The impact of microphysical parameters, ice nucleation mode, and habit growth on the ice/liquid partitioning in mixed-phase Arctic clouds



[1] The fundamental physical processes that maintain supercooled liquid in observed Arctic mixed-phase clouds are poorly constrained. To isolate the factors that control ice/liquid partitioning during the ascent of an air parcel, we apply an adiabatic parcel model that includes ice nucleation by deposition and immersion freezing and ice habit evolution. Simulations are performed for two different temperature regimes that resemble those observed during the Mixed-Phase Arctic Cloud Experiment (−13°C < T < −9°C) and the Surface Heat Budget of the Arctic Ocean (−22°C < T < −17°C). Effects on ice and liquid water evolution in an updraft are explored as a function of ice nucleus (IN) concentration and nucleation mode, updraft velocity, properties of cloud condensation nuclei, and assumption about ice particle shape (habit). For most conditions, ice and liquid coexist and increase simultaneously, and only at high IN concentrations or low updraft velocities do ice particles grow at the expense of droplets. The impact of the ice nucleation mode on ice/liquid distribution depends on the temperature and supersaturation regime. The assumption of spherical ice particles instead of nonspherical habits leads to an underestimate of ice growth. It is concluded that updraft velocity, IN concentrations, and particle shape can impact ice/liquid distribution to similar extents.

1. Introduction

[2] The large spatial coverage of Arctic low-level stratiform clouds has a profound influence on the surface energy budget of the Arctic. Such clouds often consist of both the liquid and ice phases that exhibit remarkable longevity. Many large eddy and cloud-resolving model simulations fail to reproduce the observed combinations of lifetimes, ice/liquid water ratios, and ice concentrations owing to numerous uncertainties in the representation of microphysical processes that determine ice formation and distribution [Harrington et al., 1999; Morrison et al., 2005; Klein et al., 2009]. In particular, nucleation mechanisms and vapor growth have been identified as key processes that lead to quite different predictions of the lifetime of such clouds [Khvorostyanov and Curry, 2005; Morrison et al., 2005; Fridlind et al., 2007; Avramov and Harrington, 2010].

[3] Mixed-phase clouds exist at temperatures greater than ∼−35°C, and thus ice formation is initiated by heterogeneous nucleation which implies the presence of insoluble, or partially soluble particles that act as condensation sites for freezing. However, the particle properties (surface and bulk composition) and the temperature regime determine the specific mechanisms that lead to ice nucleation: Insoluble particles that do not have a liquid coating form ice heterogeneously by direct uptake of water vapor on their surface (i.e., deposition freezing). Internally mixed particles that contain both soluble and insoluble fractions can form ice via freezing of haze particles or activated droplets (condensation freezing or immersion freezing, respectively). Contact freezing implies that haze particles or droplets freeze upon contact with ice nuclei.

[4] In many modeling studies, the prediction of ice nucleus (IN) number concentrations is based entirely on empirical approaches where ice concentration is diagnosed from a function of temperature and/or supersaturation [e.g., Meyers et al., 1992; Phillips et al., 2008; Eidhammer et al., 2009]. Other studies apply classical nucleation theory to predict the evolution of mixed-phase clouds [Khvorostyanov and Curry, 2004, 2005]. The equations from classical nucleation theory contain several parameters characterizing the IN properties and these carry large uncertainties. Some guidance on the choice of parameters such as surface tension, active sites and contact angle, can be obtained from laboratory studies [Chen et al., 2008]; however, consistent data sets relevant to different aerosol and nucleation modes are limited.

[5] The relative contribution of each nucleation mechanism to ice concentration is not clear and conclusions from model studies are ambiguous [Fridlind et al., 2000; Harrington and Olsson, 2001; Morrison et al., 2005]. Recent studies have suggested that immersion freezing is the main nucleation mechanism in Arctic mixed-phase clouds within the temperature range of ∼−20°C to −15°C [de Boer et al., 2010, 2011]. The former study deduced that submicron particles composed of >60% soluble material by mass act as cloud condensation nuclei (CCN) first and then freeze after droplet formation.

[6] The mass ratio of ice and liquid in Arctic mixed-phase clouds has been shown to be highly sensitive to the number concentration of ice particles and the evaporation rates of liquid drops [Korolev and Isaac, 2003; Korolev, 2008]. The efficiency of ice growth depends on the kinetics of vapor uptake which in turn is a function of the shape of ice particles [Chen and Lamb, 1994; Sheridan et al., 2009]. Most current models assume either spherical particles, a fixed aspect ratio [Korolev and Mazin, 2003], or predict a maximum dimension. However, it has been shown that detailed consideration of temperature-dependent habit growth, and thus vapor fields can significantly affect the glaciation timescales, which translates into uncertainties in predicted phase distributions and lifetimes [Harrington et al., 2009]. For instance, the aspect ratios of crystals change nonlinearly during vapor growth (K. Sulia and J. Y. Harrington, Theoretical studies on mixed-phase cloud lifetime: 1. Influences of predicted ice habit, submitted to Journal of Geophysical Research, 2011). A nonspherical particle acquires more tightly concentrated vapor gradients over faces with the largest curvature as the aspect ratio deviates further from unity. As a result, the flux of vapor onto the particle increases along the particle's semimajor axis, which further enhances the vapor flux. This cyclic process induces a nonlinear positive feedback between aspect ratio evolution and vapor uptake. Therefore, for the same volume and mass, nonspherical particles have a larger growth rate than do spherical particles [cf. Sulia et al., 2010, Figures 3 and 6]. Because the effect is nonlinear, the longer nonspherical ice particles grow the larger the difference in comparison to spheres. Fukuta and Takahashi [1999, Figure 18] illustrate this result in comparison to data taken in wind tunnels at liquid saturation. Omitting this effect of nonspherical growth can therefore substantially overestimate liquid mass, and therefore overestimate cloud glaciation time, especially at habit-prone temperatures.

[7] While nucleation mechanisms, habit growth, aerosol properties (IN, CCN composition) and temperature regimes are known to affect ice/water partitioning during the evolution of the cloud, it is unclear whether any one of these parameters dominates the phase distribution. The goal of this study is to explore the relative importance of these parameters on the basis of observed cloud temperature regimes for typical fall and winter clouds during the Mixed-Phase Arctic Cloud Experiment (MPACE, 27 September to 22 October 2004 [Verlinde et al., 2007]) and the Surface Heat Budget of the Arctic Ocean (SHEBA, 2 October 1997 to 12 October 1998 [Uttal et al., 2002]). We apply an adiabatic parcel model for a single ascent of an air parcel. The model includes detailed quantification of nucleation modes and habit evolution, but is limited in its representation of other microphysical processes (such as particle sedimentation and collection) and dynamics. This approach does not allow comprehensive conclusions about cloud stability, which require simulations over longer time scales (multiple cloud cycles) or, preferably, a coupled dynamical model. However, the main goal of our study is the interplay between nucleation, ice growth, and dynamics which can be studied in a single parcel cycle. While the parcel model framework is in many ways idealized, it does allow us the ability to explore the relative effects of individual parameters that affect ice formation and growth and thus the ice/liquid distribution in mixed-phase clouds that might eventually lead to cloud glaciation or maintenance. Moreover, microphysical models that capture a high level of detail can be used in parcel models, unlike Eulerian cloud models in which the microphysics must be simplistic.

[8] Recognizing the limitations of this modeling framework, we do not attempt to reproduce the exact observed microphysical cloud parameters in the model simulations, but rather use the observations to provide meteorological context for the relative importance of composition (nucleation modes, onset temperature of freezing), microphysical parameters (IN and CCN properties, updraft), and habit evolution for the ice/liquid partitioning in mixed-phase clouds.

2. Model

2.1. Model Description

2.1.1. Adiabatic Parcel Model

[9] An adiabatic parcel model, used previously to describe warm-cloud and aerosol interactions [Feingold and Heymsfield, 1992], has been extended to include ice microphysics. Aerosol particles are represented by individual particle size classes on a moving size grid, with the initial size determined by the discrete aerosol particle mass at that grid point. Two aerosol populations are defined: The first is composed of partially soluble particles that can form cloud droplets, some fraction of which can act as immersion freezing IN. The treatment also includes condensation freezing allowing deliquesced particles to freeze below liquid water saturation. Immersion and condensation freezing are implemented on the basis of that given by Khvorostyanov and Curry [2004]. The second externally mixed aerosol population is composed of completely insoluble particles that act as IN for deposition freezing. Deposition freezing follows that given by Chen et al. [2008]. Contact freezing is not considered in this study.

