Aerosol particles interacting with clouds have a significant influence on the global climate by impacting cloud life cycles, precipitation formation and the global radiation budget. Interaction between clouds and aerosol particles may occur via the initiation of ice crystal formation within clouds. There are four heterogeneous ice nucleation modes involving insoluble aerosol particles . Immersion freezing occurs if a particle is already immersed within a cloud droplet when ice nucleation is initiated, whereas condensation nucleation happens shortly after or at the time of water condensation on the particle which acts as condensation and freezing nucleus at the same time. For deposition nucleation, water vapor is directly transformed into ice at the particle's surface. Contact freezing may occur if a particle collides with a supercooled droplet.

Laboratory studies and field campaigns have investigated the role of mineral dusts and single mineral species as ice nuclei in the atmosphere. Mineral dust acts as an ice nucleus over a wide range of temperatures and supersaturations over ice, with the most active dusts nucleating ice at approximately 260 K . Using numerical modeling to estimate the climate impact of mineral dust through ice formation requires relations which connect aerosol properties, thermodynamic variables and resulting ice crystal concentrations. Two different approaches are typically used to find approximations to describe the measured ice formation rates, namely a nucleation rate approach based on classical nucleation theory (also called “stochastic” or “time-dependent” approach), or an ice-active surface site approach assuming a deterministic, time-independent behavior of ice nucleation (“singular hypothesis”). Both approaches are described briefly in the following paragraphs.

The deterministic approach implies that for heterogeneous ice nucleation the stochasticity is masked by the influence of variable aerosol properties . The observed ice formation seems to occur instantaneously upon cooling and does not explicitly depend on time. Therefore, the deterministic approach describes ice formation as a function of temperature and – for deposition nucleation – relative humidity over ice. The proposition of active sites which seemingly nucleate ice as soon as certain thermodynamic thresholds are reached motivates the ice nucleation active surface site (INAS) density concept .

The INAS density concept was applied to results from cloud chamber experiments by to derive INAS densities ns for various mineral dusts. The ice nucleation active surface site density for immersion freezing is described by ΔN=Ns⋅(1-exp⁡(-A⋅ns(T))), where ΔN is the observed ice crystal concentration at a certain temperature, Ns the initial number of droplets, A the aerosol surface and T the temperature. Note that, for immersion freezing, A exclusively refers to particles being immersed within droplets. Also, this relation (Eq. ) is only valid for a certain aerosol particle size. Equation has been expanded towards a formulation which can be applied to a polydisperse aerosol population, yielding an approximate form of the ice nucleation active surface site density valid for ice fractions smaller than fice≈10% with ns≈niceAaer, where nice is the observed ice crystal concentration and Aaer the aerosol surface area concentration.

Like the INAS density approach, classical nucleation theory formulations have already been employed in several studies investigating heterogeneous ice nucleation, e.g., in the studies by . , , , and . Classical nucleation theory is based on the premise that the ice nucleation efficiency of aerosol particles can be quantified by the contact angle θ, which is a measure of the reduction of the energy barrier that impedes the formation of ice germs at the surface of aerosol particles . For deposition nucleation, the nucleation rate J(θ) per particle is given by J(θ)=4πrN2⋅4πrg2e2πmwkTn1⋅exp⁡-Δgg(θ)kT1ngΔgg(θ)3πkT following the notation used by , with rN being the aerosol particle radius, rg the radius of the ice germ, e the water vapor pressure, mw the mass of a water molecule, k the Boltzmann constant, T the temperature in [K], n1 the number concentration of single molecules in contact with the aerosol surface, ng the number of water molecules per ice germ and Δgg(θ) the energy needed for forming a critical ice germ. Note that, to calculate n1, the desorption energy Δgd is set to an average value of Δgd=4×10-20 J . The formalism used by explicitly considers the temperature- and humidity-dependence of n1 and rg with n1=eνs2πmwkTexp⁡-ΔgdkT and rg=2vwσi/vkT⋅ln⁡Si. The surface tension σi/v is described as a temperature-dependent function according to . The activation energy Δgg(θ) is given by Δgg(θ)=4π3rg2⋅σi/v⋅f(θ), where σi/v is the surface tension at the ice–vapor interface and f(θ)=0.25⋅(2+cos⁡(θ))(1-cos⁡(θ))2 is the so-called form factor, with θ formally being the contact angle between particle surface and the ice germ. Physically, the form factor f(θ), which reduces the activation energy, can be taken as a measure of the ice nucleation efficiency. Several studies have pointed out that often a single contact angle is not sufficient to characterize the ice nucleation behavior of a non-homogeneous aerosol population . Thus, the nucleation rate approach was extended towards including not only a single contact angle but a distribution of contact angles . For this study, the distribution p(θ) is assumed to be lognormal: p(θ)=1θσθ2πexp⁡-(ln⁡(θ)-ln⁡(μθ))22σθ2, with μθ being the median contact angle and σθ the logarithmic width of the contact angle distribution.

