A New Ice Nucleation Active Site Parameterization for Desert Dust and Soot
1. Introduction
Ice particles in clouds influence both the radiation budget of Earth and the lifetime of clouds and often initiate the formation of precipitation. In the troposphere, they are formed by either homogeneous freezing or heterogeneous nucleation processes. Homogeneous freezing happens at temperatures below about 238 K and high ice saturation ratios that are usually just reached in the upper troposphere. Heterogeneous ice nucleation is controlled by the abundance and type of solid aerosol particles. Well below water saturation, deposition nucleation occurs if water vapor directly deposits on the aerosols surface. Near water saturation, water can condense in pores and cavities, and subsequently freezes, if cold enough, by the pore condensation and freezing (PCF) mechanism (Marcolli 2014; Wagner et al. 2016). Above water saturation, supercooled droplets are formed and can freeze subsequently, either induced by a solid aerosol particle inside the droplet (immersion freezing), or an aerosol particle colliding with the droplet (contact nucleation) (Vali et al. 2015).
Aerosol particles in the atmosphere originate from different sources and include a variety of compounds. The most abundant particle types are composed of sulfate, mineral dust, sea salt, soot, and organic material (Stier et al. 2005). However, only a minor part of the atmospheric aerosol particles contributes to the ice formation in clouds. The ice active particle fraction strongly depends on the aerosol type and the temperature (Hoose and Möhler 2012; Murray et al. 2012). Mineral dust was found to be a major compound in residual particles of cirrus ice particles formed by heterogeneous ice nucleation (Cziczo et al. 2013; Kamphus et al. 2010). Signatures from biomass burning and sea salt aerosols as well as mixtures of sulfate, organics, and nitrate were also found in the cirrus ice residuals, depending on the geographic region and season.
The Fifth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC AR5; Boucher et al. 2013) and Komurcu et al. (2014) showed that the simulated ice clouds in global climate models are very sensitive to the implemented parameterization of the aerosols’ ice-nucleating ability. The early descriptions for heterogeneous ice nucleation by Fletcher (1962) or Meyers et al. (1992) are neither aerosol specific nor applicable over the whole tropospherically relevant temperature and humidity range. The first ice-nucleating particle (INP) parameterization frameworks meeting these conditions were derived from field and laboratory measurements (Phillips et al. 2008, 2013) or were based on classical nucleation theory (CNT) fitted to laboratory data (e.g., Hoose et al. 2010; Savre and Ekman 2015).
This study is based on data measured with the AIDA cloud chamber, which will briefly be described in section 2a. Sections 2b and 2c will document the data processing and evaluation and will give an overview of the aerosol samples used for the AIDA experiments. The INAS density results for immersion freezing and deposition nucleation, and our new parameterizations will be presented in section 3. In section 4, the potential use of the parameterization in models will be discussed.
2. Data and methods
All experiments were performed in the AIDA cloud chamber at the Karlsruhe Institute of Technology. AIDA can be operated as a cloud simulation chamber to investigate the formation of clouds and, in particular, the primary ice formation inside clouds under realistic atmospheric conditions.
a. Experimental setup
The core of the AIDA cloud chamber is an 84-m3-sized aluminum vessel in which the ascent of a moist air parcel in the atmosphere is simulated by evacuating the vessel. After some time of expansion cooling, the air inside AIDA exceeds saturation with respect to ice and/or water so that the present aerosol particles can act either as INPs and/or as cloud condensation nuclei (CCN) to form pure ice clouds, pure supercooled liquid clouds, or mixed-phase clouds. A more technical description of the AIDA cloud chamber and its instrumentation can be found in, for example, Möhler et al. (2005a, 2006), Benz et al. (2005), or Wagner et al. (2012).
Figure 1 shows the ice number concentrations and the total particle concentration for a typical (Fig. 1a) immersion freezing and (Fig. 1b) deposition nucleation experiment. The ice number concentration is measured by two optical particle counters Welas 1 and 2 (Palas GmbH) (Benz et al. 2005). The detection range of Welas 1 is 0.7–46 μm and of Welas is 2 5.0–240 μm (Wagner and Möhler 2013). With start of the expansion, the temperature decreases and the ice saturation ratio increases. For specific thermodynamic conditions, ice starts to form indicated by the first red vertical line. The second red vertical line indicates the stop of new ice formation. The differences between the Welas 1 and 2 ice number concentrations are caused by the different detection ranges.
