions gained from the physical analysis of the ensemble members. Our analysis indicates that a small sample n≤10 is sufficient for variables such as the CDNC and outgoing shortwave radiation, while a large sample often exceeding 100 is required for variables such as cloud fraction, cloud top height, or accumulated precipitation. The number of samples required depends on the amplitude of the aerosol perturbation (factor of 100 between low- and high-aerosol scenario, factor of 100 between the low- (high-) and the standard-aerosol scenario) as well as the location in the aerosol space (different for increase or decrease relative to the standard-aerosol scenario). In general, more observations are required for an increase in aerosol number concentrations above the standard scenario, which is related to the thermodynamic constraints on aerosol-induced changes in the considered case discussed in . The only exception is accumulated surface precipitation, for which fewer observations are required for an increase above the standard scenario. This reflects the larger aerosol-induced signal in accumulated precipitation for increased compared to decreased aerosol concentrations.

While the meteorological ensemble allows us to put the aerosol-induced changes in cloud properties into the context of changes related to meteorological variability, the considered changes in meteorology are fairly small (Sect. ). Even if the represented meteorological variability is assumed to be representative of all possible meteorological conditions on the investigated day, they do not cover the full range of meteorological conditions that could occur for convection along sea-breeze convergence zones. However, even this very conservative estimate on the meteorological variability is for many variables on the same order of magnitude or larger than the aerosol-induced changes. We expect that the number of samples required to retrieve a statistically robust aerosol-induced change would increase if the climatological variability of the meteorological conditions is considered.

The results presented in this paper certainly only pertain to the specific cloud type investigated and the relative magnitude of aerosol- and meteorology-related changes in cloud properties may be different for other cloud types. This will be investigated in future studies. In addition to the results presented here, some previous studies have highlighted the importance of considering the intrinsic predictability of investigated cases before drawing conclusions about the significance of aerosol-induced changes in cloud properties . These studies used prescribed large-scale conditions and applied random perturbations to thermodynamic fields throughout the simulations. The present study complements their analysis by considering the impact of changes in the large-scale conditions, which are small compared to observational uncertainties and much smaller than the expected variability in meteorological categories used to retrieve aerosol signals from general circulation models e.g.. Consistent with previous studies, we find that the aerosol signals in variables closely related to aerosol concentrations, such as cloud droplet number concentrations, are easier to retrieve than for variables that are linked to aerosol concentrations by a series of complex processes, such as accumulated surface precipitation. From the limited number of studies available, the set of variables in either category appears to vary for different cloud types and geographic location. However, our and previous studies all suggest that aerosol-induced change in surface precipitation is very difficult to retrieve reliably e.g..

The evidence presented in the to-date very limited number of studies considering the relative impact of meteorological and aerosol conditions on cloud properties suggests that it is crucial to carefully consider intrinsic predictability, meteorological conditions, and co-variability between aerosol and meteorological conditions in modelling and observational studies of aerosol indirect effects. While these aspects have been highlighted by and , only a few modelling studies have investigated these aspects and there is a clear need for future studies extending the analysis to other cloud types and meteorological scenarios. An improved knowledge and quantification of these aspects is mandatory for progress in our understanding of aerosol-induced changes in cloud properties and for retrieving observational evidence thereof.