[10] All (partially) soluble particles have the same mass fractions of (in)soluble material and thus all particles of the same size form cloud droplets if the critical supersaturation or a minimum size threshold for cloud droplets is exceeded. In contrast, ice nucleation is treated using a probabilistic approach. At any given model time step (typically one second) a small fraction of particles of a given size class may freeze. In order to avoid the formation of an infinite number of ice classes, a binning method is applied that populates a new ice particle class if at least 1% of a droplet size class or insoluble particle size class is predicted to freeze by immersion or deposition freezing, respectively. Consequently, a maximum of 100 times more ice classes might be formed than the number of initial aerosol/drop classes. Usually, this maximum number is not reached because often more than 1% of the initial classes freeze in a time step, in which case all the frozen particles are combined in a single new class. In addition, in most simulations not all IN exceed their freezing threshold.

[11] The model does not include removal of particles by sedimentation. However, as a proxy for the possible effects of this process, the fall velocity for all particles is calculated assuming that they fall with their maximum dimension perpendicular to the fall direction. A parameterized approach is applied that is based on laboratory measurements and takes into account different size ranges and shapes (plates, columns) of ice particles [Mitchell, 1996] (section 4.1). Radiative cooling and ventilation effects on the diffusional growth of ice particles and interactions of ice particles with other particles or droplets (riming and aggregation, respectively) are not accounted for. Neglect of these processes might lead to a biased prediction of the ice/liquid partitioning.

2.1.2. Habit Growth Model

[12] The model predicts the shape (aspect ratio) of ice particles as a function of temperature on the basis of the capacitance model and the mass distribution hypothesis of Chen and Lamb [1994]. Ice aspect ratio evolution is based on laboratory data. Implementation in this work follows the method of Sulia and Harrington (submitted manuscript, 2011): Ice particles are represented as spheroids, allowing for the evolution of the primary habits (lengths of prism axis a and basal axis c). Ice grows with a shape determined by the inherent growth ratio Γ using the values compiled by Chen and Lamb [1994], which were extracted from various laboratory and some in situ data sets [Chen and Lamb, 1994]. Since Γ is the ratio of the deposition coefficients of the c axis to the a axis, it contains the inherent growth dependence of an ice crystal on temperature, and is used to dictate how the available vapor mass is distributed onto both crystal faces (basal and prism). Through this method, ice particles can grow nonisometrically along two axes, and at any given time step full information of the aspect ratio (ϕ = c/a) and equivalent diameter (equivalent to the diameter of a sphere) of all ice size classes is stored. Secondary habits are approximated on the basis of temperature and ice supersaturation through the deposition density [Chen and Lamb, 1994], which is always smaller than the density of solid ice. The deposition density is an approximate way to account for the increasing branching and hollowing that characterizes real crystals as the saturation state rises: For the same a and c axes lengths as a real crystal, a spheroid (or a sphere) overestimates the particle volume. Density is traditionally reduced to account for the difference in volume between real crystals and spheres or spheroids [e.g., Fukuta and Takahashi, 1999]. The density of the spheroidal ice is a volume-weighted combination of the preexisting and the newly deposited mass.

[13] While this model is restricted to spheroids and thus cannot predict the great variety of shapes encountered in the atmosphere (e.g., dendrites, rosettes), it provides a first-order measure of the primary habit by tracking the evolution of two axes and thus represents an improvement of current methods that assume either spherical particles or in situ mass-size relations (where only one size is stored). The model was tested against independent laboratory measurements taken in a wind tunnel at liquid saturation [Takahashi et al., 1991], and it was shown that the model produces a relatively accurate prediction of the particle aspect ratio and mass [Chen and Lamb, 1994]. The basic approach has also been successfully applied in recent cloud modeling studies [Hashino and Tripoli, 2007, 2008].

2.2. Model Initialization of Base Case Simulations

[14] All model simulations are initialized at a relative humidity (RH) of 95% and a temperature of −9°C (MPACE [Klein et al., 2009]) and −17°C (SHEBA [Morrison et al., 2011). Simulations are performed up to a height of 500 m above the initial 95% RH conditions. The air parcel has a constant updraft of w = 10 cm s−1. We do not follow an air parcel through multiple cloud cycles and thus the simulations are not designed for cloud evolution over longer time scales; it does, however, allow us to explore the effects of our target parameters (IN concentration and properties, ice nucleation mode, particle habit) on the ice/liquid partitioning. Since we are primarily interested in ice initiation, a single updraft is sufficient for examining the various microphysical connections. Nevertheless, our results do bear on cloud lifetime and stability since the effects we describe will also affect clouds in later stages of development.

[15] The initial temperature of the simulations is the only parameter that differs between the two cases; all other parameters were kept identical for the comparison, although both meteorological and aerosol parameters were clearly different during the two field experiments, as discussed in section 4.2.

[16] The aerosol grid points are distributed logarithmically over a radius range of 0.01 μm < rdry < 1.2 μm for both CCN (immersion freezing nuclei) and the externally mixed (insoluble) deposition freezing nuclei; both initial size distributions are lognormal (σ = 1.4, rg = 0.04 μm). For what we refer to as the base case simulations, the only ice nucleation mechanism allowed is deposition freezing, and the total number of particles that could potentially freeze is N(IN) = 1 L−1. The base case simulations assume a CCN concentration, N(CCN) = 100 cm−3, and are assumed to be composed of 90% soluble material (ammonium sulfate). Surface properties of IN can be varied by changing the contact angle θ and/or the number of active sites α. For the base case simulations, the deposition freezing IN have a geometric factor of f = 10−4 which translates to θ = 10°, a value typical of dust IN [Chen et al., 2008]. In sensitivity studies, where immersion freezing is explored, only a small fraction of CCN is allowed to act as IN (1 in 105 of the 100 cm−3 yields a concentration of 1 L−1). Immersion freezing IN have a contact angle (θ ∼ 60°) resembling freezing characteristics that have been observed for coated dust particles [Marcolli et al., 2007]. While our model might be applicable to any mixed-phase cloud conditions, the low aerosol concentrations applied here are usually only encountered in the Arctic and thus conclusions drawn will tend to hold for clouds in those latitudes.

[17] Parcel model simulations are useful in that they allow the identification of the key parameters under investigation. In this regard they are similar to laboratory studies in which single parameters can be varied in a controlled sense. Given this motivation, only one parameter at a time was changed in our sensitivity simulations in order to evaluate its influence on the ice/liquid distribution. In addition, to give a rough estimate of the effects of particle sedimentation, sensitivity tests are performed, in which all particles falling faster than the updraft are removed from the cloud (section 4.1).

[18] In section 3, we explore the sensitivities of ice mass and size distributions to w, number concentration and composition of both IN and CCN, and habit formation. In Tables 1 and 2, the following key parameters are summarized at three different heights (100 m, 300 m, 500 m): the phase distribution of ice to liquid water content (IWC/LWC), the fraction of frozen particles relative to the initial IN concentration N(IN)frozen/N(IN), average equivalent diameter (Dav), and average aspect ratio (ϕav).

Table 1. Summary of Model Results for the MPACE Case (−12.7°C < T < 9.1°C) at Three Heights Above Model Initialization, With RH = 95%a
SimulationModel Conditionsb100 m (−10°C)300 m (−11.5°C)500 m (−12.7°C)
N(IN)frozen/N(IN)IWC/LWCDav (μm)equation imageavN(IN)frozen/N(IN)IWC/LWCDav (μm)equation imageavN(IN)frozen/N(IN)IWC/LWCDav (μm)equation imageav
  • a

    Fractional ice particle number (N(IN)frozen/N(IN)), ice-to-water mass ratio IWC/LWC, average equivalent diameter of ice particles Davσ), and average aspect ratio of ice particles ϕavσ). Note that Simulations 7 and 12 are only performed for the SHEBA case since immersion freezing is not active at temperatures < −12°C.

  • b

    Here imm means that only immersion freezing IN is considered.

