This work uses the number concentration-effective diameter phase-space to test cloud sensitivity to variations in the aerosol population characteristics, such as the aerosol size distribution, number concentration and hygroscopicity. It is based on the information from the top of a cloud simulated by a bin-microphysics single-column model, for initial conditions typical of the Amazon, using different assumptions regarding the entrainment and the aerosol size distribution. It is shown that the cloud-top evolution can be very sensitive to aerosol properties, but the relative importance of each parameter is variable. The sensitivity to each aerosol characteristic varies as a function of the parameter tested and is conditioned by the base values of the other parameters, showing a specific dependence for each configuration of the model. When both the entrainment and the bin treatment of the aerosol are allowed, the largest influence on the droplet size distribution sensitivity was obtained for the median radius of the aerosols and not for the total number concentration of aerosols. Our results reinforce that the cloud condensation nuclei activity can not be predicted solely on the basis of the

Because of their role as cloud condensation nuclei (CCN) and ice nucleating particles, aerosols can affect the cloud optical properties

Many studies have been dedicated to quantifying the effect of aerosols on clouds via sensitivity calculations, using both modeling and observational approaches. Knowing the real values of each parameter that characterize the aerosol is difficult. Furthermore, detailed modeling of droplet nucleation implies a high computational cost. Thus, sensitivity studies intend to determine whether the variability of some characteristics of the aerosol population can be neglected without introducing significant errors in the description of clouds.

A major debate refers to the relative importance of aerosol composition with respect to size distribution and total number concentration

To further evidence the importance of aerosol composition on clouds,

Previous research investigating the aerosol effect on clouds has employed adiabatic parcel models to perform multiple sensitivity calculations

Moreover, most previous studies are based on the information from cloud base. However, given the possibility of the occurrence of cloud-top nucleation

Another feature that is relatively common in cloud physics modeling studies is the treatment of aerosol species as a single-moment bulk variable, i.e., considering only one bin for the

With an ample water vapor supply, high temperatures and a wide spectrum of aerosol conditions, the troposphere over the Amazon constitutes an ideal scenario for the study of aerosol–cloud–precipitation interactions. The Amazonian clouds that form during the wet and transition seasons are found to be very sensitive to aerosols

Here we propose to explore the cloud sensitivities to several aerosol properties, by simulating some characteristics of Amazon clouds. We focus on the information from cloud top, during the warm stages of cloud life-cycle, using a sample strategy that also includes the information from the cloud base at the initial stage of development of the cloud. Our approach is similar to

The simulations performed here employs variations of the Tel Aviv University (TAU) bin microphysics parameterization

In our simulations, a 1

As initial conditions, vertical profiles of potential temperature and water vapor mixing ratio (

Vertical profiles employed as initial conditions in the simulations.

The contribution of the entrainment in the equations for the evolution of

For the simulations performed in this work, we used the TAU size-bin-resolved microphysics scheme that was first developed by

In this version of the TAU microphysics (available at:

To account for changes in the PSD, we introduced a set of 19 bins for dry aerosols, with radii (

At a given temperature and supersaturation, the critical dry size (

The aerosol regeneration is included here following the approach of

This scheme provides a reasonable way to parameterize the aerosol regeneration without using a 2-D probability density function to track the aerosols. It does not consider the processing of the aerosols inside the cloud; therefore, it could induce errors in the activation rate in situations where the collision–coalescence process is a significant sink of small aerosols and a source of larger aerosols

We employ a phase space defined by two bulk properties of the DSD (hereafter “bulk phase space”):

Sensitivity tests in the bulk phase space provide a very efficient means of evaluating how a specific parameter variability can affect the evolution of cloud-top DSDs. Here, we test the sensitivity of

The choice of the intervals of values for the aerosol properties was made in a way that allowed for the exploration of the largest subset of realizable values of the parameters, while maintaining a reasonable computation time. For certain combinations of the size distributions parameters, the PSD can be very narrow, with a very small concentration of aerosols larger than the activation threshold. This configuration, along with a small

Due to a deficient treatment of the activation scavenging, when a bulk treatment of the aerosol is used, the lower values of the aerosol parameters at which a reasonably dense cloud can be generated are much smaller. By not allowing the PSD to freely evolve, there is a continuous, spurious source of large aerosols that induces unrealistically high values of

Aerosol parameters used for the sensitivity tests using bin and bulk approaches for the aerosol: intervals for values and steps between them. For additional details, the reader is referred to the text.

The sensitivities were calculated as the slope of the linear fit between

The latter differentiates our approach from previous studies.

The control run of the model produced a shallow cumulus that grew to a depth of 4000 m in about 30 min. Figure

Evolution of

The bulk phase space view is introduced in Fig.

Figure

Illustration of the sensitivity of cloud top bulk properties to

Note that the fraction of activated droplets in the first level is similar among all simulations in Fig.

Figure

The tests in Fig.