Note that some parameterizations have sought to reconcile classical nucleation theory and the INAS density concept because both approaches offer frameworks for fitting and parameterizing experimental data, although they treat the inherent time dependence of ice nucleation differently . However, in this study only the INAS density approach and classical nucleation theory will be compared to each other.

Besides the INAS density approach and classical nucleation theory which can be used to describe the ice nucleation efficiencies of certain well-defined aerosol species, there are also parameterizations which have been derived for either unidentified aerosols or certain subgroups of the aerosol population. used laboratory data from diffusion chamber experiments to derive a saturation-dependent relation for immersion freezing and deposition nucleation. The ice crystal concentration cIN [L-1] is described by cIN=exp⁡[-0.639+0.1296⋅(100(Sice-1))], which is valid for temperatures between 253 and 266 K and only depends on the supersaturation over ice Sice-1. The parameterization developed by links aerosol properties and ice crystal concentration in a more direct way by explicitly including the aerosol surface area and aerosol-specific freezing thresholds. The contribution of mineral dusts and metallic compounds to atmospheric ice nuclei (cIN,DM) is given by cIN,DM=∫log⁡[0.1µm]∞1-exp⁡[-μDM(DDM,Sice,T)]⋅dnDMd(log⁡DDM)d(log⁡DDM), where μDM(DDM,Sice,T) is the average number of activated ice embryos per aerosol particle. μDM(DDM,Si,T) is defined in as a function of aerosol diameter DDM, temperature T in ∘C and the saturation over ice Sice. nDM is the number mixing ratio of aerosol particles belonging to the dust/metallic compounds group, given in per kg of air.

The approaches that are described in this section can all be used to develop ice nucleation parameterizations. For immersion freezing, several studies have investigated the performance of different approaches regarding the description of ice nucleation efficiencies . For deposition nucleation, only very few studies have compared different parameterizations, e.g., . In this study deposition nucleation experiments conducted at the Aerosol Interaction and Dynamics in the Atmosphere cloud chamber (AIDA, Karlsruhe Institute of Technology) are presented and accompanied by a comparison of the INAS density approach with classical nucleation theory.

The manuscript is organized as follows: the instrumentation used at the AIDA cloud chamber and a typical deposition nucleation experiment are described in Sect. 2. In Sect. 3, the experimental results are presented, starting with ice-active fractions and ice nucleation active surface site densities. The impact of temperature, aerosol particle size and cooling rates on the observed deposition nucleation efficiency was investigated.

In this work, Arizona Test Dust (ATD, Powder Technology Inc.) is used as a substitute for naturally occurring desert dusts. ATD consists of desert dust that was washed, dried and milled in order to provide enough material in all size classes. Thus, the composition of individual ATD particles is probably more homogeneous than the composition of original desert dusts, and also the surface properties may differ from natural dusts.

Several sets of experimental runs were conducted, starting at approximately 250, 235 or 223 K. In order to investigate the impact of time dependence and variations in the aerosol size distribution on the deposition nucleation efficiency of ATD, the experimental cooling rate was varied between 0.3 and 2.9 Kmin-1, and also the aerosol size distribution was varied by either including or discarding particles larger than about 1 µm.

In Sect. 3, ice nucleation thresholds, INAS densities and contact angle distribution parameters as derived from the experimental data are presented. Additionally, an average INAS density function is derived and compared to two empirical parameterizations with regard to their sensitivity to temperature and relative humidity over ice.