Number concentration of all particles detected by Welas 1 and ice number concentration measured with Welas 1 and Welas 2. (a) As a function of temperature for an immersion freezing experiment on desert dust (ACI04_19) and (b) as a function of ice saturation ratio for a deposition nucleation experiment on desert dust (YETI04_56). The red dashed vertical lines indicate the ice nucleation time interval.
Citation: Journal of the Atmospheric Sciences 74, 3; 10.1175/JAS-D-16-0074.1
b. Data processing
This ice nucleation time interval is further split into smaller time bins for the analysis. To obtain representative statistics, each bin 
c. Origin, preparation, and characterization of the aerosol samples
1) Desert dust
The desert dust samples in this study originate from seven different locations around the world and were collected from the ground (see Table 1). The sample SD1 was collected as sedimented particles 50 km north of Cairo City during a sand storm event on 18 February 2003 (Megahed 2007, labeled as CD1 therein). With a back-trajectory analysis, Megahed (2007) showed that the origin of sample SD1 is the Sahara desert. SD4 was collected at the same location as sample SD1 (Kanji et al. 2011; Niemand et al. 2012). In contrast, SD2 was sampled 1.5 m below ground. All samples were sieved to remove particles larger than 75 μm. Before injecting the aerosol into the AIDA cloud chamber, most of the samples passed a cyclone impactor with a cutoff value between 1 and 5 μm to further remove larger particles.
Labels and origin of the desert dust samples.
Elemental analysis of the sieved samples SD1, SD2, SD4, AD1, and AD2 showed strong signals of silicon dioxide indicating that the samples contain quartz (Megahed 2007; Möhler et al. 2006). For SD2, Linke et al. (2006) (therein labeled as Cairo2) have not been able to detect iron oxides by using x-ray diffractometry (XRD). By ion-chromatographic analysis of aqueous extracts of SD1, SD2, SD4, AD1, and AD2, Megahed (2007) found that the samples contain less than 0.6 percent by weight (wt%) of ionic species indicating that the samples may contain a very low amount of anthropogenic pollutants. The samples ID1 and CID1 were collected after Saharan dust storm events (Kanji et al. 2011; Koehler et al. 2010). Koehler et al. (2010) suggested that the CID1 sample may contain beach sand and small amounts of ancient coral. All samples were considered to provide a representative spectrum of natural desert dust.
2) Soot
The soot samples used in this study were generated with four devices. A Combustion Aerosol Standard (CAST) burner (Jing Technologies) was used to generate soot in a coflow diffusion of the fuel gas propane and synthetic air (Möhler et al. 2005a, their Fig. 1). The controlled variation of the propane-to-air ratio (and therewith the C:O ratio; Schnaiter et al. 2006) determines the organic-to-elemental carbon (OC–EC) ratio of the soot. A modified version of the CAST burner, the so-called mini CAST burner (mCAST), operates in a similar way, but generates soot with a somewhat higher OC-to-EC ratio for the same fuel C:O ratio (Crawford et al. 2011, their Fig. 3). A detailed description of the operating principle of the CAST and mCAST burner can be found in, for example, Möhler et al. (2005a), Crawford et al. (2011), and Schnaiter et al. (2006).
The third device is a graphite spark generator (GFG 1000, Palas GmbH). The soot from this device is formed from evaporated and recondensed graphite. The generated particles are transported within a carrier gas (argon or nitrogen), where they coagulate to larger agglomerates.
The diesel soot sample was generated with a diesel engine test bench (Laborde et al. 2012) with and without a particle filter. To reduce the concentration of water, volatile organics, and nitrogen oxides, the motor exhaust passed a series of denuders before it was added to the AIDA cloud chamber (Saathoff et al. 2003).
In the following, the soot aerosol is characterized for its organic carbon (OC) content using the thermographic carbon analysis according to the German VDI-guideline 2465, part 2 (VDI 1999). The OC mass content refers to the fraction of carbon which thermally desorbs at 650°C in a pure helium atmosphere (Schnaiter et al. 2006). For the CAST and mCAST burner, the OC content of the soot increases with increasing C:O ratio (Schnaiter et al. 2006; Crawford et al. 2011). For the experiments, three types of CAST soot with different OC contents were generated. These are labeled as CAST_minOC, CAST_medOC, and CAST_maxOC, having OC mass contents of 5, 30, and 60 wt%, respectively (Crawford et al. 2011). The three soot types for the mCAST burner are generated with the same C/O ratios but had different OC mass contents of about 30, 70, and 90 wt% and are labeled as mCAST_minOC, mCAST_medOC, and mCAST_maxOC, respectively (Crawford et al. 2011).
