A comprehensive parameterization of heterogeneous ice nucleation of dust surrogate : laboratory study with hematite particles and its application to atmospheric models

A new heterogeneous ice nucleation parameterization that covers a wide temperature range (−36 to−78 C) is presented. Developing and testing such an ice nucleation parameterization, which is constrained through identical experimental conditions, is important to accurately simulate the ice nucleation processes in cirrus clouds. The ice nucleation active surface-site density (ns) of hematite particles, used as a proxy for atmospheric dust particles, were derived from AIDA (Aerosol Interaction and Dynamics in the Atmosphere) cloud chamber measurements under water subsaturated conditions. These conditions were achieved by continuously changing the temperature (T ) and relative humidity with respect to ice (RHice) in the chamber. Our measurements showed several different pathways to nucleate ice depending on T and RHice conditions. For instance, almost T -independent freezing was observed at −60 C<T <−50 C, where RHice explicitly controlled ice nucleation efficiency, while both T and RHice played roles in other two T regimes: −78 C<T <−60 C and −50 C<T <−36 C. More specifically, observations at T lower than −60 C revealed that higher RHice was necessary to maintain a constant ns, whereas T may have played a significant role in ice nucleation at T higher than −50 C. We implemented the new hematite-derived ns parameterization, which agrees well with previous AIDA measurements of desert dust, into two conceptual cloud models to investigate their sensitivity to the new parameterization in comparison to existing ice nucleation schemes for simulating cirrus cloud properties. Our results show that the new AIDA-based parameterization leads to an order of magnitude higher ice crystal concentrations and to an inhibition of homogeneous nucleation in lower-temperature regions. Our cloud simulation results suggest that atmospheric dust particles that form ice nuclei at lower temperatures, below −36 C, can potentially have a stronger influence on cloud properties, such as cloud longevity and initiation, compared to previous parameterizations.