In the last part of Sect. 3, the relevance of time dependence for deposition nucleation initiated by ATD particles is investigated by using either a linear time-dependent source term or a time-dependent exponential function in addition to the formerly time-independent average INAS density relation. The average INAS density function, both with and without the time-dependent contributions, was then tested with the box model ACPIM (Aerosol–Cloud Precipitation Interaction Model) regarding the impact of variations in cooling rate and aerosol number concentration on the observed ice fractions. The modeling results are presented at the end of Sect. 3.

The experiments presented in this study were conducted at the AIDA cloud chamber facility, located at the Karlsruhe Institute of Technology. With the AIDA cloud chamber, the ascent of air parcels can be simulated by expanding moist air within the chamber vessel. Thus, the ice nucleation properties of various aerosol types can be investigated under atmospherically relevant conditions for mixed-phase and cirrus clouds.

Figure  shows a schematic drawing of the AIDA cloud simulation chamber: the cloud chamber itself is enclosed by a thermally isolated housing. With two pumps the chamber volume can be expanded at controllable rates corresponding to defined cooling rates. Background aerosol concentrations within the cloud chamber were typically below 0.1 cm-3.

On the left side of Fig. , the aerosol instrumentation is shown. A rotating brush generator (RBG 1000, Palas) is used for dry dispersion of the dust samples. Additionally, cyclone impactors are generally used to eliminate particles larger than about 1 µm. Aerosol number concentrations are measured with a condensation particle counter (CPC3010, TSI), whereas the aerosol size distribution was measured by combining SMPS (Scanning Mobility Particle Sizer – TSI) and APS (Aerodynamical Particle Sizer – TSI) measurements. From these data, the total aerosol surface area concentration can be inferred by translating the size distribution into a surface distribution after converting mobility and aerodynamic diameters into equivalent sphere diameters . To this surface distribution a lognormal fit is applied from which the total aerosol surface area concentration can be estimated through integrating the distribution. An exemplary aerosol surface distribution is shown in Fig. . Note that APS and SMPS data in combination cover the whole size range.

Values for the relative humidity over ice (RHice) and over water (RHwater) are derived from tunable diode laser (TDL) absorption spectroscopy measurements. Infrared absorption is measured at a wavelength around λ=1.37 µm and converted into water vapor concentrations with an accuracy of ±5% . From these water vapor concentration values, the relative humidities RHwater and RHice are calculated using the water vapor saturation pressures over liquid water and ice and measurements of the gas temperature in the cloud chamber. The total water content is also measured by a chilled-mirror hygrometer. For the deposition nucleation experiments, however, only the TDL measurements were considered.

The AIDA cloud chamber is also equipped with several optical instruments – three of these instruments (welas, welas2 and SIMONE (Scattering Intensity Measurements for the Optical Detection of Ice)) are also sketched in Fig. . Ice crystal concentrations are derived from the particle concentrations and size distributions measured with two optical particle counters (welas and welas2, Palas GmbH). Particle sizes are calculated from the intensity of light scattered by particles crossing the beam of an internal white light source. Note that aerosol particles, droplets and ice crystals are detected alike if they are large enough to scatter sufficient light into the detector, but only ice crystals grow rapidly to sizes which eventually exceed those of the initial aerosol particles. Droplet formation is expected to be negligible during the experimental runs presented in this work because ice nucleation was only investigated in conditions subsaturated with respect to liquid water, and the amount of soluble components is expected to be very small . The distinction between aerosol particles and ice crystals is made by selecting a suitable size threshold. The formation of small ice crystals is also indicated by the change in depolarization detected by SIMONE . SIMONE is used for observing scattering signals from particles crossing the pathway of a polarized laser beam (λ=488 nm) which horizontally traverses the cloud chamber. Besides scattering in forward (at 2∘) and near-backward (at 178∘) direction, the depolarization is measured using a Glan laser prism to separate the parallel and the perpendicular polarized components of the near-backward-scattered light.