The CAST soot is often used as a model for Diesel soot, which covers a large range of OC:EC ratios depending on engines, fuels, and after-treatment methods. The GSG soot is a sample representing black carbon soot with a low OC mass content of approximately 12 wt% (Henning et al. 2012).
3. Results
As mentioned in section 2, the ice nucleation ability is quantified by the INAS density. For the immersion freezing regime, previous studies (Connolly et al. 2009; Hoose and Möhler 2012; Niemand et al. 2012) introduced the INAS density as a function of the temperature. More recent studies (Hiranuma et al. 2014b; Steinke et al. 2015) extended this surface site approach to deposition nucleation, where the ice nucleation activity depends on both the temperature and the ice saturation ratio.
a. Immersion freezing
1) Desert dust
Table 2 lists all AIDA immersion freezing experiments on desert dust performed in the past 11 yr with their corresponding initial aerosol number and surface area concentration, the temperature, the ice saturation ratio, and the INAS density for the first analyzed time bin as described in section 2b. As we improved the evaluation algorithm in this study (see section 2b), also earlier published experiments from Niemand et al. (2012) and Connolly et al. (2009) were reanalyzed. Those experiments are marked in Table 2. For the experiments where no ice was detected (Table 3), the temperature at start of droplet formation and at stop of evacuation are listed instead.
Conditions for immersion freezing experiments with desert dust: nae,0 is the initial aerosol number concentration measured by the CPC; sae,0 is the initial aerosol surface area concentration; and Tstart, Si,start, and nS,start are the temperature, ice saturation ratio, and INAS density at start of ice nucleation, respectively. When two values are listed in the sae,0 column, the first value is the smaller mode and the second value is the larger mode of the aerosol surface area lognormal distribution. Previously published experiments are labeled as N12 (Niemand et al. 2012) and C09 (Connolly et al. 2009).
Conditions for immersion freezing experiments with desert dust where no freezing was observed: nae,0 is the initial aerosol number concentration measured by the CPC, sae,0 is the initial aerosol surface area concentration, Tdroplet is the temperature at the start of droplet formation, and Tstop is the temperature at which the expansion stopped. Previously published experiments are labeled with N12 (Niemand et al. 2012) and C09 (Connolly et al. 2009).
Figure 2a shows the temperature-dependent INAS densities for desert dust aerosol from all experiments listed in Table 2. Note that, because of the time-bin-wise evaluation, one or more data points per experiment can be obtained. A typical error bar for the temperature and the INAS density is shown for only one data point.
INAS densities as a function of temperature for all immersion freezing experiments on (a) desert dust listed in Table 2 and (b) soot listed in Table 4. In (a), the new parameterization (dashed line) and the parameterization of Niemand et al. (2012) (dotted line) are shown. The root-mean-square error of 
Citation: Journal of the Atmospheric Sciences 74, 3; 10.1175/JAS-D-16-0074.1
The comparison of the new parameterization [Eq. (5)] with the one from Niemand et al. (2012) (see Fig. 2a) yields a mean shift by a factor of 1.64 to higher 
2) Soot
So far, only a few experiments with soot were done in the immersion freezing regime. Heterogeneous ice formation was only observed in two experiments with CAST_minOC soot (ACI03_5 and IN09_6) and an experiment with GSG soot (IN09_3) (Table 4), but overall only five or fewer ice particles were counted. During five experiments with GSG soot (see Table 4), supercooled droplets formed at about 240 K, but only homogeneous freezing was observed upon further cooling to about 238 K. For the experiment HALO06_2, supercooled droplets existed in the temperature range from 251 to 248 K, but no freezing was observed. Based on the Welas detection limit, only an upper limit for the INAS density value was determined for these experiments in contrast to the analysis of the previously shown desert dust experiments. These upper limits were calculated by taking a total number of five ice crystals as the Welas ice number detection limit in the whole time period with the supercooled droplet cloud present in the AIDA chamber.
Conditions for immersion freezing experiments with soot: nae,0 is the initial aerosol number concentration measured by the CPC; sae,0 is the initial aerosol surface area concentration; nS,max is the upper-limiting INAS density; Tmax and Si,max are the corresponding temperature and ice saturation ratio, respectively; and Tdroplet is the temperature at start of droplet formation. If labeled with an asterisk, no upper-limiting nS was determined.