1Base case0.870.08250 ± 690.81 ± 0.150.910.19439 ± 440.61 ± 0.180.920.34584 ± 310.49 ± 0.17
2w = 2 cm s−10.862.6568 ± 160.80 ± 0.180.8918000986 ± 920.62 ± 0.200.89760001100 ± 760.57 ± 0.19
3w = 40 cm s−10.910.02106 ± 270.74 ± 0.110.910.016215 ± 150.54 ± 0.120.880.034298 ± 110.43 ± 0.11
4w = 100 cm s−10.910.01659 ± 160.76 ± 0.080.910.005139 ± 70.51 ± 0.100.950.009188 ± 50.41 ± 0.09
5N(IN) = 0.2 L−10.870.015251 ± 690.81 ± 0.150.910.025439 ± 440.61 ± 0.180.940.053584 ± 310.49 ± 0.17
6N(IN) = 5 L−10.920.6250 ± 690.81 ± 0.150.911.45440 ± 440.60 ± 0.180.9142000584 ± 310.49 ± 0.17
7N(IN) = 1 L−1 imm------------
8N(CCN) = 10 cm−30.900.19249 ± 700.80 ± 0.160.910.15448 ± 400.61 ± 0.170.920.36529 ± 290.50 ± 0.16
9N(CCN) = 300 cm−30.870.08251 ± 690.80 ± 0.16  439 ± 440.61 ± 0.18  615 ± 290.47 ± 0.16
10ɛsol = 0.50.880.081250 ± 690.81 ± 0.150.910.13439 ± 430.61 ± 0.180.920.34584 ± 310.49 ± 0.17
11ɛsol = 0.10.890.083249 ± 690.81 ± 0.150.910.14440 ± 430.61 ± 0.180.920.34585 ± 310.49 ± 0.16
12ɛsol = 0.1; N(IN) = 1 L−1 imm------------
13Γ = 1 (constant)0.870.00784 ± 410.910.004129 ± 510.920.004150 ± 51
14θ imm = 30°1.00.54264 ± 910.85 ± ± 1790.57 ± ± 880.44 ± 0.26
Table 2. Summary of Model Results for the SHEBA Case (−22°C < T < 17.8°C) at Three Heights Above Model Initialization, With RH = 95%a
SimulationModel Conditionsb100 m (−18.7°C)300 m (−20.4°C)500 m (−22°C)
N(IN)frozen/N(IN)IWC/LWCDav(μm)equation imageavN(IN)frozen/N(IN)IWC/LWCDav (μm)equation imageavN(IN)frozen/N(IN)IWC/LWCDav (μm)equation imageav
  • a

    Fractional ice particle number (N(IN)frozen/N(IN)), ice-to-water mass ratio IWC/LWC, average equivalent diameter of ice particles Davσ), and average aspect ratio of ice particles ϕavσ).

  • b

    Here imm means that only immersion freezing IN is considered.

1Base case0.930.82243 ± 270.15 ± 0.040.930.34425 ± 220.13 ± 0.030.930.36514 ± 230.14 ± 0.03
2w = 2 cm s−10.856600562 ± 200.07 ± 0.010.8542000818 ± 200.07 ± 0.0090.8584000919 ± 210.07 ± 0.009
3w = 40 cm s−10.940.12114 ± 120.25 ± 0.050.940.03202 ± 90.22 ± 0.040.940.03243 ± 90.23 ± 0.04
4w = 100 cm s−10.940.165 ± 90.37 ± 0.070.940.007124 ± 60.32 ± 0.050.940.007150 ± 50.33 ± 0.05
5N(IN) = 0.2 L−10.930.1245 ± 260.15 ± 0.040.930.054426 ± 220.13 ± 0.030.930.06515 ± 220.14 ± 0.03
6N(IN) = 5 L−10.911000233 ± 280.16 ± 0.040.927060406 ± 230.14 ± 0.030.9226000486 ± 230.14 ± 0.04
7N(IN) = 1 L−1 imm0.470.02164 ± 180.27 ± 0.260.980.1304 ± 700.38 ± ± 810.67 ± 0.5
8N(CCN) = 10 cm−30.932.7241 ± 290.16 ± 0.040.930.36427 ± 240.14 ± 0.030.930.38517 ± 240.14 ± 0.03
9N(CCN) = 300 cm−30.930.7243 ± 270.15 ± 0.040.930.34424 ± 220.13 ± 0.030.930.36513 ± 230.14 ± 0.03
10ɛsol = 0.50.930.86243 ± 270.15 ± 0.040.930.34425 ± 220.13 ± 0.030.930.36514 ± 230.14 ± 0.03
11ɛsol = 0.10.930.97243 ± 280.15 ± 0.040.930.34423 ± 230.13 ± 0.030.930.36514 ± 230.14 ± 0.03
12ɛsol = 0.1; N(IN) = 1 L−1 imm0.970.07163 ± 200.23 ± 0.050.930.18316 ± 740.40 ± 0.270.930.24455 ± 560.44 ± 0.31
13Γ = 1 (constant)0.930.0289 ± 510.930.007147 ± 210.930.007154 ± 21
14f(m, x) = 0.00075 (deposition freezing)0.0016.3e-5171 ± 180.27 ± 0.030.0053e-4340 ± 480.32 ± 0.160.0248.5e-4517 ± 240.5 ± 0.4

3. Results

3.1. IWC and LWC for the Base Cases

[19] Figure 1 shows the mixing ratios [g kg−1] of ice and liquid water as a function of temperature for the base cases. Note that the height (right axis) is defined here as the height above the level at which the model simulations were initialized (RH = 95%). For these adiabatic simulations, the total water mixing ratio (vapor + ice + liquid) is constant over the simulation time and differs by a factor of ∼2 between the two cases (MPACE: 1.9 g kg−1; SHEBA: 0.9 g kg−1). Comparing Figures 1a and 1b, it is apparent that at higher temperatures (MPACE) liquid forms before the ice, whereas in the cold case (SHEBA), ice formation starts immediately. The fact that IWC and LWC increase simultaneously in both base cases shows that both ice and water are able to grow simultaneously and that ice does not grow at the expense of liquid droplets, similar to results of Korolev and Field [2008]. The predicted clouds consist mostly of a liquid phase with about three times more liquid than ice at 500 m.

Figure 1.

Ice water content (IWC) and liquid water content (LWC) as a function of temperature for the base case simulations (Simulation 1 in Tables 1 and 2): (a) MPACE and (b) SHEBA. The vertical line depicts the total water (vapor + ice + liquid) content of the adiabatic system; “height” on the right axis refers to the level above model initialization (RH = 95%).

[20] In sections 3.23.7, the results will be shown as IWC and LWC fractions (%IWC, %LWC) in order to facilitate comparison of the relative contributions of the phases. The total (100%) is always based on the total adiabatic water mixing ratio (liquid ( = water associated with aerosol particles and cloud droplets) + ice + vapor) in Figures 1a and 1b. Results of the base case simulations are depicted as a red line in Figures 27 and 1012.

3.2. Effect of Updraft Velocity

[21] The updraft velocity w impacts the supersaturation in the air parcel and thus feeds back to the activation of CCN and IN. In the MPACE case (−13.1°C < T < −9.1°C) at w ≥ 10 cm s−1, the predicted LWC exceeds IWC over the depth of the cloud and the IWC/LWC ratio decreases with increasing w (Table 1). At very low updraft, w = 2 cm s−1, ∼0.5% of the total water mixing ratio (corresponding to ∼0.01 g kg−1) is converted to ice before the LWC increases (Figure 2a). The increase of LWC is in competition with continuous ice growth, which in turn suppresses any further increase in the liquid water saturation Sw. This abundance of ice leads to further efficient ice growth and evaporation of the droplets owing to the Bergeron-Findeisen (BF) process [Wegener, 1911; Bergeron, 1935; Findeisen, 1938]; LWC can only be maintained up to a height of ∼150 m, above which the cloud glaciates completely. This is in qualitative agreement with results by Korolev [2008] and Korolev and Field [2008], who showed that the BF process is most efficient at low updraft velocities (w → 0) and a mixed-phase system can be only maintained if the updraft velocity is greater than a threshold that is dependent on the integral radius of ice.

Figure 2.

Percentage contribution of IWC and LWC to total adiabatic water content as a function of temperature (left-hand scale) and height in cloud (right-hand scale) for different constant updraft velocities w (Simulations 1–4 in Tables 1 and 2): (a) MPACE and (b) SHEBA.

[22] The lower supersaturation in SHEBA together with the relatively long ice growth time before LWC starts increasing leads to negligible LWC at w = 2 cm s−1 and a pure ice cloud (no solid black line in Figure 2b since the %LWC < 0.1% at all times). At higher w (40 cm s−1; 100 cm s−1), the combination of shorter ice particle growth times and the added source of Sw maintain the liquid, resulting in reduced IWC/LWC. The fractional ice particle number (N(IN)frozen/N(IN)) in the higher w cases is similar to the base case such that Dav decreases with increasing w.

