We present a novel method of exploring the effect of uncertainties in aerosol properties on cloud droplet number using existing cloud droplet activation parameterisations. Aerosol properties of a single involatile particle mode are randomly sampled within an uncertainty range and resulting maximum supersaturations and critical diameters calculated using the cloud droplet activation scheme. Hygroscopicity parameters are subsequently derived and the values of the mean and uncertainty are found to be comparable to experimental observations. A recently proposed cloud droplet activation scheme that includes the effects of co-condensation of semi-volatile organic compounds (SVOCs) onto a single lognormal mode of involatile particles is also considered. In addition to the uncertainties associated with the involatile particles, concentrations, volatility distributions and chemical composition of the SVOCs are randomly sampled and hygroscopicity parameters are derived using the cloud droplet activation scheme. The inclusion of SVOCs is found to have a significant effect on the hygroscopicity and contributes a large uncertainty. For non-volatile particles that are effective cloud condensation nuclei, the co-condensation of SVOCs reduces their actual hygroscopicity by approximately 25 %. A new concept of an effective hygroscopicity parameter is introduced that can computationally efficiently simulate the effect of SVOCs on cloud droplet number concentration without direct modelling of the organic compounds. These effective hygroscopicities can be as much as a factor of 2 higher than those of the non-volatile particles onto which the volatile organic compounds condense.

The Earth's weather and climate are both strongly influenced by clouds

In general, there is a positive correlation between aerosol number
concentration and cloud droplet number concentration (

A dominant factor influencing aerosol composition is the co-condensation of
semi-volatile organic compounds (SVOCs) onto CCN (

Depending on geographical location, between 5 and 90 % of total
aerosol mass can be composed of organic material

Multiple parameterisations of cloud droplet activation have been developed

In the case of involatile particles, the hygroscopicity depends solely on chemical composition and is independent of particle size. In environments that contain SVOCs, the hygroscopicity becomes more ambiguous. Due to the condensed mass of SVOCs depending on relative humidity, aerosol particles have chemical compositions and sizes that vary with the RH. Consequently, the properties of aerosol particles, including the hygroscopicity, change drastically as they rise in the atmosphere from subsaturated air into cloud.

In field measurements, atmospheric aerosol is passed through instruments
under subsaturated conditions in order to measure the size distribution and
composition

In Sect.

There are many sources of uncertainties discussed in this paper and, in order
to study their effect on cloud droplet formulation, we encapsulate the
uncertainty into a single parameter called the hygroscopicity. The
hygroscopicity parameter,

Both the critical diameter and supersaturation are dependent on the chemical
composition of the aerosol particles with less hygroscopic particles
requiring a larger supersaturation to activate, which also corresponds to a
larger critical diameter. Typically, the critical diameter and
supersaturation pairs are obtained from experiments

In this section we demonstrate how the parameterisations can be used to
calculate the uncertainty in

Particle sizes are assumed to follow a lognormal size distribution of the form

A schematic of the Monte Carlo method to
calculate the hygroscopicity,

In order to encapsulate the uncertainty in the measured size distribution in

The focus of this paper is on the effect of SVOCs
on the hygroscopicity and, consequently, a thorough analysis of the
sensitivity of

Mean and standard deviation of the size distribution parameters of the non-volatile particles.

To simulate the uncertainty in the solubility and dissociation we randomly
sampled the van 't Hoff factors from normal distributions with means, standard
deviations and maximum and minimum values stated in Table

Parameters of the normal distributions from which the van 't Hoff factors are sampled; the standard deviations are chosen to be 10 % of the mean. Randomly sampled values that lie outside of the range of the minimum and maximum are ignored.

Using the methodology described in Sect.

Our Monte Carlo simulation was run for 1000 different particle size
distributions, each of which were run at 10 different updraughts, evenly
distributed in log space from 0.01 to 10 m s

In Fig.

The mean values that our method calculate are in excellent agreement with
those given in Table

Growth-factor-derived hygroscopicity,

Growth-factor- and CCN-derived mean and uncertainties in

n/a

The volatile nature of SVOCs results in new pathways through which the SVOCs
affect

We introduce three single-parameter measures of the hygroscopicity that
incorporate the SVOCs in different ways. The first, which we denote by

In our model, we use the

Volatility distribution of SVOCs from

The range of effective material parameters used for the compounds in each volatility bin. Minimum and maximum values are stated as well as the mean and standard deviation of the normal distribution from which values are sampled.

A Monte Carlo simulation was carried out that calculated the range of

We first investigate the effect of uncertainty in these measurements on

Using the methods detailed in Sect.

Hygroscopicity including the SVOCs,

Hygroscopicity,

The influence of SVOCs reduces the hygroscopicity of ammonium sulfate,
sodium chloride and sulfuric acid. The hygroscopicity of levoglucosan is
largely unchanged, with only a very slight increase, due to its chemical
properties being very similar to that of the SVOCs and, consequently, the
mixing rule creates little difference between

We also calculated a range of hygroscopicities that include the initial
condensed mass of organic vapours at 50 % RH but do not consider any
co-condensation that would occur during ascent to cloud base. We denote this
as

Figure

The difference between

Hygroscopicity,

Effective hygroscopicity,

In this section, we suggest a potential method to include the effects of
SVOCs on cloud droplet activation in large-scale models that is
computationally efficient and does include the process of co-condensation as
the relative humidity exceeds 100 %. This approach, additionally, allows
for a dependence on aerosol properties rather than assuming an arbitrary
effective radius of the cloud droplets. Our method involves using our
Monte Carlo simulations using the cloud droplet activation parameterisation
including the effects of SVOCs

Effective hygroscopicity,

At very low updraughts, the parameterisation can be insensitive to the
hygroscopicity and, consequently, there may not exist a value of

Figure

Similar calculations can be carried out to study potential consequences of
neglecting just the co-condensation of SVOCs in large-scale models. The
effective hygroscopicity of the aerosol size distribution at 50 % RH,

We propose that SVOCs have a significant impact on
the hygroscopicity of atmospheric aerosol, and therefore the ability for
these aerosols to form cloud droplets. The effects of SVOCs can both increase
and decrease

The effects of SVOCs are also subject to the complexity of their inclusion in
the model. We have shown that by omitting the effects of semi-volatile
compounds during co-condensation, we obtain a lower hygroscopicity values
than if co-condensation is fully included since

SVOCs in the atmosphere give an effective

Fortran 90 code to perform these calculations is available
from

The authors declare that they have no conflict of interest.

The research leading to these results has received funding from NERC, through the Research Experience Placement (REP) scheme, and the European Union's Seventh Framework Programme (FP7/2007-2013), under grant agreement no. 603445. Edited by: Barbara Ervens Reviewed by: Dean Atkinson and one anonymous referee