Introduction
Ice clouds represent a significant source of uncertainty when predicting Earth's climate change according to the recent Intergovernmental Panel on Climate Change report (i.e., Chapter 7 of IPCC 2013; Boucher et al., 2013).Rare airborne particles that can act as ice nucleating particles (INPs) at supercooled temperatures indirectly influence Earth's forcing by changing microphysical properties of ice clouds, such as reflectivity, longevity and precipitation.However, understanding ice cloud formation over a wide range of atmospherically relevant temperatures and humidity is challenging (e.g., De-Mott et al., 2011;Murray et al., 2012), and our knowledge of ice formation through various nucleation modes is still scarce and limited, such that the ice nucleation processes are currently very poorly represented in global climate models (e.g., Hoose et al., 2010;Liu and Penner, 2005).In particu-Published by Copernicus Publications on behalf of the European Geosciences Union.
N. Hiranuma et al.: Parameterization of heterogeneous ice nucleation of dust surrogate lar, heterogeneous ice nucleation processes proceed through various modes including deposition nucleation, immersion, condensation and contact freezing (Chapter 9 of Pruppacher and Klett, 1997;Vali, 1985).Briefly, deposition mode induces ice formation when water vapor is directly deposited onto the INP, immersion and condensation freezing can induce ice formation when freezing is initiated by the INP immersed within the supercooled droplet or solution droplet, and contact freezing can initiate at the moment when an INP comes into contact with a supercooled droplet.
A global model simulation of INPs in tropospheric clouds showed that more than 85 % of heterogeneous ice nucleation results from freezing of supercooled cloud droplets, in which INPs are either immersed or condensed (Hoose et al., 2010).However, freezing mechanisms in cirrus clouds are still uncertain (e.g., Sassen and Khvorostyanov, 2008).It is understood that various INPs can nucleate ice at water subsaturation and a range of supercooled temperature conditions as comprehensively illustrated in Fig. 2 of Hoose and Möhler (2012).The potential importance of ice nucleation under ice supersaturated conditions below the homogeneous freezing threshold line (i.e., Koop line; Koop et al., 2000;Ren and MacKenzie, 2005) has already been proven in earlier studies, suggesting the need for further investigations in the water subsaturated region.For example, Christenson (2013) experimentally showed that the capillary condensation of supercooled liquid on surface defects facilitated subsequent homogeneous nucleation and growth of ice below water saturation.Marcolli (2014) suggested that the inverse Kelvin effect below water saturation helps to form water in pores or cavities and hypothesized that this condensed water could freeze through the homogeneous-or immersion-mode freezing.This freezing mechanism was referred to as pore condensation and freezing.Previous laboratory studies introduced the concept of a freezing mechanism of solutions on particles at below water saturation (Zuberi et al., 2002;Hung et al., 2003;Archuleta et al., 2005).More recently, Welti et al. (2014) explored the relevance of soluble components of mineral dust (i.e., Fluka kaolinite) to condensation freezing below water saturation in the context of classical nucleation theory (CNT).Furthermore, recent aircraftbased field observations suggested that predominant heterogeneous ice formation at cirrus temperatures occurs under water subsaturated conditions, in particular when RH ice is below 140 % (Cziczo et al., 2013).In addition, Storelvmo and Herger (2014) demonstrated that forward modeling simulation with 50 % of the mineral dust particles acting as INPs was in good agreement with an observation reported by Cziczo et al. (2013).Another airborne observation during an Asian mineral dust event suggested that ice nucleation in cirrus clouds occurs under water subsaturation conditions below 130 % RH ice (Sakai et al., 2014).
Previously, empirical descriptions given in Meyers et al. (1992; hereinafter referred to as M92) were derived from the limited field measurements of ice nu-clei concentrations measured at −23 • C < T < −7 • C and 102 % < RH ice < 125 %.Recently, Phillips et al. (2008Phillips et al. ( , 2013) ) empirically parameterized the heterogeneous ice nucleation of various types of aerosols as a function of humidity (RH ice > 100 %) and temperature conditions (0 to −100 • C).Besides, CNT-based ice nucleation descriptions have also been widely used and implemented in cloud models (e.g., Barahona and Nenes, 2009a, b;Kärcher and Lohmann, 2003;Khvorostyanov and Curry, 2004).These parameterizations can predict different cloud properties for identical environmental conditions.For example, Barahona et al. (2010) showed that the ice crystal number can vary by up to an order of magnitude in a global chemical transport model depending on the choice of the heterogeneous ice nucleation parameterization.The authors found the lowest global mean ice crystal concentration from the parameterization of Phillips et al. (2008).Moreover, sensitivity of ice cloud properties to the parameterization was observed by Liu et al. (2012).They showed that the heterogeneous INP number concentration obtained from a CNT-based parameterization is typically higher by several factors than that of Phillips's parameterization under identical test conditions.To gain insight on what triggers such deviation and to constrain model uncertainties, more and better in situ measurements are necessary (Cziczo and Froyd, 2014).Specifically, identifying and quantifying sources, global spatiotemporal distribution and mixing state of INPs might help to reduce model assumptions.In parallel, systematic laboratory measurements are indeed needed to develop water subsaturated ice nucleation parameterizations for the range of atmospherically relevant T and RH ice conditions for a better representation of ice nucleation processes in cloud models and to support in situ measurements.
Recently, Hoose and Möhler (2012) compiled previously reported aerosol-specific heterogeneous freezing efficiencies from laboratory experiments based on a single parameter, n s (e.g., Niemand et al., 2012;Connolly et al., 2009).In addition, the authors formulated ice nucleation efficiency by evaluating aerosol-specific "singular" freezing onsets when or after specific ambient conditions were met.Such timeindependent and surface-area-scaled n s formulations can be further adapted to comprehensively assess the ice nucleation in a wide range of atmospherically relevant T and RH ice conditions.Accordingly, the n s concept was adapted to deposition nucleation at low temperatures (up to −80 • C).
Within the framework of the Ice Nuclei Research Unit (INUIT), we comprehensively investigated the ice nucleation efficiency of pristine cubic hematite particles as a model proxy for atmospheric dust particles.Hematite is used as an example of atmospheric mineral dust particles, which can also be found in the form of cloudborne particles in shallow stratocumulus clouds (Matsuki et al., 2010).Natural hematite often exists in supermicron-sized silt particles and accounts for a few percent of the total dust particle mass (Claquin et al., 1999).Ice nucleation efficiencies of cubic hematite particles were measured using the AIDA (Aerosol Interaction and Dynamics in the Atmosphere) cloud chamber.We also reexamined the previously reported AIDA results of hematite ice nucleation (Hiranuma et al., 2014;Skrotzki et al., 2013) and combined them with the results from this work in order to examine the ice nucleation efficiency of hematite particles in the temperature range between −36 and −78 • C. In addition to developing the new dust parameterization from these AIDA measurements (Sects.3.1-3.3),the fitted n s parameterization was also applied to atmospheric modeling simulations (Sect.3.4).We implemented the parameterization in the Single-column version of the Community Atmospheric Model version 5 (SCAM5, Neale et al., 2010) and the Consortium for Small-scale Modeling (COSMO, Baldauf et al., 2011;Doms et al., 2011) models to assess the newly developed parameterization and compare them with existing parameterizations.It is important to note that the purpose of the current study is to perform a conceptual study with laboratory-synthesized hematite particles as a model aerosol for deposition ice nucleation, over a wide range of T and RH ice , but not to quantify how much hematite content contributes to ice formation in cirrus clouds.

Description of hematite particles
Laboratory-generated cubic hematite particles that have homogeneous chemico-physical properties were used as a proxy for atmospheric dust particles.These particles had a uniform composition, morphology and well-defined surface area.Hence, they are suited well for investigating T -and RH ice -dependent ice nucleation efficiency and relating it to the surface area (Hiranuma et al., 2014).Detailed information on the manufacturing process of cubic hematite particles is available elsewhere (Sugimoto and Sakata, 1992).Three different sizes of quasi-monodispersed hematite particles (∼200, ∼500 and ∼1000 nm diameter, respectively) were used in this work.The morphology and size of the hematite particles were characterized by scanning electron microscopy and determined based on an equivalent circle diameter derived from the observed 2-D particle projection area (Vragel, 2009;Hiranuma et al., 2014).A small-scale powder disperser (SSPD, TSI, Model 3433) was used to drydisperse the quasi-monodispersed hematite particles into the AIDA vessel as demonstrated in Skrotzki et al. (2013).