Accordingly, Fig. 2b depicts one INAS density upper-limit value for each experiment together with literature data. Compared to the data points calculated by DeMott (1990), the 
3) Comparison to other immersion freezing parameterizations
Figure 3 shows a summary of the parameterization for desert dust and soot together with INAS density parameterizations from the literature. The lines for the dust components illite NX (Hiranuma et al. 2015), K-feldspar (Atkinson et al. 2013), and kaolinite (Murray et al. 2011) were scaled to their mean mass fraction in natural desert dusts following Atkinson et al. (2013, supplemental Table 1 therein). The line for milled hematite (Hiranuma et al. 2014a) was not scaled, because the mass fraction within natural desert dusts is unknown. Furthermore, note that illite NX, kaolinite, and K-feldspar are not pure samples but include some minor fraction of other minerals. Nevertheless, the scaled parameterization for illite NX does agree very well with the parameterization for desert dust. Therefore, illite seems to be a good proxy for ice nucleation of desert dust. Kaolinite, feldspar, and hematite are only minor components of natural desert dusts and show a much steeper decrease in INAS density with increasing temperature. When accounting for the different determination of the aerosol surface area (BET analysis versus geometric), the INAS densities for K-feldspar and kaolinite would shift slightly to higher values when using geometric surface areas. Compared to desert dust, soil dust shows a higher ice nucleation activity especially for warmer temperatures (Steinke et al. 2016; Hill et al. 2016). Recent studies showed that soil dust samples featured a significant fraction of organic matter and biological active particles, which might influence the ice nucleation at warmer temperatures (Tobo et al. 2014; Hill et al. 2016).
Comparison of INAS density parameterizations for immersion freezing experiments with natural dust, soot, and dust components. The parameterization of Atkinson et al. (2013) and Murray et al. (2011) used the BET surface area, whereas the other study used the geometric surface area to calculate 
Citation: Journal of the Atmospheric Sciences 74, 3; 10.1175/JAS-D-16-0074.1
The high uncertainty of the immersion freezing efficiency of soot aerosol is represented in the deviation of the parameterization line of Murray et al. (2012) and the rescaled Murray-parameterization line for the upper-limiting 
b. Deposition nucleation
1) Desert dust
Figure 4a shows the INAS densities (filled symbols) in the ice saturation ratio–temperature plane for all deposition nucleation experiments on desert dust listed in Table 5. The open symbols show results from two previous AIDA deposition nucleation studies (Möhler et al. 2006; Field et al. 2006). These data points were calculated by dividing the published activated fraction by the aerosol surface area calculated from the median diameter and the aerosol number concentration also given in the papers by Möhler et al. (2006) and Field et al. (2006). The range of the INAS density is indicated by the different colors and typical error bars for temperature and ice saturation ratio are indicated for one data point.
INAS densities as a function of temperature and ice saturation ratio for all deposition nucleation experiments on (a) desert dust listed in Table 5 and (b) soot listed in Table 6. The black dashed line indicates the ice saturation ratio Si at water saturation and the gray dotted line the homogeneous freezing threshold for solution droplets (Δaw =0.34; Koop et al. 2000). The different symbols indicate the different samples and the different colors the order of magnitude of the INAS density as follows: orange, 5 × 108 ≤ nS < 5 × 109 m−2; red, 5 × 109 ≤ nS < 5 × 1010 m−2; green, 5 × 1010 ≤ nS < 5 × 1011 m−2; and blue, 5 × 1011 ≤ nS < 5 × 1012 m−2. The open symbols in (a) are AIDA deposition nucleation experiments with SD2 and AD1 evaluated by Möhler et al. (2006) and Field et al. (2006), respectively.
Citation: Journal of the Atmospheric Sciences 74, 3; 10.1175/JAS-D-16-0074.1
Conditions for deposition nucleation experiments with desert dust: nae,0 is the initial aerosol number concentration measured by the CPC; nae,0 is the initial aerosol surface area concentration; and Tstart, Si,start, and nS,start are the temperature, ice saturation ratio, and INAS density at start of ice nucleation, respectively. When two values are listed in the sae,0 column, the first value is the smaller mode and the second value is the larger mode of the aerosol surface area lognormal distribution.