The course of a typical AIDA expansion experiment is depicted in Fig.  and briefly described in the following paragraphs. The first panel shows the pressure p, which decreases during an expansion run; the gas temperature Tg within the vessel drops simultaneously. During this expansion experiment, the pressure p within the AIDA vessel is lowered from ambient pressure to approximately 800 mbar. The starting temperature was 235 K, whereas the minimum temperature was about 226 K. Over the course of an expansion experiment, the temperature Tw at the chamber walls remains virtually unchanged. Panel b depicts the relative humidity values (RHwater and RHice) as derived from the TDL measurements. Water saturation is not reached during this experiment. Therefore, neither significant droplet activation nor immersion freezing can occur: ice crystals form almost completely by deposition nucleation. The peak relative humidity over ice was about 118%.

Figure c shows the forward-to-backward scattering ratio as derived from the SIMONE scattering signals alongside the depolarization signal measured for the backward-scattered light. The ice nucleation onset with the formation of small ice crystals is indicated by an increase in depolarization as well as a slightly delayed increase of the forward-to-backward scattering ratio. The increase in depolarization is a further indication that only deposition nucleation was observed because the formation of spherical droplets leads to a clear decrease in the depolarization signal. The last panel in Fig.  shows the aerosol concentration (measured by CPC3010) and the ice crystal concentrations (derived from welas/welas2 data). The aerosol concentration given per cubic centimeter decreases over the course of the experiment due to the volume expansion. The ice crystal concentration as derived from the welas/welas2 data shows a steep onset at approximately RHice=103%. The maximum fraction of ice-active particles observed during this experiment was fice=40%. Note that for the calculation of the ice nucleation active surface site densities only ice fractions fice<10% were considered. Initially, the growing ice particles deplete the vapor phase only negligibly, and relative humidity over ice is an almost linear function of temperature.

Table  lists all experimental runs that were conducted as a part of this study. All AIDA expansion experiments described in Table  started at 250, 235 or 223 K. The cooling rate was varied between 0.3 and 2.9 Kmin-1 as indicated. Note that the cooling rate determines the timescale that is relevant to the observed ice nucleation processes and thus gives experimental access to the time dependence of heterogeneous ice nucleation. Additionally, the aerosol surface area concentration was varied either by changing the aerosol number concentration or by including particles larger than ca. 1 µm.

For the experiments starting at 250 K, the cooling rate was varied between 0.3 and 2.7 K min-1. The variations of the aerosol surface area concentration during these experiments were achieved by varying the aerosol number concentration. In addition to varying the cooling rate between 0.7 and 2.9 K min-1 and to systematically changing the aerosol number concentration, two experiments starting at about 235 K (exps. 14 and 15) were conducted without using cyclone impactor stages, which resulted in a shift of the aerosol size distribution towards larger particles. The ice nucleation efficiency was also investigated at colder temperatures, i.e., for expansion runs starting at approximately 223 K.

The deposition nucleation experiments described in Table  are used to derive different measures for the ice nucleation efficiencies. In particular, humidity thresholds at ice nucleation onset, INAS densities and contact angle distribution parameters were analyzed.

Deposition nucleation on ATD particles was investigated with AIDA cloud chamber experiments, following expansion trajectories starting from ice-subsaturated conditions at about 250, 235 or 223 K. The aerosol surface area concentrations and cooling rates were varied for all expansion experiments, because one of the goals of this experimental study was to determine the relevance of timescales to the observed ice nucleation efficiencies.

The ice nucleation efficiency observed for each experimental run was quantified by the measured ice nucleation thresholds at fice=1%, by deriving the INAS densities and by fitting the contact angle distribution parameters using nucleation rate formulations.

Ice nucleation onsets (fice=1%) were observed at relative humidities over ice between 118 and 121% at warmer temperatures (Tstart≈250 K), whereas ice activation of 1% of all ATD particles occurred between 101 and 107% at colder temperatures (Tstart below 235 K). No direct relation between ice nucleation thresholds and cooling rates could be deduced from the experimental data. The time dependence of deposition nucleation was presumably small and could not be quantified from the ice nucleation thresholds. It should be noted that the observed freezing thresholds could also be partly explained by a freezing mechanism other than deposition nucleation, namely pore condensation freezing. Pore condensation freezing was proposed by as an explanation for freezing below water saturation. Note, however, that in our experimental setup we cannot clearly distinguish between these freezing mechanisms and thus make the assumption that ice nucleation is mostly caused by deposition nucleation.