AIDA cooling expansion
The AIDA expansion freezing experiments were achieved by mechanical pumping (Möhler et al., 2003).Mechanical pumps can be operated at different pumping speeds simulating atmospherically relevant adiabatic cooling of rising air parcels in the cylinder of 84 m 3 in volume (i.e., 7 m height × 4 m width thermally conductive aluminum vessel) installed inside the thermostatic housing.For this study, a cooling rate of 5 • C min −1 was typically applied at the beginning.Then, the cooling rate decreased to < 0.1 • C min −1 within 400 s for each pumping expansion experiment, which was mainly due to an increasing heat flux from the chamber walls.Afterwards, an almost constant temperature was maintained by the stirred and well-mixed volume of the cold chamber.During the experiment, the pressure in the vessel decreased from 1000 to 800 mb.
The mean gas temperature in the AIDA vessel was determined by five thermocouples installed at different vertical levels.The sensors of these thermocouples were located about 1 m off the vessel wall and, thus, fully exposed to the chamber air.Stirring of the air by the mechanical ventilator prior to and during pumping ensured a homogeneous temperature distribution in the vessel of ± 0.3 • C (Möhler et al., 2003).The relative humidities with respect to water (RH water ) and RH ice were determined with an accuracy of ± 5 % using the mean gas temperature and the mean water vapor concentration.The water vapor concentrations were measured in situ by tunable diode laser (TDL) water vapor absorption spectroscopy throughout the expansion experiments.Since this direct long-path absorption technique is described and evaluated in detail in other publications (Fahey et al., 2014;Skrotzki et al., 2013), no further information is given here.
Under atmospheric pressure, prior to each expansion experiment, a combination of a scanning mobility particle sizer (SMPS, TSI, Model 3080 differential mobility analyzer and Model 3010 condensation particle counter), an aerosol particle sizer (APS, TSI, Model 3321) and a condensation particle counter (CPC, TSI, Model 3076) collectively measured the total number and size distribution of aerosols at the horizontally extended outlet of the AIDA chamber.Subsequently, the total aerosol surface area was estimated as presented in Hiranuma et al. (2014).During expansion, we quantified the ice nucleation of hematite particles with two different light scattering instruments: an optical particle counter welas (PALAS, Sensor series 2300 and 2500) (Benz et al., 2005) and SIMONE (German acronym of Streulichtintensitätsmessungen zum optischen Nachweis von Eispartikeln, which translates to the scattering intensity measurement for the optical detection of ice; Schnaiter et al., 2012).More details on the application of this specific combination of two instruments for the AIDA ice nucleation experiments are given in Hiranuma et al. (2014).

Ice nucleation parameterization and modeling
The size-independent singular ice nucleation efficiency, n s , was calculated by normalizing the observed AIDA ice crystal concentration (N ice ) to the total surface area of aerosols, which can be calculated by multiplying the surface area of an individual particle (S i ) by the total number concentration of aerosols (N ae ) (e.g., Niemand et al., 2012;Hoose and Möhler, 2012).For size-selected hematite particles, this linear approximation (i.e., n s = (−ln(1-α)) / S i ∼α / S i ) was mostly valid for the observed ice number fraction (α = N ice / N ae ).An overestimation of ice due to the use of linear approximation only amounted up to about a factor of 3 at n s ≤ 10 12 m −2 .Subsequently, the n s values estimated for the wide range of experimental conditions (−36 • C < T < −78 • C and 100 % < RH ice < water saturation) were used to depict and fit constant n s contour lines.
Here, these lines are referred to as the n s isolines or simply as the isolines.
The isoline-based parameterizations were derived (see Sect. 3.3) and then implemented in two atmospheric models (a single-column version of a global-scale model and a convection resolving model; see Sects.2.3.1.and 2.3.2. for model descriptions).The unique advantages of the use of both models in this study are (1) to demonstrate that our AIDA n s -based parameterization can be directly applied on different scales of atmospheric models and (2) to estimate the number of ice crystals simulated in two different atmospheric scenarios that complement each other and cover a wide range of atmospheric temperature and saturation conditions (ice formation at higher RH ice , up to ∼180 %, and lower T , down to ∼ −70 • C).More specifically, the former represents a finely resolved parameterization-oriented model embedded in the global model while the latter is a more physically based high-resolution grid-scale model, typically used to analyze small-scale complex systems for a fundamental understanding of ice formation.Altogether, results from two independent models were examined for a detailed modeling of atmospheric ice formation on all scales.
The mean size and surface area of hematite particles were prescribed with an assumption that either these particles are spherical and have a mean particle diameter of 1000 nm or the size of these particles follows a log-normal distribution, with a mean volume-equivalent diameter of ∼1000 nm (σ g = 1.05), which is consistent with the AIDA experiments described earlier (Hiranuma et al., 2014).The cloud microphysical sensitivity of these two size treatments was characterized.In addition, the sensitivity simulations of two lower boundaries of RH ice (i.e., 100 vs. 105 %) were also carried out.This sensitivity analysis was specifically useful to examine uncertainty involved in the TDL measurement (RH ice ± 5 %) concerning the condensed n s spacing (up to several orders of magnitude) in a narrow RH ice range and a certain T region.In both models, hematite particle number concentrations are given to be 200 L −1 , which is about the average dust concentration simulated by the SCAM5 model over the Southern Great Plain (SGP) site in springtime.Since the n s -isoline parameterization tested in this study is applicable at T below −36 • C, an additional parameterization was used to simulate ice formation of background particles at T > −36 • C, namely, the aerosol-independent M92 scheme.These parameterizations were combined to ensure more atmospherically relevant processes and conditions (e.g., distri-butions of water vapor) when compared to the application of the n s -isoline parameterization alone.
To better understand to what an extent the AIDA n sbased parameterization differs from other parameterizations commonly used in atmospheric models, the existing empirical parameterization of heterogeneous ice nucleation by Phillips et al. (2013; hereinafter denoted as P13) was implemented as well.The P13 scheme reflects the aerosol specific ice nucleation.In particular, the contribution of mineral dust with the background troposphere baseline surface area mixing ratio of ice-nucleating mineral dust particles (i.e., 2.0 × 10 −6 m 2 kg −1 ) was considered in this study.Ice formation occurring below water saturation only was considered and, thus, Eq. ( 1) in Phillips et al. (2008) was used for parameterizing ice nucleation.