Finally, Fig.

To illustrate this sensitivity variation, we calculated

Figures

Sensitivities of the droplet number concentration and effective diameter to the aerosol number concentration,

Sensitivities of the droplet number concentration and effective diameter to the median radius of the PSD,

The impact of

Figure

The same applies to the sensitivity to

Sensitivities of the droplet number concentration and effective diameter to the geometric standard deviation of the PSD,

Sensitivities of the droplet number concentration and effective diameter to the aerosol hygroscopicity,

Note that

Finally, the sensitivity to

Despite the limited dynamical capabilities of our 1-D framework, here we adopted a simplified approach to consider the mixing between the in-cloud and environmental properties. We considered that the column in the model is located in the center of a plume with radius

Some cloud-top mixing is resolved in the model grid. However, it can be affected by the numerical diffusion and dispersion introduced by the scheme that solves the advective terms. The representativeness of the mixing induced by such an advection at cloud top must be analyzed carefully, and is outside the scope of this paper. For now, we limit our analysis to the results with and without the inclusion of some lateral entrainment rates, as a proxy for the effect of the dilution caused by mixing with the air in the neighborhood of the clouds.

By using bins for the aerosol, we allow the PSD to evolve freely. This way, after activation, the tail of the PSD can only be filled again if new particles are advected, entrained or replenished due to droplet evaporation. Furthermore, as the newly activated droplets fill several bins of the DSD, the development of wider DSDs is favored, accelerating collection processes. This method has been extensively employed

Figures

The values of the aerosol parameters in the tests without bins for the aerosols (third column in Figs.

Sensitivity of

Sensitivity of

Figure

When the entrainment is not considered,

Mean and standard deviation of

In Figs.

Furthermore, the absolute value of

Finally, it can be observed in Figs.

Overall, our analysis shows that increases in

The values of sensitivities reported by

From our analysis, it turns out that

For the first (and most complete) situation considered, it can be seen that the state of the system is not sufficiently determined by

In turn, Fig.

Conversely, the results indicate that the importance of

The simulations performed here represent an idealized cloud resulting from observed humidity and temperature profiles. However, even if we assume that it represents a realizable situation, corresponding to an average behavior, it does not include the variety of possibilities existing in real cases. Important processes such as turbulent entrainment and dynamic feedbacks can introduce a significant departure from the idealization we are considering. Full dynamical models account for dynamics feedbacks and several subgrid processes that could enhance or reduce the range of sensitivities that are demonstrated here. Nevertheless, the qualitative behavior of our main results, i.e., the dependency of the DSD sensitivity to the aerosol properties according to its position in the full parameter space, might not change. For example,

We illustrated the influence of the aerosol number concentration, the median radius and geometric standard deviation of the PSD, in addition to the hygroscopicity of the aerosols on the number concentration and effective diameter of droplets at the top of warm-phase clouds for initial conditions typical of the Amazon. The sensitivities behaved in according to the relation between the supersaturation and the aerosol availability, which determine the rate of aerosol activation, as described by

We showed that the sensitivity to each aerosol characteristic varies as a function of the parameter tested and its value depends on the base value of the other parameters. The median radius of the aerosols is the most important parameter, of those analyzed, which influences the sensitivity to the other parameters. This expands on the result of

Given the tested variations in the aerosol properties, the responses of the DSDs depend on the model assumptions regarding the entrainment and the treatment of the aerosol size distribution. This reinforces the importance of carefully considering the characteristics of the model when analyzing the responses to changes in aerosol loading in global or regional studies.

Overall, when nucleation is favored, an increase in the droplet number concentration is accompanied by a decrease in the droplet effective diameter. However, as our sensitivity analysis involves the evolution of the cloud top with time and height, the results are not directly comparable with previously reported sensitivity calculations at cloud base. When a series of consecutive nucleation events is considered, such as those during the evolution of the cloud top, the intensity of the nucleation at a certain time can modulate its intensity afterwards. The simulation with a bulk treatment of the aerosols constitutes an extreme case of slow aerosol depletion, where the responses of the nucleation to changes in the aerosol properties can impact the cloud top in a more homogeneous way. That is the reason for the agreement in the sensitivity obtained from those simulations and previous cloud-base sensitivity calculations.

The code for the modifications introduced in the KiD model, as well as in the TAU scheme, can be made available upon request from the corresponding author.

LHP performed the model simulations, the model–data analysis and prepared the paper. LATM and MAC provided guidance regarding the definition of the model initial conditions. LATM, MAC and MSG provided guidance regarding the choice of the variables and the interval of values and the model–data analysis. All authors contributed to the design of the study and the preparation of the paper.

The authors declare that they have no conflict of interest.

This research has been supported by the São Paulo Research Foundation (grant nos. 2015/14497-0, 2016/24562-6, and 2017/04654-6).

This paper was edited by Barbara Ervens and reviewed by two anonymous referees.