[23] In the SHEBA case, ice nucleation starts at lower heights, and thus the predicted ice fractions at 100 m are much higher than in the MPACE case (Table 2). However, with increasing height, very similar ice and liquid fractions are predicted for both MPACE and SHEBA cases with updraft velocities w ≥ 10 cm s−1. At 500 m the resulting IWC/LWC ratio is about 0.35 in both MPACE and SHEBA, decreasing to <0.01 with increasing updraft velocity. The smaller Dav in SHEBA points to less efficient ice growth at lower temperatures, which is a consequence of the decreasing difference between the liquid and ice equilibrium vapor pressures with temperature. The more isometric particles in MPACE (aspect ratio close to unity; Table 1) lead to less efficient ice growth rates because spherical particles have weaker vapor gradients (see section 1). However, this effect is compensated by the higher supersaturation, which explains the very similar IWC/LWC ratios in both cases.

[24] These results suggest that deposition freezing could have a sensitive control on the ice/liquid distribution of mixed-phase clouds as it can form ice before droplets are activated and significant LWC is built up. A mixed-phase cloud might not develop if ice is efficiently formed before droplet activation by either a sufficiently long growth time scale (low w) or by an abundance of ice particles. These ice particles, together with w, control Sw and prevent an efficient increase of LWC [Korolev and Field, 2008].

3.3. IN Number Concentration

[25] As shown above, the amount of ice that forms before liquid saturation is reached might control the LWC and the subsequent phase distribution of IWC/LWC in the cloud. The concentration of ice formed is controlled to some extent by the number of available IN. The number concentration of IN is varied here by a factor of five as compared to the base case (0.2 L−1 < N(IN) < 5 L−1) by scaling down (up) the size distribution of initial IN, leading to ratios of N(IN)/N(CCN) from 0.2·10−5 to 5·10−5, respectively. For MPACE, liquid water is maintained at all considered cloud depths (≤500 m) with almost all assumed IN concentrations (Figure 3a). Only with the highest IN concentration (N(IN) = 5 L−1) does the LWC decrease rapidly, and the cloud completely glaciates. For SHEBA, a similar trend in the predicted ice mass is observed; however, at a concentration of N(IN) = 5 L−1, no appreciable LWC is formed (no solid blue line in Figure 3b) since the amount of ice is sufficient to suppress the supersaturation and prevent droplet activation. In previous model studies the minimum supersaturation that needs to be exceeded in order to allow the formation of a mixed-phase cloud has been parameterized by a threshold updraft velocity that is a function of the ice mass present [Korolev and Field, 2008].

Figure 3.

Percentage contribution of IWC and LWC to total adiabatic water content as a function of temperature (left-hand scale) and height in cloud (right-hand scale) for different IN number concentrations N(IN) (Simulations 1, 5, and 6 in Tables 1 and 2): (a) MPACE and (b) SHEBA.

[26] For SHEBA, IWC starts increasing immediately (i.e., at RH = 95%) and controls Sw by the depositional sink onto the ice particles that suppresses the increase of LWC with increasing height (Figure 3b). When comparing MPACE and SHEBA clouds at 500 m, the IWC/LWC ratio is comparable for the same N(IN). The equivalent diameters Dav are also similar even though the average aspect ratios differ by a factor of 3–4 (Tables 1 and 2). The minor variations in Dav for different IN concentrations show that the final particle sizes are not affected by competition for water vapor as the vapor supply is strong enough to allow similar growth rates for all cases.

3.4. Nucleation Mode

[27] The base case considers deposition freezing as the only nucleation mode, consistent with many prior model studies of Arctic mixed-phase clouds [Harrington et al., 1999; Prenni et al., 2007]. However, a recent study hypothesized that in SHEBA (∼−20°C < T < −15°C), immersion freezing was the predominant nucleation mode [de Boer et al., 2010]. Similar conclusions are drawn on the basis of measurements during the Aerosol, Radiation and Cloud Processes affecting Arctic Climate (ARCPAC) campaign at temperatures of −14°C and −10°C [Lance et al., 2011] and has been suspected in earlier studies [e.g., Hobbs and Rangno, 1998].

[28] In order to explore the effects of the nucleation modes on cloud phase without the complication of different concentrations, a fraction of 10−5 of all CCN are regarded as IN, resulting in the same IN concentration as considered for the base case (N(IN) = 1 L−1). Deposition freezing is not included in sensitivity simulations discussed below. The surface properties of the immersion freezing IN causes freezing to begin at ∼−18.2°C, and thus results are only presented for the SHEBA case. The freezing process does not occur at the start of the simulation (T ∼ −17.8°C) unlike in the base case simulations where deposition freezing was the only mechanism (Figure 4a). At higher temperatures, the predicted ice mass due to immersion freezing is significantly smaller (by a factor of 40) than for the base case (Table 2); however, at higher altitudes the difference is reduced to a factor of 2–3 compared to the deposition freezing results. Several processes favor the progressive decrease in this difference: (1) in the case of immersion freezing, the frozen fraction builds up slowly with increasing altitude, allowing the supersaturations with respect to ice and water to increase even at lower heights and, in turn, ice and liquid water can grow efficiently (Figure 5). (2) When droplets are converted to ice mass, they represent a relatively large mass compared to insoluble (deposition freezing) IN that do not collect any liquid prior to freezing. The different onset temperature of freezing (deposition freezing: ∼−18°C; immersion freezing <−18°C) produces different initial crystal shapes that in turn cause different vapor deposition rates. However, the aspect ratio in the immersion freezing case is closer to unity (Table 2 and section 3.6.1), which suggests a slower growth rate. The enhanced mass growth rate therefore occurs in spite of differences in aspect ratio.

Figure 4.

Percentage contribution of IWC and LWC to total adiabatic water content as a function of temperature (left-hand scale) and height in cloud (right-hand scale) for deposition and immersion freezing (Simulations 1 and 7 in Table 2, SHEBA): (a) N(IN) = 1 L−1 and (b) N(IN) = 5 L−1.

Figure 5.

Supersaturation for deposition and immersion freezing (SHEBA, Simulations 1 and 7, Table 2) with respect to (a) water and (b) ice.

[29] To explore whether this delay in the onset of freezing could become important if more IN are available, the simulations are repeated for N(IN) = 5 L−1 (Figure 4b). In the deposition freezing simulations, N(IN) = 5 L−1 results in a pure ice cloud as discussed for Figure 3b, while nearly equal amounts of IWC and LWC are predicted when only immersion freezing is considered. A tentative conclusion from Figures 4a and 4b is that the temperature of onset of freezing and the time scale of ice growth are more important in determining the phase partitioning of the cloud than the nucleation mode (i.e., composition of the particles). Sensitivity studies exploring this idea are discussed in section 4.2.1.

[30] Ice particle size distributions originating from immersion freezing have a wider spread in the predicted average equivalent diameters and aspect ratios as compared to those that are predicted for deposition freezing (Table 2). This might be an artifact associated with the initialization of our model at RH = 95% (with respect to liquid) and T = −17.8°C. Particles start freezing by deposition nucleation at the beginning of the simulation; that is, many ice particles from different aerosol size classes nucleate simultaneously and grow for the same duration throughout the simulation. The absolute differences in their initial (dry) sizes are marginal compared to the resulting sizes of the ice particles. The resulting Dav of ice particles is likely biased low as it can be expected that in simulations initialized further below the cloud; that is, at higher temperatures and lower RH, some (large) aerosol particles will start freezing earlier and have more time to grow before they reach cloud top. To test this idea, we simulated a deposition freezing case that is initialized at RH = 86%. The resulting size distribution has a wider spread of particle sizes and aspect ratios since the particles exhibit a wider range of onset temperatures of freezing as a function of their dry sizes (section 3.6). However, the resulting IWC and LWC are very similar compared to the base case simulations and exhibit the same IWC and LWC as in Figure 1. Lower initial RH values do not affect any results predicted in the MPACE case since freezing only starts well below the initial temperature in the base case.

3.5. CCN Properties

3.5.1. CCN Concentration

[31] The role of CCN and its influence on the evolution of mixed-phase clouds has been discussed in a number of studies [e.g., Hobbs and Rangno, 1998; Harrington et al., 1999; Rangno and Hobbs, 2001; Fridlind et al., 2007; Lebo et al., 2008; de Boer et al., 2010, 2011]. The influence of CCN concentration on mixed-phase cloud dynamics through changes in drop concentration is thought to be relatively weak [e.g., Harrington et al., 1999]. CCN concentrations can influence mixed-phase clouds in various ways. One particular control is on the supersaturation. Large CCN concentrations in warm (liquid only) clouds will lead to high drop concentrations that effectively reduce the supersaturation to lower values. Hence, in liquid phase clouds it is really the CCN concentration that has an indirect impact on the state of the supersaturation. In mixed-phase clouds, the CCN loading has less of an effect, and it is primarily the growth of the ice crystals that control the supersaturation state.