SCAM5
Single-column models are widely used to test physical parameterizations for use in the general circulation model (GCM).The model has 30 vertical levels, and the model time step is set to 10 min.The single-column model resembles a single column of a GCM and can be derived from observations or model output.The complex feedbacks between the simulated column and other columns due to large-scale dynamics are not considered.Therefore, the single-column model is an ideal tool for testing ice cloud parameterizations.The SCAM5 model was modified to incorporate the new parameterization developed in this study.The Barahona andNenes (2008, 2009a, b) scheme, which provides an analytical solution of the cloud parcel model equations (hereinafter called BN scheme), is used for calculating ice nucleation in cirrus clouds.The new AIDA n s -isoline-based parameterizations as well as the P13 scheme were implemented in the model.The simulation was performed for 1 month (April 2010) at the United States Department of Energy's Atmospheric Radiation Measurement facility located at the SGP site (Hiranuma et al., 2014).

COSMO
The nonhydrostatic weather forecast model, COSMO, was adapted to systematically investigate the impact of hematite particles under the simulated upper-tropospheric conditions.COSMO is the high-resolution limited-area model to assess clouds and convection at a horizontal spatial resolution of 2.8 km with 50 layers of stretched vertical grids.The time step is set to 20 s.In this study, we simulated a period of 2 days (23-25 July 2011) on a domain of 450 × 450 horizontal grid points centered over the German Alps (longitude: 0.1-18.7 • E, latitude: 41.7-53.2• N).The initial and boundary conditions were provided by the European Centre for Medium-Range Weather Forecasts.They are available at the Meteorological Archival and Retrieval System.In order to account for the spatiotemporal evolution of mass  and HALO06_20,200 nm).This agreement verified the reproducibility of the AIDA chamber experiments, ice nucleation efficiency of hematite particles and size independence of the n s calculations.The advantage of using 1000 nm diameter hematite particles was that, due to their comparatively larger surface area, they were efficient in forming ice in cooling expansion experiments at −40 • C < T < −36 • C (Hiranuma et al., 2014).
The temporal profiles of deposition nucleation experiments from HALO campaigns, including N ice , gas T , RH ice and RH water measured by the TDL as well as the polarized light scattering properties in near-backscattering direction measured by SIMONE, are shown in Fig. 1.The depolarization ratio, which is sensitive to ice particle nucleation and growth, can be deduced from the latter.During a typical expansion, the air mass in the vessel experiences continuous cooling (for up to 500 s) and an increase in relative humidity (for up to 200 s; Fig. 1i, ii). Figure 1iii shows the temporal plot of the depolarization ratio.At the beginning of the expansion, the depolarization ratio increases because ice is nucleating on the hematite particles.Conversely, repartitioning of gas-phase water to ice-phase water due to growing ice crystals triggers the declines in both depolarization ratio (i.e., sizing effect, Schnaiter et al., 2012) and RH, usually after 100 s.The time delay in our welas ice detection (typically 1 µm is the minimum ice detection diameter for 200 and 500 nm diameter hematite particles) due to slower depositional growth after ice nucleation at lower T is accounted for in our error analyses (Fig. 2).We evaluated only up to several hundred seconds of each expansion experiment as the ice nucleating period.Similar experimental profiles for INUIT campaigns are presented in Fig. S1 in the Supplement.2014) only extend up to ∼10 9 m −2 , the data points of higher n s values were extrapolated based on the observed values from two measurements.Figure 2 shows several important features of n s -isoline curves.First, below −60 • C, n s isolines showed an increase in RH ice required to maintain a constant n s (i.e., n s > 2.5 × 10 8 m −2 ) with decreasing T (i.e., RH ice -dependent ice nucleation regime).For example, at RH ice = 120 % and T = −75 • C, cooling by 1 • C corresponds to a 10 % decrease in n s .This observation is interesting because the increase in RH ice required to maintain constant n s values is consistent with the CNT for deposition nucleation (Eq.A11 in Hoose and Möhler, 2012).Second, the highest sensitivity of RH ice is observed in a region where n s isolines are perpendicular to temperature isolines (∼ −60 • C < T < ∼ −50 • C).Here, n s is almost independent of T , and solely dependent on RH ice .Finally, we observed strong T -dependent nucleation near water saturation (i.e., while cooling along the water saturation line to- wards ∼ −50 • C).At a constant RH ice (e.g., 114 %), for example, cooling by 1 • C from −41 to −42 • C corresponds to an increase in n s of approximately half an order of magnitude (see inset in Fig. 2).This suggests that the n s values depend on temperature.Interestingly, we observed a continuous increase in n s during cooling even after the depletion of supersaturation below −40 • C (Fig. S2 in the Supplement).CNT does not explain this predominant T contribution near water saturation (Fig. A1 in Hoose and Möhler, 2012).Therefore, other microphysical processes at the particle surface and/or perhaps even within the bulk phase may be responsible for this T -dependent behavior and these results appear to support the existence of a pore-or surface-freezing process, as discussed in recent literature (e.g., Marcolli, 2014).In particular, we suspect that water condensation on the particle surface plays an important role on subsequent freezing.To support this, the surfaces of our hematite particles are not perfectly smooth and contain some active sites (e.g., pores and steps; Hiranuma et al., 2014).Moreover, water vapor may preferably fill the surface cavities due to the reduced saturation pressure in pores or at steps because of negative curvature Kelvin effects (Marcolli, 2014), thus leading to namely "surface condensation freezing" (SCF).As described in pre-viously published literatures (Christenson, 2013;Marcolli, 2014), SCF may be of relevance to homogeneous nucleation (i.e., spontaneous ice nucleation in supercooled aerosol) at relevant T (< −36 • C) and/or immersion mode freezing under water subsaturated conditions.Thus, SCF may arise from both homogeneous and heterogeneous nucleation.