INAS densities were derived for all experiments and were found to depend both on temperature T and the ice saturation ratio Sice with ns(xtherm)=1.88×105⋅exp⁡(0.2659⋅xtherm)[m-2], where the temperature- and saturation-dependent function xtherm is defined by xtherm=-(T-273.2)+(Sice-1)×100. The INAS density approach was found to be independent of shifts in the particle size distribution, i.e., from shifting the median diameter from dmed≈0.23 µm to dmed≈0.35 µm. As a parameterization for numerical models, the INAS density relation is only strictly valid for temperatures between 226 and 250 K and for humidities with 1<Sice<1.2. Especially at temperatures below 220 K, xtherm may be better described by a relation different from Eq. (). Note that an extrapolation to lower temperatures relying on Eq. () would also predict very high INAS densities already at Sice close to 1. To describe deposition nucleation even more precisely, xtherm could be parameterized as a higher-order function of temperature and relative humidity over ice in order to achieve a better match with observations, both at low temperatures above ice saturation and at higher temperatures close to water saturation. Deposition nucleation at higher temperatures should be investigated for a wider range of thermodynamic conditions in order to better characterize the dependence of xtherm on temperature and relative humidity and also for natural mineral dusts which are typically less ice-active than ATD particles . Ice crystal concentrations predicted by ns(xtherm) match the observed ice crystal concentrations for most experiments of this study within 1 order of magnitude regardless of the cooling rate or the aerosol surface area concentration.

In comparison to INAS density values derived from other empirical parameterizations or laboratory studies, the ice nucleation efficiency of ATD in deposition nucleation mode as derived from AIDA cloud chamber measurements is larger by at least 1 order of magnitude. Note that, in contrast to the parameterization derived from our measurements, the parameterizations by and suggest a much weaker or no temperature dependence of deposition nucleation.

Applying classical nucleation theory to the observed ice fractions yields average contact angle distribution parameters. For high-temperature deposition nucleation (Tstart≈250 K) the contact angle distribution parameters which best described all experimental runs (r2=0.48) were μθ=22.1∘ and σθ=0.095. For deposition nucleation at lower temperatures, the contact angle parameters were found to be μθ=36.2∘ and σθ=0.520 (r2=0.52) for experiments at Tstart≈235 K, and μθ=16.9∘ and σθ=0.540 (r2=0.89) for Tstart≈220 K. The large variability of the contact angle distribution parameters suggests that the application of classical nucleation theory to deposition nucleation by certain aerosol species such as mineral dust would require a detailed investigation of the contact angle distribution parameters for different thermodynamic conditions. Additionally, the contribution of pore condensation freezing to heterogeneous nucleation observed close to water saturation might lead to difficulties with applying classical nucleation theory directly.

The time dependence of deposition nucleation initiated by ATD particles was investigated by assuming that time dependence might be represented by either a linear source term a3⋅t or a factor describing the delayed activation of ice nucleation active surface sites according to 1-exp⁡(-b3⋅t). Note that, for t→∞, ns is limited by two factors: first, the activation of all aerosol particles and, secondly, by the size of an active site which is assumed to cover Asite=10 nm2 , with the surface area covered by active sites not exceeding the available aerosol surface area.

To evaluate the potential role of time-dependent ice nucleation in the atmosphere, the box model ACPIM was used to simulate the ascent of air parcels. For these case studies, ice nucleation was described by a purely thermodynamically driven INAS density function and two parameterizations with additional time-dependent terms. The time-dependent terms are potentially important at low to moderate updraft velocities and for small ice fractions. However, the results obtained from the three different parameterizations did not differ much from each other under the prescribed experimental conditions. It should be noted, however, that the modeling case studies in this work are based on ice nucleation results for ATD obtained under certain thermodynamic conditions.

The ATD experiments and modeling studies presented in this work are supposed to be a first step in rigorously investigating deposition nucleation over a wide temperature and saturation range in order to gain a better understanding of the factors which are relevant for deposition nucleation. This knowledge was then used to develop a metric which can be easily employed for the comparative analysis of other heterogeneous nucleation studies. Further investigations of atmospherically relevant dust samples are needed in order to better inform future parameterizations describing deposition ice nucleation.