Deposition nucleation experiments with desert dust were so far only conducted at temperatures above 206 K. These experiments yield INAS densities from 5 × 108 to 5 × 1012 m−2. The samples AD1, AD2, and SD2 show a similar ice nucleation behavior over the whole temperature range. The samples CID1 and SD19 have a somewhat higher-deposition nucleation activity at lower ice saturation ratios. The INAS density data from ID1 are located between the two other groups.
2) Soot
Figure 4b shows the INAS densities in the ice saturation ratio–temperature plane for all deposition nucleation experiments with soot listed in Table 6. Crawford et al. (2011) already published the onset ice active fractions for the experiments from the campaigns IN09 and IN11. However, these experiments were reevaluated because of the refined evaluation algorithm. In Fig. 4b, the soot samples are listed with increasing OC mass content. Typical error bars for the temperature and the ice saturation ratio are shown for one data point. Note that the deposition nucleation INAS densities are not just upper-limit values as were reported for soot immersion freezing.
Conditions for deposition nucleation experiments with soot: nae,0 is the initial aerosol number concentration measured by the CPC; sae,0 is the initial aerosol surface area concentration; and Tstart, Si,start, and nS,start are the temperature, ice saturation ratio, and INAS density at start of ice nucleation, respectively. When two values are listed in the sae,0 column, the first value is the smaller mode and the second value is the larger mode of the aerosol surface area lognormal distribution. If ice nucleation starting conditions are not given (asterisk), no heterogeneous ice nucleation was observed. Previously published experiments are labeled with Cr11 (Crawford et al. 2011).
Deposition nucleation was observed for temperatures from 195 to 235 K within INAS densities ranging from 9 × 108 to 8 × 1013 m−2. The INAS density data for a higher OC mass content (≥20 wt%; triangles and diamonds) lie at higher ice saturation ratios than the results for a lower OC mass content (circles and squares), clearly showing that the OC material suppresses the deposition nucleation activity of the soot particles. This is in agreement with the findings of Möhler et al. (2005a), who also found a decreasing deposition nucleation activity of CAST soot with increasing OC mass content.
3) Parameterization and discussion
Fit parameters of Eq. (7) for desert dust and soot with an organic carbon content of less than or equal 20 wt%.
Parameterization of the INAS density nS as a function of temperature T and ice saturation ratio Si using Eq. (7) and the fit parameters listed in Table 7 for (a) soot with OC ≤ 20 wt% and (b) desert dust only including data points from samples AD1, AD2, ID1, and SD2. The root-mean-square error of log10nS is 1.08 in (a) and 1.87 in (b). The black dashed line indicates the ice saturation ratio at water saturation and the gray dotted line the homogeneous freezing threshold for solution droplets (Δaw = 0.34; Koop et al. 2000). The white solid line shows the isoline for nS = 1011 m−2 and the white points are the corresponding data points.
Citation: Journal of the Atmospheric Sciences 74, 3; 10.1175/JAS-D-16-0074.1
Note that INAS densities above about 3 × 1015 m−2 (assuming spherical particles with diameters of less than 0.01 μm) are not relevant for atmospheric ice nucleation. The extrapolation on the temperature scale is discussed in section 4. The u-shaped form of the INAS density isolines was already suggested by Hoose and Möhler (2012). The authors defined three regimes determining the ice nucleation behavior below water saturation. The three regimes can be identified in the dataset of the soot and are shown as gray boxes in Fig. 4b. In regime A, the isolines decrease with increasing temperature showing that for the same ice activity a higher ice supersaturation is required. Thomson et al. (2015) explained this behavior from theory with the pressure induced rarification of the water vapor, which leads to an increase in ice saturation ratio and therewith to the limitation of ice nucleation. Regime B is a transition regime between A and C and is defined by nearly horizontal isolines, meaning that 
Figure 6 shows a comparison of the immersion freezing parameterization and the deposition nucleation parameterization for desert dust and soot. The linear extrapolation of the parameterization line for immersion freezing on desert dust to temperatures between 238 and 245 K would result in INAS densities that are two orders of magnitude higher than the deposition nucleation isoline close to water saturation. For soot, both parameterizations yield similar INAS density values at water saturation and a temperature of about 238 K. However, the 
Comparison of the INAS density parameterization for immersion freezing (solid dark blue line) and deposition nucleation (blue contours) for different water saturation ratios. (a) Desert dust with a linear extrapolation of the immersion freezing line (dashed) and (b) soot.