Comparison with previous studies
The n s isolines of hematite particles were compared to previous measurements made using different aerosol species.This comparison was performed to (1) confirm that our n s fit reproduces the overall trend shown by previous studies under certain T and RH ice conditions and (2) to demonstrate that the parameterization with laboratory-synthesized hematite particles quantitatively represents ice nucleation properties of atmospheric dust particles.
Comparison of the hematite n s isolines to previous deposition freezing observations are shown in Fig. 3.More specifically, previous measurements were performed with natural Saharan desert dust (SD2, Möhler et al., 2006), reference Arizona test dust (ATD, Möhler et al., 2006;Welti et al., 2009), volcanic ash (Steinke et al., 2011), soot (Möhler et al., 2005), clay minerals (Welti et al., 2009;Koehler et al., 2010) and organics (Shilling et al., 2006;Wang and Knopf, 2011).These previous experimental studies used various types of ice nucleation instruments, such as substrate-supported cold stages coupled with an optical microscope (Shilling et al., 2006;Wang and Knopf, 2011), portable ice nuclei counters (Koehler et al., 2010;Welti et al., 2009) and the AIDA cloud simulation chamber (Möhler et al., 2005;Möhler et al., 2006;Steinke et al., 2011).They revealed the importance of both RH ice and temperature onto deposition-mode ice nucleation of specific particle compositions.In Fig. 3a, previous AIDA results for dusts, ash and soot are presented.Specifically, we utilized the T and RH ice data at α = 0.08 of SD2 and ATD reported in the previous AIDA study (Möhler et al., 2006) to define isolines.It is noteworthy that an α of 0.08 corresponds to ∼ 10 11 m −2 in n s when assuming uniform distributions of spherical particles of 0.5 µm diameter (n s = (−ln(1α)) / (π (0.5 × 10 −6 ) 2 )), which is in good agreement with the 10 11 m −2 n s -isoline of hematite particles.For volcanic ash, we adapted n s values (10 9 , 5 × 10 9 and 10 10 m −2 ) originally reported in Steinke et al., (2011).Möhler et al. (2005) found that the ice nucleation of soot starts at the initial increase in polarized light scattering intensity in near-backscattering direction at 488 nm (n s values are inaccessible).Except for these AIDA studies, other isolines in Fig. 3b and c were defined based on the reported ice nucleation measurements.For instance, Koehler et al. (2010) studied the deposition-mode nucleation of size-selected (i.e., 200, 300, 400 nm) natural dusts, and reported ice nucleation conditions (T and RH ice ) of ATD at α = 0.01 and of Canary Island dust and Saharan dust at α = 0.05.Welti et al. (2009) also studied the deposition nucleation abilities of size-segregated mineral dusts (i.e.,  100-800 nm diameter of ATD, illite, kaolinite and montmorillonite) based on α = 0.01.Shilling et al. (2006) reported the ice nucleation onsets of ammonium sulfate and maleic acid detected by the decreasing partial pressure of water with FTIR-reflection absorption spectroscopy (e.g., 1 in 10 5 nucleation at about −33 • C for a spherical particle size of 1-10 µm diameter).Wang and Knopf (2011) investigated deposition freezing of various mineral and organic particles including kaolinite, Suwannee River standard fulvic acid and Leonardite standard humic acid particles.The authors reported the mean size of particles and associated ice-activated fractions at the given T and RH ice .
As seen in Fig. 3, the results from previous studies suggest the necessity of increasing RH ice to maintain a constant n s value below T ∼ −55 • C.They also indicate that nucleation may be triggered by SCF in the region where data and isolines approach water saturation where temperature plays a significant role on ice nucleation.It can also be observed that the contour of our new n s -isoline parameterization of cubic hematite particles in T and RH ice coordinates generally agrees with the onsets determined by previous studies of other atmospherically relevant aerosols.In particular, the n s isolines estimated from ATD and SD2 (∼10 11 m −2 ; Fig. 3a), which reasonably agree with the hematite n s -isoline, suggest that atmospheric dust may have similar deposition-mode ice nucleation efficiency.