[32] During glaciation, ice crystals cause the evaporation of cloud drops and as the smallest drops evaporate they pass over their Köhler curve maxima. Since the maxima are at a saturation that is higher than liquid saturation, the evaporation of the smallest drops keeps the environment slightly supersaturated with respect to liquid. Large drops that exist in this environment can then grow from the vapor at the expense of the smaller drops. This process can lead to the production of both larger ice particles and larger drops, through vapor growth alone; thus, an increase in N(CCN) could influence the ice growth at the expense of droplets [e.g., Lebo et al., 2008].

[33] In addition to this rather weak feedback of CCN and cloud droplet number concentration on ice mass, CCN can have other indirect impacts on mixed-phase cloud structure and lifetime. Since larger droplets tend to be more dilute than smaller droplets, immersion freezing could act in a preferential way such that ice production is self-limiting in mixed-phase clouds: More dilute drops would tend to freeze first, producing ice which then causes evaporation of smaller drops. As these drops evaporate, they become more concentrated solution drops, which suppresses their freezing point [e.g., de Boer et al., 2010]. Interestingly, a number of observations have shown that regions of higher ice concentrations tend to be correlated with larger liquid drops [e.g., Rangno and Hobbs, 2001] which has led to speculation about both large drops and liquid in general as being precursors for ice formation [de Boer et al., 2011; Lance et al., 2011].

[34] Finally, it is possible that the initial chemical CCN composition is modified during cloud processing so that the resulting composition of the drop residuals exhibits different physical and chemical properties (e.g., solubility) that might impact the IN ability of this particle in subsequent cloud cycles [e.g., Rosinski and Morgan, 1991]. Some modeling studies suggest that this mechanism could be a pathway for continual ice production [e.g., Fridlind et al., 2007].

[35] However, as discussed in section 3.1, in the base case scenario and many of the other simulations, both IWC and LWC increase simultaneously. In Figures 6a and 6b, no appreciable change in either LWC or IWC is observed in simulations of deposition freezing with 10 cm−3N(CCN) ≤ 300 cm−3. Only at a very early stage of cloud formation (∼100 m above model initialization) does higher N(CCN) show a slightly lower LWC. These marginal differences confirm that indeed droplet and ice particle growth occur largely independently of each other as long as the ice concentrations are relatively low and w is relatively high. The parameters in Tables 1 and 2 exhibit only small differences for all simulations shown in Figures 6a and 6b.

Figure 6.

Percentage contribution of IWC and LWC to total adiabatic water content as a function of temperature (left-hand scale) and height in cloud (right-hand scale) for different CCN properties (number concentration, solubility) (Simulations 1 and 8–12 in Tables 1 and 2): (a, d) MPACE and (b, c, and e) SHEBA.

[36] The influence of solute concentration on the freezing point depression of immersion freezing particles has been suggested to have a major effect on ice formation by preventing concentrated particles (droplets) from freezing [de Boer et al., 2010]. The premise is that in the case of immersion freezing, a lower CCN number concentration leads to larger drop radii, smaller solute concentration in the activated particles, and therefore higher ice mass. Our results show that a reduction of N(CCN) by a factor of 20 leads to a small increase in the predicted ice mass (black: 100 cm−3 versus orange: 5 cm−3; Figure 6c). However, such a change might determine the fate of a mixed-phase cloud if the system is near an unstable state where the phase distribution could be crucially perturbed by a small increase in the total ice growth rate to the total drop growth rate (see section 4.4). Low CCN concentrations have been observed occasionally in the Arctic [Mauritsen et al., 2011], and there might be situations where such a dearth of CCN might lead to the full glaciation of mixed-phase clouds. However, our model simulations do not confirm the strong correlation between large droplets and ice mass that has been suggested by numerous studies.

3.5.2. Soluble Fraction of CCN

[37] The fraction of soluble material in CCN impacts the cloud supersaturation prior to ice formation. In our simulations, varying the soluble portion of CCN (ɛsol) in the base case (deposition freezing) simulations from 90% to 50% or 10%, leads to no change in the predicted IWC/LWC distribution (Figures 6d and 6e) since the feedback of the CCN composition to the supersaturation is small compared to the condensation-supersaturation feedbacks due to ice particle growth. (The change in ɛsol has no effect on the deposition freezing mechanism itself in this temperature/supersaturation regime.)

[38] A sensitivity study of the soluble fraction assuming immersion freezing reveals that indeed a smaller ɛsol leads to higher ice masses (Figure 6c). In the case of high N(IN) = 5 L−1, the higher ice formation efficiency might even lead to the efficient removal of LWC by ice particle growth at the expense of the droplets. This finding is in qualitative agreement with the hypothesis and model study of de Boer et al. [2010], who argued that particles with high soluble fractions are necessary to maintain a mixed-phase cloud since small, concentrated particles will remain in the liquid phase and only a few large, dilute particles will freeze. These large ice crystals will grow and fall out of the cloud without removing a significant amount of the liquid water.

[39] In spite of this qualitative consistency with de Boer et al. [2010], we propose that the results shown in Figure 6c can be explained by the fact that on a mass-to-mass basis, a higher insoluble mass fraction of an IN provides a larger surface area upon which ice can nucleate since the ice nucleation rate j [s−1] is directly proportional to the surface area of an insoluble core:

equation image

where k is Boltzmann constant [1.3806504 × 10−16 erg K−1], T is temperature [K], h is Planck constant [6.62606896 × 10−27 erg s], cl,s is surface concentration of liquid molecules per cm2 (∼1015 cm−2), rN is radius of insoluble core, ΔFact is activation energy at the solution-ice interface, and ΔFcr is critical energy of germ formation.

[40] Our sensitivity studies with respect to CCN properties suggest that clouds containing ice formed by immersion freezing are affected primarily by the surface area of the individual IN (4π rN2, which is dependent on (1-ɛsol)) and only weakly by the number concentration of CCN. Thus an increase in the size of IN for immersion freezing will lead to a greater surface area for nucleation and higher ice mass. The solute concentrations of droplets appear to be low enough in our simulations that the effect of freezing point depression is negligible.

3.6. Habit Evolution: Assumption of Spherical Particles

[41] Ice particle shape impacts the simulated properties of Arctic mixed-phase clouds and strongly influences cloud lifetime and radiative feedbacks [e.g., Avramov and Harrington, 2010]. In many previous model studies spherical particles have been assumed [e.g., Korolev and Isaac, 2003] or simple shapes characterized by mass-size relations [e.g., Avramov and Harrington, 2010]; all of these studies attempt to capture ice crystal evolution with a single size using assumptions to approximate the primary habits. Habit evolution could be important because particles with nonspherical shapes grow faster than isometric particles of the same mass and volume. For instance, Fukuta and Takahashi [1999] show that the Maxwellian spherical growth model underestimates the growth of ice in comparison to wind tunnel data taken at liquid saturation. Moreover, Sulia et al. [2010] show that equivalent density spheres produce a lower estimate of ice growth in comparison to the nonspherical growth method of Chen and Lamb [1994]. These results show that for the same mass and volume, spherical particles produce a lower estimate of ice growth in comparison to nonspherical particle growth. All ice particles in our model forming in the deposition mode grow on (dry) aerosol and so have the same initial masses. Recent studies are showing that the evolution of ice habit is critical to predicting the IWC and LWC distribution in mixed-phase clouds, especially at certain temperatures [Sulia et al., 2010]. Moreover, studies also indicate that using simple shapes [Harrington et al., 1995] or reduced-density spheres [Fridlind et al., 2007] can produce uncertainties in model simulations of water paths [Avramov and Harrington, 2010].

[42] In Figure 7, model results for IWC and LWC based on the assumption of spherical particles (with assumed bulk density ρ(ice) = 0.92 g cm−3) are compared to the base case simulations where habit evolution of all individual ice particles is represented. These two simulations represent the lower and upper bound for ice particle growth rates, respectively. The assumption of a constant ice bulk density is an oversimplification of the actual ice density, however for the MPACE case this may be a good estimate since many of the observed ice crystals were spherical and relatively small [McFarquhar et al., 2007]. Nevertheless, many previous model studies use reduced-density spheres to account for both the primary and secondary ice habits [e.g., Fridlind et al., 2007]. We therefore performed simulations that account for the lower density of depositing ice using the same approach as for the nonspherical particles in our base case simulations [Chen and Lamb, 1994]. The density of newly added ice is a function of the excess vapor density over an ice crystal with an inherent growth ratio Γ ( = 1 for spherical particles). The ice crystal density is updated at every model time step as a volume-weighted value of the preexisting and newly added ice mass.