Citation: Journal of the Atmospheric Sciences 74, 3; 10.1175/JAS-D-16-0074.1
4) Comparison to other deposition nucleation parameterizations
Figure 7 shows a comparison of the new parameterization for desert dust and soot below water saturation with parameterizations from the literature for soil dust (Steinke et al. 2016), ATD (Steinke et al. 2015), and hematite (Hiranuma et al. 2014b) and 
Comparison of the new deposition nucleation parameterization for desert dust and soot with parameterizations for soil dust, Arizona test dust, and the dust components hematite and kaolinite. For clarity, only isolines for nS = 1010 m−2 are shown. Note that all shown parameterizations are only valid for Si ≥ 1.0. The black dashed line indicates the ice saturation ratio Si at water saturation and the gray dotted line the homogeneous freezing threshold for solution droplets (Δaw = 0.34; Koop et al. 2000).
Citation: Journal of the Atmospheric Sciences 74, 3; 10.1175/JAS-D-16-0074.1
The soot shows a higher ice nucleation activity than the desert dust in the temperature range between 215 and 235 K. However, soot is less ice active compared to soil dust, ATD, and the dust components hematite and kaolinite.
One striking feature shown in Fig. 7 is the similar slope of all dust sample isolines, which are much flatter than the soot isolines. This supports the suggestion of the previous section: that the pore water freezes homogeneously for soot and heterogeneously for dusts.
4. Discussion of potential use in models and comparison to other parameterizations
Various types of parameterizations for the heterogeneous ice nucleation ability of aerosols have already been published. Parameterizations based on CNT (e.g., Hoose et al. 2010; Chen et al. 2008; Barahona 2012; Savre and Ekman 2015) depend on parameters that are difficult to determine. Therefore, the free parameters like contact angle or surface tension differ significantly from study to study. Additionally, the results of these parameterizations do not agree with laboratory results over the whole temperature range (Hoose and Möhler 2012). Especially, the suppression of deposition nucleation for warmer temperatures is not reproduced. Savre and Ekman (2015) recently presented a parameterization based on CNT addressing this issue by introducing a contact-angle distribution function and therewith matching better laboratory observations. However, CNT-based parameterizations using contact angle distributions are complex to implement in models and need generally more computing time, in particular, if the depletion of the most efficient INPs is taken into account.
The second type of parameterizations is empirical. Here, the most commonly used aerosol-specific parameterization framework is that of Phillips et al. (2008, 2013). The framework is based on laboratory as well as field studies and includes also the suppression of deposition nucleation for warmer temperatures. Some of the numerous input parameters that define, for example, the aerosol composition are difficult to be derived from atmospheric measurements (DeMott et al. 2010). More simple descriptions of heterogeneous ice nucleation (e.g., DeMott et al. 2010, 2015) are easier to use in models but, in general, are not applicable to all atmospherically relevant conditions or atmospherically relevant aerosol types. In the case of a Saharan dust layer, DeMott et al. (2015) showed good agreement between their parameterization and the AIDA-based parameterization of Niemand et al. (2012).
Until now, there is no parameterization framework available that is based on well-constrained laboratory experiments covering the whole atmospherically relevant temperature and humidity range. The parameterization framework presented here is in principle limited to the detection limits of the AIDA cloud chamber instruments and the number of evaluated experiments. Therefore, also the AIDA parameterization has to be extrapolated to cover the atmospheric relevant temperature and ice saturation ratio ranges when used in models. In particular, in the cirrus regime, ice nucleation data are lacking at high ice supersaturation and temperatures below 200 K, which makes the parameterization more uncertain in these regions.
The dashed red lines in the top panels of Fig. 8 show the proposed extrapolation of the developed immersion freezing parameterization. The parameterization line is not extrapolated to higher temperatures, because this study as well as previous laboratory studies did not observe ice nucleation of desert dust as well as main dust components above 260 K (Hoose and Möhler 2012). Between 245 K and the homogeneous freezing temperature, the parameterization is linearly extrapolated, because DeMott et al. (2011) showed no leveling off of the ice active fractions from different measurements with Saharan dust. For soot, the rescaled parameterization line from Murray et al. (2012) is simply extrapolated to the homogeneous freezing temperature and to the melting temperature. Below water saturation and temperatures above 240 K, the ice activated fraction is much lower than 1% for a typical aerosol diameter of 1 μm. Therefore, the extrapolation to warmer temperatures is unproblematic (see Fig. 5). However, the extrapolation to higher ice saturation ratios has to be limited to INAS densities less than or equal 1.0 × 1015 m−2.