n s -isoline-based parameterizations
Next, the ice nucleation efficiency of hematite particles was parameterized over a wide range of T and RH ice .Three types of parametrical descriptions used in this study are shown in Fig. 4. First, based on the AIDA experimental results, a series of constant n s curves was interpolated to produce isolines in the range of 10 6 m −2 < n s < 10 12 m −2 (Fig. 4a).The lower bound of the n s value (10 6 m −2 ) was set based on the minimum n s observed during AIDA expansions.Since the certain regions of n s isolines (i.e., n s < 7.5 × 10 10 m −2 ; blue lines in Fig. 2) can submerge below ice saturation, the correction was applied to shift them and maintain all isolines above 100 % RH ice .The procedure to constrain n s to >100 % RH ice is described in the supplement (Fig. S3 in the Supplement).Above the upper bound of 10 12 m −2 , n s presumably remains constant up to the water saturation line in the T and RH ice space (no experimental data is available in this range).This assumption is valid in the present study because this n s upper limit was hardly reached in our modeling case.However, more cloud simulation chamber measurements and data points for n s 10 12 m −2 are required to correctly constrain the n s upper limit.It also has to be noted that the modeled ice crystal number concentration (L −1 ) derived from ice nucleation of hematite in this study is approximated by multiplying n s by a simulated total surface of hematite (6.3 × 10 −10 m 2 L −1 ).
In the second fit approach (Fig. 4b), the interpolated n s values were used to formulate the n s -isoline with a third-degreepolynomial fit as a function of T ( • C) and RH ice (%) as n 3d s (T , RH ice ) = −3.777× 10 13 − 7.818 × 10 11 where n 3d s (T , RH ice ) is the n s derived from the third-degree fit.The resulting spatial plot of isolines for constant n s is shown in Fig. 4b.Note that the upper temperature boundary of −36 • C was assigned as the interface between immersionmode and deposition-mode ice nucleation (Hiranuma et al., 2014), and the lower boundary of −78 • C is the limit introduced by interpolating the hematite-isoline curves.The third approach (Fig. 4c) consisted in applying the equivalent n s for deposition nucleation of hematite particles parameterized using the method introduced by Phillips et al. (2008Phillips et al. ( , 2013)).Specifically, we characterized the nucleation activity solely of mineral dust through the deposition-mode by adapting Eq. (1) from Phillips et al. (2008), which accounts for nucleation under water subsaturated conditions, and excluded the contribution at water saturation, i.e., Eq. (2) of Phillips et al. (2008).AIDA n s -isoline-based parameterization suggests strong supersaturation dependence of n s at low T .Observed diversity between a new parameterization (Fig. 4a, b) and P13 (Fig. 4c) may result in different ice crystal forming propensities and may predict different cloud properties.The potential consequence of observed diversity is demonstrated using conceptual models and discussed in the following section.

Model simulations
The SCAM5 results for monthly mean profiles of the simulated in-cloud N ice (Ni ∼ N ice ) over the ARM SGP site for five cases are shown in Fig. 5.These include (case 1) the pure homogeneous ice nucleation case, (cases 2-4) cases with contributions from both homogeneous and heterogeneous ice nucleation (hereinafter referred to as the combined cases) described in Fig. 4a-c (corresponding to simulations A, B and C), and (case 5) the simulation of the different lower boundaries of RH ice (RH * i , simulation D).In addition, the observed profile of ice crystal number concentrations is also shown in comparison to the simulations in Fig. 5.The observational data were collected over the SGP site on 8 days of April 2010 during the Small Particles In Cirrus (SPARTICUS) campaign (Zhang et al., 2013).The results of our simulations suggests that ice crystal formation due to heterogeneous ice nucleation processes inhibits homogeneous ice nucleation and significantly reduces the ice number concentrations for the AIDA parameterizations (Fig. 4a, b).In contrast, due to the much less ice crystal production from P13, as shown by the pure heterogeneous case in Fig. 5, homogeneous ice nucleation in the P13 case (Fig. 4c) is less affected by heterogeneous nucleation.The observed mean profile of in-cloud ice crystal number concentrations is in agreement with the simulated ones.The differences between the three parameterizations derived from AIDA measurements, corresponding to simulations A, B and D, are small for both the combined case and the pure heterogeneous ice nucleation case as presented in Fig. 6.This is because the BN scheme used in SCAM5 is based on parcel model theory and uses the predicted maximum ice supersaturation (S max ) to calculate deposition ice nucleation rates.S max is determined by assuming that the supersaturation will reach its maximum where the depletion of water vapor compensates the supersaturation increase from cooling in a cloud parcel (i.e., BN scheme).The three parameterizations (i.e., simulations A, B and D) have the largest differences when RH ice is below 120 % while S max calculated in the model is often larger than 115 %.This also explains the low sensitivity of N ice to the lower bound of the onset RH ice value (Figs. 5,6).We also investigated the impact of different particle size distributions on the calculation (not shown).The impact is small and negligible.The negligible sensitivity to the choice of AIDA parameterizations in SCAM5 simula-  The results of the COSMO model for the vertical profiles of N ice (presumably equivalent to the heterogeneous INP number concentration) are summarized in Fig. 7.These results simulate the three different parameterization schemes (corresponding to Fig. 4a-c) in combination with homogeneous freezing.N ice was spatially averaged over all areas of the model domain which in principle allow for deposition nucleation in our simulations, i.e., conditions below −36 • C and above 100 % RH ice .Because n s is not always larger than the lower bound of the n s value (10 6 m −2 , i.e., white areas in Fig. 4), also areas without ice formation are contained.It is also noteworthy that only purely heterogeneous ice formation is presented rather than the total ice occurring in the model.As shown in Fig. 7, the mean N ice resulting from the parameterization based on P13 is smaller than that obtained from the AIDA n s -isoline-based parameterization by more than 2 orders of magnitude.This large difference results predominantly from the inactivity of P13 at low RH ice .Unlike the SCAM5 results, the COSMO results show the sensitivity to the different lower boundaries of RH ice (i.e., RH * i = 105 %, simulation D).For instance, the mean N ice below −36 • C with a higher RH ice boundary (105 %) is reduced by 12 %.This difference is perhaps due to the use of finely resolved grid-scale humidity in COSMO rather than parameterizing S max as done in SCAM5 (Gettelman et al., 2010).gated in fine T and RH ice spacing (1K and 2 % bins, respectively) based on the thermodynamic conditions under which ice crystals were formed in COSMO and summed up over the time of simulation.This segregation allows for an estimation of the relative contribution of different thermodynamic conditions to the simulated ice formation.Our results show diversity between P13 and the AIDA n s -isoline-based parameterization.Ice crystal formation was less for P13 and more for the new parameterization.A possible explanation for the observed deviation may be due to the difference in parameterization based on laboratory or field data.For instance, atmospheric aging and processing (i.e., surface coating and associated heterogeneous surface reactions) may have altered ice nucleating propensity and limited deposition nucleation of dust-derived INPs in the P13 parameterization for the field data-derived parameterization as discussed in Phillips et al. (2008).