Figure 7.

Percentage contribution of IWC and LWC to total adiabatic water content as a function of temperature (left-hand scale) and height in cloud (right-hand scale) for nonspherical (habit evolution) and spherical particles (bulk density or reduced density) (Simulations 1 and 13 in Tables 1 and 2): (a) MPACE and (b) SHEBA.

[43] When bulk-density spheres are assumed, ice masses are smaller by more than an order of magnitude for both model cases. The fact that the same number fraction of particles is predicted to freeze whether habits or spheres are assumed (N(IN)frozen/N(IN) = 0.93 and N(IN)frozen/N(IN) = 0.87 for MPACE and SHEBA, respectively; Tables 1 and 2) shows that it must be the ice growth occurring after ice nucleation that causes these large differences. The average equivalent diameter Dav is smaller by factors of 3–4 when particles are assumed to be spherical. Assuming reduced-density spheres decreases the difference in predicted ice mass for spheres and nonspheres to a factor of 2. The relative order of magnitude of density and shape effects on growth rates does depend, in general, on the temperature regime and the amount of ice present [e.g., Fukuta and Takahashi, 1999].

[44] A more detailed look at the size distribution of the individual ice particles shows that spheres clearly underestimate ice particle sizes and the breadth of the size distribution as compared to those obtained assuming nonspherical particles (Figure 8). (This result is similar to that obtained by Sheridan et al. [2009] in cirriform clouds.) In Figure 8, all ice particle classes are shown. Since the large number of ice classes makes it hard to distinguish features of the distributions, binned size distributions are also shown for clarity. Even though in MPACE at −10°C (100 m), many nearly spherical ice particles are predicted (ϕ ∼ 1), their sizes are significantly larger than the largest particles predicted in the simulations of spherical particles. The reason for the differences is related to the temperature-dependent inherent growth ratio Γ. A consequence of the Chen and Lamb [1994] method is that particles will tend to retain their initial habit as they grow. Consequently, ice particles that begin their growth near the transition temperatures (Γ = 1) will experience nearly isometric (spherical) growth causing them to obtain a more isometric habit. This result then can lead to less extreme habits during the course of the simulation. While observations do show that particles can retain their initial shapes as they evolve [Takahashi et al., 1991], they do not always do so: It is also well known that columns can develop caps, and dendrites can develop columns growing from their tips [Pruppacher and Klett, 2003]; however, these complex secondary habits are beyond the scope of the current parameterization method.

Figure 8.

Ice particle size distributions at in-cloud heights of 100 m and 500 m for (a, b) MPACE and (c, d) SHEBA. The size distributions of all ice particles' classes are shown as well as binned ice particle size distributions (10 size classes) for the assumption of nonspherical (color-coded by aspect ratio ϕ) and spherical particles with bulk density (gray symbols). The dotted lines in Figures 8c and 8d show the binned size distributions for simulations that were initialized at RH(0) = 86%.

[45] All predicted aspect ratios in both temperature regimes are below unity (i.e., plates, Figure 8 and Tables 1 and 2) because ice particles nucleate between −15°C < T < −10°C and −17.8°C < T < −22°C, respectively, even though the inherent growth ratio exceeds unity at temperatures below −22°C (Figure 9). The consequences of these aspects of ice growth can be seen in the simulations: During MPACE, the particles form right near the transition temperature (Figure 9). This produces growth that is more isometric and leads to aspect ratios that are closer to unity. However, in the SHEBA case, particles form and grow through a temperature range that favors plate growth. This early growth produces plate-like crystals with aspect ratios that deviate substantially from unity as indicated in Tables 1 and 2 (the base case aspect ratio is much smaller and less variable for the SHEBA case, 0.13 ≤ ϕav ≤ 0.15, than for MPACE 0.49 ≤ ϕav ≤ 0.81). Nevertheless, the sizes of the particles tend to be larger in the MPACE case (Dav = 584 μm at 500m) versus SHEBA (Dav = 514 μm at 500 m). This result is most likely due to the greater difference between the equilibrium vapor pressure of liquid and ice at the temperatures during MPACE. Keep in mind, as discussed in section 3.4, that ice crystal sizes are biased low in our SHEBA simulations because we initialize the model at RH = 95%. At that relatively high initial RH and low temperature, many particles start freezing at the same time (i.e., at the initial temperature of the simulation) and thus exhibit the same final size. Initializing at RH = 86% provides a longer duration for growth, somewhat larger Dav (548 nm), and a broader size distribution (dotted lines in Figures 8c and 8d).

Figure 9.

Inherent growth ratio Γ as a function of temperature [Chen and Lamb, 1994]. The notation “columns, spheres, plates” refers to the shape the particle would attain if it were nucleated and grown primarily within that temperature range. Temperature regimes for the simulations of the MPACE and SHEBA cases are marked, respectively.

3.7. Summary of Model Results

[46] Tables 1 and 2 summarize the results of the simulations shown in Figures 14, 6, and 7. While these results do not allow direct conclusions on cloud maintenance and lifetime, their impact on the ice/liquid distribution in an adiabatic system can be used to identify sensitivities to the efficiency of ice formation. The sensitivity of the evolution of mixed-phase clouds is demonstrated by means of several parameters, chosen because they give information on the ice/liquid partitioning in the simulated clouds.

[47] The phase distribution IWC/LWC is most sensitive to w and N(IN) for both MPACE and SHEBA. In SHEBA, deposition freezing occurs very close to the initial height of the simulations (<100 m) and the ratio N(IN)frozen/N(IN) = 0.93 does not change with increasing height. In MPACE, at T = −10°C the frozen IN fraction is 0.87 and this number increases to 0.95 at a height of 500 m (Table 1).

[48] The predicted average equivalent diameters Dav and aspect ratios ϕav for most simulations for a given temperature and height are in a very narrow range and differ by <15%. This consistency indicates that despite variations of many parameters (N(IN), CCN properties) over relatively wide ranges, the resulting size and shape distributions exhibit relatively narrow ranges. Clear deviations from these consistent values are only predicted in the simulations with different w or when spherical particles (ϕ = 1; ρ(ice) = 0.92 g cm−3) were assumed. However, we caution against comparing with observed size distributions since our model does not account for processes that could change individual particles sizes (riming, secondary ice production) or for removal and mixing processes within the cloud. A particularly interesting result is that IWC scales approximately linearly with N(IN) in the updraft if both ice and liquid phases are present. At high enough IN concentrations, the depositional sink due to the abundance of numerous, nearly equally sized IN crucially impacts the LWC and thus the IWC/LWC balance which might initiate complete glaciation.

[49] In summary, the sensitivity simulations show that the ice/liquid distribution is mostly controlled by the supersaturation, which in turn is most significantly impacted by the updraft velocity and the number concentration of IN. Ice and water can coexist provided w is large enough and/or N(IN) is small enough [Korolev and Field, 2008]. While other parameters (e.g., CCN composition and number concentration) could still add to these major factors and eventually lead to the glaciation of the cloud (e.g., Figure 6c), their parameter ranges are too narrow to indicate a significant perturbation to the system. Neglecting the shape of ice particles and assuming spherical particles with a bulk density of ρ(ice) = 0.92 g cm−3 leads to a significant overprediction of LWC and thus to an underprediction of IWC. The underestimate of IWC is reduced if reduced-density ice spheres are assumed. Caveats are in order because our model does not include particle removal and therefore leads to an overestimate of the predicted ice mass and thus to a biased phase distribution. Within the limitations of our model, these issues will be explored further in section 4.

4. Discussion

4.1. Impact on IWC/LWC by Ice Particle Removal

[50] For the simulations discussed in section 3, the calculation of fall velocities is only diagnostic, and particles are not removed from the air parcel. The fall velocity of the particles is calculated as a function of the aspect ratio and their projected area, which is a function of the particle dimensions (a and c axes). The calculation follows the parameterized approach by Mitchell [1996]. In order to provide an estimate of the amount of ice that is removed from the cloud by sedimentation, we performed additional simulations in which we assumed that the concentration of all particles with fall velocity > w is zero and is not replenished throughout the simulation. This assumption is simplistic since the strength of cloud turbulence combined with fall speed will determine the particles' in-cloud residence time and whether particles might cycle through the cloud. Nevertheless, the simulation does provide an additional bound for our results.