Comparison of the new parameterization framework with the equivalent INAS densities as derived from the parametrizations of Phillips et al. (2013) and Savre and Ekman (2015) for dust and soot/BC in the (top) immersion freezing and (bottom) deposition nucleation regime. The new parameterization for immersion freezing is extrapolated to T ∈ [235, 261] K for desert dust and to T ∈ [235, 273] K for soot. For the black carbon group of the Phillips parameterization Ξ = 0.1. The small colored numbers on the isolines in the bottom panels indicate the exponent x for nS(T, Si) = 10x m−2.
Citation: Journal of the Atmospheric Sciences 74, 3; 10.1175/JAS-D-16-0074.1
Figure 8 shows the new parameterizations for desert dust and soot together with the schemes of Phillips et al. (2013) and Savre and Ekman (2015). For the Phillips parameterization, the equivalent INAS density (Hoose and Möhler 2012) is shown, with a black carbon IN propensity fraction of 
For deposition nucleation, the scheme of Savre and Ekman (2015) covers only a small temperature range because of the used datasets [dust: Kanji et al. (2011), soot: Möhler et al. (2005b)]. Therefore, the application of this scheme is doubtful especially for cold cirrus clouds. However, the order of magnitude of the INAS density is comparable to the values of the new scheme. The parameterization of Phillips et al. (2013) does not show the observed u-shaped isolines and shows overall lower INAS density values for a given temperature and ice saturation ratio for both dust and soot. Because of the shape of the isolines, the scheme of Phillips et al. (2013) would give significant INP concentration for soot only near water saturation. Below about 220 K, the INAS densities from the Phillips parameterization are very small and for ice saturation ratios above 1.6, homogeneous freezing of solution droplets would be more likely.
5. Conclusions
The comprehensive database from AIDA cloud chamber experiments of the last 11 yr was used to develop a parameterization framework for immersion freezing and deposition nucleation. The objective was to parameterize the ice nucleation ability in terms of the INAS density for desert dust and soot but to develop the parameterization in a way extendable to other aerosol types. The already-existing INAS density approach for immersion freezing was extended to deposition nucleation.
As part of the evaluation algorithm, the determination of the aerosol surface area concentration from SMPS and APS measurements was improved by accounting for the reduction of the total surface area concentration due to incomplete CCN activation and by adding a time-bin-wise correction term concerning the reduction of the total aerosol surface area due to the ongoing activation of aerosol particles to ice particles. Therewith, the calculation of the INAS density is more accurate.
For immersion freezing on desert dust, the reanalysis of the AIDA data confirmed the temperature trend of the parameterization line from Niemand et al. (2012) but gave somewhat higher values. The range of variability for INAS densities around the fit line was about the same for samples collected from ground and samples that were transported through the atmosphere, indicating that the fit line may be representative for a wide range of atmospheric desert dust types.
For immersion freezing on desert dust, an exponential function is describing the relation of INAS density and temperature. The comparison of the parameterization for desert dust with dust components shows that the temperature trend of the INAS density line for illite is closest to our INAS fit line for desert dust. For immersion freezing on soot, only upper-limit INAS densities were determined and fitted by the rescaled parameterization line from Murray et al. (2012). The comparison of the different soot results indicates a high variability for the ice nucleation efficiency of different soot types.
For the ice nucleation activity of desert dust in the cirrus regime, some influence of the sample origin was found. In particular, the sample CID1 shows a higher ability than the other samples, in contrast to the findings in the immersion freezing regime. This difference may be caused by the different porous structure of the aerosol samples, in particular, in regimes where the PCF mechanism dominates the ice nucleation behavior. The soot samples showed a strong influence of the organic carbon content on ice nucleation ability with lower ice nucleation efficiency at higher organic carbon content.
In the deposition nucleation mode, u-shaped isolines of INAS density were found for soot and desert dust. Therewith, the deposition nucleation regime seems to be split into three subregimes. The strong temperature dependency at higher temperatures with INAS density steeply decreasing with temperature my caused by the PCF mechanism. Toward lower temperatures, the 
For both ice nucleation modes, more experiments are needed to fill gaps in the datasets and to provide a more robust base for accurate parameterizations, in particular at high ice supersaturations and low temperatures of the cold cirrus regime. We also plan to evaluate AIDA experiments with other atmospherically relevant aerosols like organics and coated aerosols in order to extend the INAS density parameterization.