Discussions
As described in the previous section (Sect.3.1), depositionmode freezing cannot solely explain the n s -isoline observation below water saturation (-50 • C < T < −36 • C in Fig. 2).Although we presumed that SCF acts as a subset of immer-Atmos.Chem.Phys., 14, 13145-13158, 2014 www.atmos-chem-phys.net/14/13145/2014/sion freezing and plays an important role in this region, further insight and evidence of SCF beyond cloud simulation chamber observations are required to correctly understand the contributions of both homogeneous and heterogeneous nucleation.High-resolution microscopic techniques with an integrated continuous cooling setup are needed to visualize the freezing process of a single particle and to fully understand the complex freezing processes involved in SCF on particle surfaces.
Comparison of the new parameterization to a previous empirical parameterization (P13) showed that the new AIDA n sisoline-based scheme predicts more ice .In particular, the T and RH ice dependence of N ice and n s at low T that may coincide in the upper troposphere highlights the need for further investigations.However, it should be noted that there is some evidence for the atmospheric relevance and applicability of the new parameterization.First of all we demonstrated that the new n s parameterization based on the experiments with hematite particles agrees well with previous literature results for mineral dust aerosol (e.g., Möhler et al., 2006;Welti et al., 2009;Koehler et al., 2010).Second, Niemand et al. (2012) demonstrated that different dusts exhibit similar n s in immersion-mode freezing and perhaps such a similarity remains true for the deposition-mode ice nucleation of desert dusts.Lastly, the comparison between the observed profile of ice crystal number concentrations and the simulated ones (Figs. 5, 6) also suggests the validity of the new parameterization.These premises must be further examined in comparing to atmospherically relevant substrates (fresh and aged ones) and their ice nucleation activities in laboratory settings.In situ INP measurements, such as the number concentration and the types of INPs, at the upper troposphere can also help to constrain the parameterization.
Finally, to further develop more atmospherically relevant parameterizations other than the fit-based parameterization with artificial test aerosol, the relationship between 1/T and ln S ice for a constant nucleation rate or n s based on the CNT can be analyzed (i.e., Eqs.A10-A11 in Hoose and Möhler, 2012).In this way, the composition-specific n s (T −S ice ) values, where the transition from SCF to deposition nucleation (or vice versa) occurs, may be better defined and can be then be used as an inexpensive model friendly parameterization.

Conclusion
A new heterogeneous ice nucleation parameterization was developed using results obtained from AIDA cloud simulation chamber experiments.The new n s -isoline-based parameterization is applicable to a wide temperature range from −36 to −78 • C and, hence, allows for the examination of ice nucleation spectra in a simple framework for modeling application.
Our experimental results provide a good basis for the T and RH ice dependence of deposition nucleation, and the formulated hematite n s isolines are comparable to that of desert dust samples.Consequently, our results with synthesized hematite particles can also be relevant to cirrus applications despite their smaller atmospheric relevance compared to natural hematite.Our isoline formulation suggested three different ice nucleation pathways over the wide range of temperature.Specifically, a RH ice -dependent ice nucleation regime was observed at temperatures below ∼ −60 • C, where deposition mode is presumably responsible for triggering ice nucleation.At −60 • C < T < −50 • C, ice nucleation efficiency was T -independent (i.e., RH ice -dependent).Conversely, a predominant influence of T on ice nucleation was observed near the water saturation condition (T > ∼ −50 • C), which may be indicative of nucleation due to condensation of water at the particle surface followed by homogeneous freezing of the condensed water (i.e., SCF).The observed active SCF near water saturation and physical processes at the transitions of nucleation modes still remain to be studied in detail for various types of atmospheric particles.
Our conceptual model examinations also considered the competition between heterogeneous freezing and homogeneous freezing of solution particles to evaluate the relative importance of the different freezing processes in two models (SCAM5 and COSMO).The inhibition of homogeneous nucleation due to heterogeneous freezing was commonly observed in both SCAM5 and COSMO simulations.Our new parameterization revealed a minimum deviation of N ice values estimated by SCAM5 at minimum RH ice values for ice formation (100 or 105 %) compared to COSMO.This deviation suggests different sensitivities of the model to the lower bound of the RH ice value owing to the presence of the modelresolved supersaturation to calculate the ice nucleation rate.Overall, our new hematite-based parameterization strongly suggests the role of T and more ice nucleation when compared to the existing empirical parameterization, presumably allowing for more ice activation under water subsaturated conditions.
The Supplement related to this article is available online at doi:10.5194/acp-14-13145-2014-supplement.