[51] Figure 10 shows that all ice particles reach fall velocities greater than 10 cm s−1 and thus no ice is maintained at heights above a few hundred meters. The ice removal is more efficient at the lower temperatures (Figure 10b) since more ice is formed at lower heights. The corresponding simulations for spherical particles show that those particles will be removed even faster. Even though these particles grow much less efficiently than nonspherical particles with resulting average volumes being at least an order of magnitude smaller, their high density and small surface area lead to higher fall velocities. A direct comparison of the results in Figure 10 to observations might not be meaningful since (1) falling ice particles might also remove liquid water while sedimenting through the cloud and (2) sedimenting particles from above might replenish ice particles.

Figure 10.

IWC and LWC as a function of temperature for the base case simulations and for simulations where particle removal is considered by removing all particles whose absolute terminal fall velocity exceeds the updraft velocity w: (a) MPACE, nonspherical particles, (b) SHEBA, nonspherical particles, (c) MPACE, spherical particles (bulk density and reduced density), and (d) SHEBA, spherical particles (bulk density and reduced density). In Figures 10c and 10d, LWC for all simulations are on top of each other.

[52] The comparison of these two sets of simulations suggests that the assumption of spherical particles in a more comprehensive model might lead to an even greater underestimate of IWC/LWC since growth rates are underestimated whereas removal rates are overestimated. The density of spherical particles (bulk or reduced density, see section 3.6.1) has little effect on the predicted ice mass. While reduced density spheres would fall more slowly than ones with bulk density of identical sizes, the higher growth rates of reduced density spheres leads to larger particles and thus density and size effects nearly cancel, resulting in similar fall velocities.

[53] However, since ice spheres fall more rapidly, they might affect the vertical distribution of ice within the supercooled liquid portion of the cloud. These issues cannot be explored within the current framework, nevertheless the results are consistent with those of Harrington et al. [1999], who showed that liquid could be maintained with higher IN concentrations if spherical ice particles were assumed. It is also important to note that during drop freezing, polycrystalline forms of ice can result and that irregular ice is often found in clouds [e.g., Korolev et al., 1999].

4.2. MPACE and SHEBA: Observational Context to the Model Simulations

[54] Owing to the limitations of the parcel model, a direct and detailed comparison of observations and model simulations is not feasible, but we nevertheless attempt to place the findings in the context of the observed parameter space. While our model simulations only include cloud evolution in one updraft, observed cloud systems represent a multitude of “air parcels” with different history and evolution through multiple cloud cycles. We focus on two cases that have both been extensively studied: SHEBA 7 May 1998 and the MPACE 9 October 2004.

[55] Updraft speed is a critical controlling factor for mixed-phase cloud formation and maintenance [Korolev and Isaac, 2003; Korolev, 2008; Korolev and Field, 2008]. During the MPACE case, the turbulent boundary layer with strong advection led to relatively high vertical velocities (∼50 – 100 cm s−1) resulting in high liquid water content (∼0.3 g/m3) and deep clouds (cloud depth of ∼400 – 800 m [Verlinde et al., 2007]. In SHEBA the vertical velocity was much weaker (∼40 cm s−1 [Shupe et al., 2008]), and observed clouds were much shallower (cloud depth ∼150 m [Zuidema et al., 2005]) with lower liquid water contents (<0.05 g/m3) [Fridlind et al., 2011]. The effective ice particle mean diameters observed in MPACE were distinctly larger (∼150 μm estimated on the basis of IWC and ice crystal concentration [Fridlind et al., 2011], up to 250 μm [McFarquhar et al., 2007] than in SHEBA (effective mean diameter ∼100 μm [Zuidema et al., 2005]).

[56] These different cloud properties during the two experiments suggest that we should compare observed and predicted trends in cloud properties between deeper, more vigorous MPACE clouds (w = 100 cm s−1 and cloud depth ∼500 m; Simulation 4, Table 1), and shallower, less vigorous SHEBA conditions (e.g., w = 40 cm s−1 and cloud depth 100 m; Simulation 3, Table 2). The predicted Dav for MPACE (188 μm) is clearly higher than that for the SHEBA case (114 μm), in rough agreement with the observed trends in particle sizes. The observed particles sizes in MPACE are likely to be more significantly impacted by longer processing times, riming, aggregation and the natural size sorting that occurs in the vertical through sedimentation, than the particles observed during the SHEBA case.

[57] Most of our model simulations were performed for N(IN) = 1 L−1 but as shown, higher (lower) IN concentrations lead to smaller (larger) particle sizes. The average IN concentration in MPACE was about 0.2 L−1 [Prenni et al., 2007] whereas it was about an order of magnitude higher during SHEBA (2 L−1) [Rogers et al., 2001], providing further support for the trend of larger ice particles in MPACE. This distinct difference in observed IN concentrations is likely not due to different aerosol sources during the fall and spring transition seasons, but rather due to different removal processes [Garrett et al., 2010]. In that study, it was shown that wet deposition is the main aerosol removal process in warmer Arctic clouds such as in MPACE. In colder conditions (SHEBA), precipitation grows by vapor deposition resulting in large ice particles, which do not collect as many other particles by collision or aggregation, leading to less efficient removal of drops and ice (and therefore aerosol) even though the total precipitating mass might be the same. In addition, cloud structure might not have been as homogeneous as assumed here since during MPACE pockets of ice and liquid were observed [Shupe et al., 2008]. Such processes would likely affect the ice/water partitioning in the observed clouds.

[58] In the MPACE cases, a significant number of smaller spherical ice particles was observed throughout the cloud, but so were some crystals that are columnar and crystals that automated classification identified as rosettes but McFarquhar et al. [2007] describe as branched. This corresponds in a very rough sense to the predictions by our model (Table 1 and Figure 8a): At the smaller sizes, the crystals are predicted to be relatively isometric since they begin growing as spheres. However, as the particles grow into larger sizes they tend to become thinner, plate-like crystals that are more typical of branched structures. At present, the model cannot capture the growth of multiple habits and so columns were not predicted, which is a limitation.

[59] Cloud particle imager (CPI) images taken during SHEBA show that the predominant shapes were plates or plate-like crystals [Fridlind et al., 2011] (and data available from NASA at html). The images show a number of hexagonal plates and plate assemblages, which grow primarily along the a axes. This is in rough agreement with our simulations that show fewer spherical and isometric particles in the SHEBA case than for MPACE (Figure 8 and ϕ in Tables 1 and 2). A number of the CPI images also show hexagonal plates with riming along the edges, but our model cannot predict these characteristics.

[60] The fact that all ice particles are predicted to have fall velocities that exceed the updraft velocity of 10 cm s−1 of our base case (Figure 10) is in general agreement with the range that has been determined on the basis of observations during MPACE (50 – 100 cm s−1 [Verlinde et al., 2007]). However, it should be noted that ice crystal aggregation and riming are not considered in the current model, and thus fall velocities are underestimated as aggregates and rimed crystals fall much faster than pristine ice crystals. While our model only simulates the updraft motion of an air parcel, particles might also reach larger sizes because of recirculation in the cloud.

[61] For all model results where mixed-phase conditions are predicted, the ratio IWC/LWC is less than unity except in shallow clouds (100 m) when only very little ice and liquid are present. However, it should be noted that the initial conditions chosen in our simulations might still lead to glaciated clouds in further cloud cycles if ice particle removal is small enough and ice is produced continuously. Ratios of IWC/LWC >∼0.5 are in rough agreement with observations where average fractions of the liquid to total (ice + liquid) water path of ∼0.85 during MPACE have been reported [Shupe et al., 2008]. It should be noted that the ratios of water contents (IWC, LWC) as derived from our model studies, and observed water paths are not directly comparable, since the latter depend upon cloud depth whereas the former depend on local cloud properties. However, it can be hypothesized that clouds with liquid fractions <∼0.5 might not persist in any temperature regime since in such cases ice particles grow so efficiently that the BF process rapidly depletes the LWC.

[62] The results in Figure 3 suggest that in the warmer case (MPACE), both phases can be maintained with relatively high N(IN) (5 L−1) up to a height of ∼300 m whereas in SHEBA, liquid is unable to build up in the presence of such high N(IN). This trend suggests that mixed-phase clouds at low temperatures are less likely to exist if higher IN concentrations (5 L−1) are present. Observations show that in SHEBA the IN concentration was actually higher and yet mixed-phase clouds were observed. As discussed above, since our model simulations only cover a very limited time scale (one ascent), further processing of both phases in the cloud and conditions other than N(IN) may also have been different (e.g., w, particle removal, etc) during the two experiments and thus might explain this apparent contradiction. In addition, no large-scale sources of moisture or thermal energy occur in our model, which would have impacted the evolution of the observed clouds.