The new parameterization framework covers the most important INP species (dust and soot) in the troposphere (Cziczo et al. 2013). However, the parameterizations are limited to uncoated aerosol particles, although many aerosols are transported over long distances and therewith possibly coated before contributing to ice formation. Möhler et al. (2005b) found that soot coated with sulfuric acid is less ice active in the cirrus temperature regime than uncoated soot. Also an increasing organic carbon content of the soot aerosol reduces its ice nucleation efficiency, but because of only limited data we were not able to quantify this deactivation so far.
In comparison to other parameterization frameworks based on CNT or empirical studies, the here-presented framework has the benefit of a small set of input parameters. Therewith, the framework can more easily be implemented into models. The comparison of the new formulation with a CNT-based and an empirical framework showed large differences in INAS densities especially below water saturation. Hence, when applied in models, the number of ice-nucleating particles resulting from the different parameterizations will significantly differ from each other. Therefore, tests in weather and climate models and constraints to atmospheric measurements of INP concentrations are needed to validate the parameterization schemes and their accuracy for calculating atmospheric INP concentrations as a function of aerosol abundance.
Acknowledgments
The authors thank the providers of the desert dust samples Dr. Lothar Schütz, University of Mainz, Germany (Asian desert dust); Dr. Khaled Megahed (Saharan desert dust samples 1, 2, and 4); Prof. Dr. Eli Gabor, Tel Aviv University, Israel (Israel desert dust); Dr. Hans Moosmüller, Desert Research Institute, United States (Canary Island desert dust); Dr. Emre Toprak and Prof. Dr. Cemal Saydam, TUBITAK Ankara, Turkey (Saharan desert dust sample 19); and Dr. Konrad Kandler, Darmstadt University of Technology, Germany (Saharan desert dust sample 6).
This research was partly funded by the Helmholtz Association through the Helmholtz Climate Initiative REKLIM and the President’s Initiative and Networking Fund and partly funded by the Deutsche Forschungsgemeinschaft (DFG) through the research unit INUIT (FOR 1525, projects HO4612/1-1, HO4612/1-2, MO 668/4-1, and MO 668/4-2).
APPENDIX A
List of Symbols
| d | Aerosol diameter (μm) |
| dact,k | INP activation aerosol diameter for time bin k (μm) |
| dm | Median diameter of the aerosol size distribution (μm) |
| dmin | CCN activation aerosol diameter (μm) |
| fd, fi | Droplet and ice activated fraction |
| nae, nae,0 | Aerosol number concentration and nae measured by CPC at beginning of expansion (cm–3) |
| ni,k | Ice number concentration for time bin k in (cm–3) |
| nS,k, nS,start | Ice-nucleating active surface site (INAS) density for time bin k and the first time bin (m−2) |
| pk, p0 | Chamber pressure for time bin k and at start of expansion (hPa) |
| sae,0, sae,k | Aerosol surface area concentration at beginning of expansion and for each time bin (μm2 cm−3) |
| Si,k, Si,start | Ice saturation ratio for time bin k and for the first time bin |
| Tk, Tstart | Temperature for time bin k and for the first time bin (K) |
| Tdroplet | Temperature at start of droplet formation (K) |
| Tstop | Temperature at stop of expansion (K) |
 | Fit values for INAS density parameterization in deposition nucleation mode |
| Φ(z) | Standard normal distribution function with cutoff value z |
| σg | Geometric standard deviation of aerosol size distribution |
APPENDIX B
List of Abbreviations
| AIDA | Aerosol Interaction and Dynamics in the Atmosphere |
| APS | Aerodynamic Particle Sizer |
| BET | Brunauer–Emmett–Teller (method to measure the surface area of particles via gas adsorption) |
| CCN | Cloud condensation nuclei |
| CNT | Classical nucleation theory |
| CPC | Condensation particle counter |
| INAS | Ice nucleation active surface site |
| INP | Ice-nucleating particle |
| OC and EC | Organic and elemental carbon |
| PCF | Pore condensation and freezing |
| SMPS | Scanning Mobility Particle Sizer |
| Welas | White Light Aerosol Spectrometer system |
| XRD | X-ray diffractometry |
APPENDIX C
Correction of the Aerosol Surface Area Concentration
a. Reduction due to incomplete CCN activation
b. Correction due to IN activation
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