Figure 1 .
Figure 1.Temporal plots of the representative AIDA deposition-mode freezing experiments with various cooling ranges, including A. HALO06_19, B. HALO06_21, C. HALO05_18 and D. HALO05_24.Panels are arranged to show the measurements of i. AIDA mean gas temperature (T ), ii.TDL, iii.SIMONE and iv.ice crystal concentration (N ice ).Note that the red lines represent interpolated data used for the n s -isoline formulation.The I back,par in the panel iv axis denotes the backscattered light scattering intensity parallel to the incident polarization state (log-scaled).An increase in the depolarization ratio indicates the formation and growth of ice crystals.

Figure 2 .
Figure2.The constant n s magnitudes are joined by lines (blue) representing "isolines" of hematite freezing profiles in the T and RH ice space.The interpolated isolines are equally spaced at every order of magnitude from 10 12 m −2 (top) to 10 9 m −2 (bottom).Experimental trajectories of AIDA expansion experiments with hematite particles are shown as red dotted lines.The data indicated with green color on the water saturation line represent the previously reported results of immersion freezing(Hiranuma et al., 2014).The subpanel shows a magnified section of T (−35 to −45 • C) and RH ice (110-120 %) space with equidistant n s spacing (every quarter magnitude).The error bars at n s of 10 12 m −2 are from welas.

Figure 3 .
Figure 3. Ice nucleation onset T and RH ice of previously published data (a AIDA studies, b dust, and c ammonium sulfate and organics) shown together with the isolines of hematite particles from the present study (10 12 m −2 (top)-10 9 m −2 (bottom)).

Figure 4 .
Figure 4. Spatial plot of isolines for constant n s derived from (a) interpolating AIDA data, (b) applying the third-degree-polynomial fit function to interpolated AIDA data, and (c) a previously published parameterization (Phillips et al., 2013) for hematite particles.The color scale displays log-scaled n s values per square meter, applicable to all panels.The solid black lines indicate the homogeneous freezing threshold line (i.e., Koop line).

Figure 5 .
Figure 5. Monthly mean profiles of the simulated in-cloud ice crystal number concentrations (Ni ∼ N ice ) over the ARM SGP site.The four cases shown in the figure include the pure homogeneous ice nucleation case (HOM) and four combined (heterogeneous + homogeneous) ice nucleation cases: (a) AIDA interpolated + homogeneous; (b) AIDA fit + homogeneous; (c) P13 + homogeneous; and (d) AIDA interpolated (RH * i =105 %) + homogeneous.Black dots show the observed mean profile of Ni.Left and right ends of the horizontal bars indicate the 10th and 90th percentiles of the observed Ni values at each pressure level.

Figure 6 .
Figure 6.Monthly mean profiles of the simulated in-cloud ice crystal number concentrations (Ni ∼N ice ) over the ARM SGP site.The four cases shown in the figure include the pure homogeneous ice nucleation case (HOM) and four pure heterogeneous ice nucleation cases: (a) AIDA interpolated; (b) AIDA fit; (c) P13; and (d) AIDA interpolated (RH * i = 105 %).Black dots show the observed mean profile of Ni.Left and right ends of the horizontal bars indicate the 10th and 90th percentiles of the observed Ni values at each pressure level.

Figure 7 .
Figure 7.The mean heterogeneous INP number concentrations (∼N ice ) simulated in COSMO.The red dashed line represents the simulation with 105 % RH ice as the lower boundary of ice formation, while the others are based on with 100 % for the minimum RH ice value.
Author contributions.N. Hiranuma and O. Möhler designed and conceived the experiments.Parameterizations were implemented by N. Hiranuma, I. Steinke and M. Paukert.M. Paukert and K. Zhang carried out modeling studies with input from C. Hoose, N. Hiranuma and G. Kulkarni.M. Schnaiter analyzed SIMONE data.H. Saathiff contributed to TDL measurements and analysis.The manuscript was written by N. Hiranuma.All authors discussed the results and contributed ideas to the manuscript.
(Kärcher et al., 2006;Ren and MacKenzie, 2005)s (i.e., cloud droplets, raindrops, cloud ice, snow, graupel and hail), the two-moment bulk microphysics scheme was incorporated in our COSMO model version following the method described bySeifert and Beheng (2006)andSeifert et al. (2012).Apart from the AIDA isoline-based freezing parameterization of hematite, two other ice nucleation modes, namely, M92 and homogeneous nucleation of cloud or solution droplets(Kärcher et al., 2006;Ren and MacKenzie, 2005), were considered in our COSMO simulations.The latter was used to parameterize the competition of water vapor between homogeneous and heterogeneous freezing.

3 Results 3.1 AIDA ice nucleation experiments A
Skrotzki et al. (2013)ents was carried out during the INUIT01 and INUIT04 campaigns to investigate the ice nucleation efficiency of well-characterized hematite particles under water subsaturated conditions at −47 • C < T .In addition, we used the AIDA results reported bySkrotzki et al. (2013)and reconciled them with the n s values in order to parameterize the overall ice nucleation efficiency of hematite particles up to −78 • C. In total, 12 expansion experiments, 4 from the INUIT campaigns and 8 fromSkrotzki et al. (2013), were studied.Detailed experimental conditions and aerosol properties for these expansion experiments are summarized in Table1.The use of different sizes of hematite particles in different temperature regions was justified by calculating the size-independent n s values of 200 and 1000 nm diameter particles at ∼ −40 • C. For instance, the evaluated n s values (10 10 m −2 ) for these two sizes agreed very well within ± 1 % RH ice and ± 0.3 • C of chamber con-ditions (see corresponding RH ice and T at "Evaluated n s " in Table 1 for INUIT04_08, 1000 nm, HALO06_19, 200 nm,