[63] Prenni et al. [2007] have proposed that in MPACE deposition freezing was the predominant freezing mode, while in SHEBA, immersion freezing seems more plausible [de Boer et al., 2010]. While this is in general agreement with our findings that immersion freezing does not occur at higher temperatures (e.g., MPACE), more recent studies suggest that immersion freezing may be active in springtime Arctic clouds at temperatures similar to those encountered in MPACE [Lance et al., 2011] so that firm conclusions cannot be drawn. Regardless, as we have argued in section 3.4, it appears that in some cases it is not so much the nucleation mode, but rather the temperature of onset of freezing and the time period over which ice particles can grow that impact efficient ice formation. This idea is examined below.

4.3. Freezing Mechanisms

4.3.1. Temperature of Onset of Freezing

[64] The physicochemical IN properties have been chosen in our base case so that deposition freezing acts over the entire temperature range of −22°C < T < −10°C while immersion freezing is only predicted to nucleate ice at temperatures ≤−18°C. Laboratory studies have shown a large spread in freezing temperatures and ice supersaturations for both freezing modes depending on the chemical composition and surface properties of the IN [e.g., Möhler et al., 2006; Marcolli et al., 2007; Chen et al., 2008; Möhler et al., 2008; Niedermeier et al., 2010], and thus it does not seem reasonable to exclude the possibility of immersion freezing at higher temperatures and/or different freezing temperatures by any of the freezing modes. The energy of formation of an ice germ ΔFcr (equation (1)) is described by

equation image

where σ is surface tension of ice/solution (immersion freezing) or ice/particle (deposition freezing) interface [dyn cm−1], rgerm is germ radius [cm], α is fraction of surface with active sites, rN is radius of the insoluble core [cm], m is cosine of the contact angle θ, f(m, x) is geometric factor, x is rgerm/rN.

[65] Many laboratory studies have shown that the efficiency of IN freezing can be parameterized by either the contact angle θ or the number of active sites α [Chen et al., 2008; Niedermeier et al., 2010]. A decrease in θ or an increase in α lowers the energy threshold for formation of an ice germ and a higher nucleation rate is predicted (equations (1) and (2)). Note that equation (2) can be applied to calculate the energy for germ formation for both immersion and deposition freezing provided that for the latter rgerm is calculated for dry particles [Khvorostyanov and Curry, 2004; Chen et al., 2008].

[66] The results in section 3.4 (Figure 6) suggest that during the simulated time scale of a parcel updraft, IWC is mostly controlled by the temperature of the onset of freezing and the duration of ice growth. If that holds true, the nucleation mechanism itself might be less important if ice nucleation is initiated at the same temperature. In order to explore this idea, we adjusted the physicochemical properties of deposition and immersion freezing IN, respectively, in a way that ice nucleation starts at the same temperature for both nucleation modes. A reduction of the contact angle to θ = 30° in the MPACE simulations allows for immersion freezing at −9.3°C, that is, at the same temperature where deposition freezing starts in the base case. Figure 11a shows that when immersion freezing is initiated at −9.3°C there is only a minor difference in the evolution of IWC/LWC ratio compared to the base case. Only at the highest temperature (height ∼100 m), is the ice mass due to immersion freezing clearly higher than predicted by deposition freezing (Table 1). These differences can be explained by the fact that the adjustment of θ is performed so that the freezing temperature of the largest particles (i.e., the first ones frozen) matches the freezing temperature of the largest particles if deposition freezing is considered. However, one cannot necessarily expect a change in a single parameter in equation (1) to translate to a linear change in the nucleation rates of particles of a different size.

Figure 11.

Percentage contribution of IWC and LWC to total adiabatic water content as a function of temperature (left-hand scale) and height in cloud (right-hand scale) for different nucleation modes that are forced to have the same temperature of the onset of freezing Tfr (Simulation 14). (a) For MPACE, the contact angle θ for immersion freezing IN has been reduced from 60° to 30°, or the number of active sites α has been increased from 0 to 10−4 to infer freezing of the largest aerosol particles at −9.5°C ( = Tfr in base case). (b) For SHEBA, the geometric factor f(m, x) for deposition freezing IN has been increased from 10−4 to 7.5·10−4 to infer freezing at −15.5°C ( = Tfr in Simulation 7).

[67] This nonlinearity between parameters that characterize the surface properties of the IN and onset temperature of freezing can be shown even more clearly by adjusting the fraction of active sites (α in equation (2)). IN with a surface fraction of active sites α = 5 × 10−4 (and a contact angle θ = 60°) also freeze at T = −9.3°C; this surface fraction of active sites has been shown to be present on various particles [Pruppacher and Klett, 2003]. While changing θ shifts the onset temperature of freezing for all particle sizes more proportionately (if α = 0), the increase in freezing temperature due to a higher fraction of active sites might match the freezing temperature of the largest particles but it cannot be extrapolated to smaller particles. The resulting ice mass is smaller by several orders of magnitude (not shown) which can be explained by the complex dependence of ΔFcr on α and θ (equation (1)). Because we have such poor knowledge of IN activity as a function of θ and/or α, it is very difficult to draw firm conclusions, and so we provide these results to indicate the potential range of physicochemical effects.

[68] While in SHEBA both nucleation modes are predicted to be possible, in a sensitivity study we lowered the onset temperature of deposition freezing to the same as immersion freezing (−18.5°C) by varying the geometric factor f(m, x). This is equivalent to changing the contact angle [Chen et al., 2008] such that the onset of deposition freezing is delayed. In this case, the ice mass from deposition freezing is much smaller than predicted on the basis of immersion freezing. This can be explained by the fact that at −18°C, Sw reaches its maximum and droplets can form more readily. Freezing these particles converts much more mass into ice than by deposition freezing nuclei that exhibit the same dry mass but do not contain any liquid water (Figure 11b). This result appears to be at odds with Figure 4, where it was shown that immersion freezing leads to smaller ice mass, because freezing starts at lower temperatures than deposition freezing. However, this result reinforces the notion that immersion freezing could produce more ice if it were to start at the same time (and temperature) as deposition freezing, provided appreciable amounts of liquid are present.

[69] These sensitivity studies show that assumptions about the physicochemical surface properties of IN, which determine the temperature of the onset of freezing, might be more crucial for cloud evolution than other parameters explored in section 3, even if the main ice nucleation mode is known. Laboratory studies that derive single surface parameters (θ, α) might be misleading since extrapolation to different sizes can lead to very different predictions in the germ formation energy ΔFcr. Experimental guidance on the parameter(s) that describe IN surface properties in equation (1) is sorely needed.

4.3.2. Feasibility of Nucleation Modes

[70] The geometric factors discussed in section 4.3.1 (10−4 < f(m, x) < 7.5 × 10−4) fall well within the range derived for various IN based on laboratory studies (9·10−6 < f(m, x) < 0.07 [Chen et al., 2008; Kulkarni and Dobbie, 2010]). However, the change of less than an order of magnitude in f(m, x) that is required to predict either an IWC/LWC ratio of ∼0.3 (base case) or a pure liquid cloud suggests that in the cold scenario the onset of deposition freezing is highly sensitive to changes in IN surface parameters which then strongly affects the cloud phase distribution. Similar conclusions can be drawn for the variation of the contact angle θ since a change of a factor of two (30° versus 60°) can determine if immersion freezing is active in a given temperature and supersaturation regime. These values of θ also lie well within the range suggested by Chen et al. [2008] for various IN. Owing to the high sensitivity of these parameters to the surface properties of IN, it is difficult to draw conclusions regarding the most likely nucleation mode in the two simulated cases.

[71] The chemical composition of Arctic aerosol particles suggests that they have undergone aging and thus exhibit either surface coatings and/or homogeneous internal mixtures of many compounds including high fractions of sulfate and nitrate [Quinn et al., 2007]. Such aged particles are transported from nonlocal sources and thus are likely present aloft. While in our model, we assume that they are mixed into the clouds from below, a more realistic treatment of aerosol mixing by entraining from above would not change any of our conclusions regarding the relative importance of various parameters if multiple cloud cycles were considered. Laboratory studies have shown that sulfate coatings can impede the nucleation ability of dust particles [e.g., Möhler et al., 2008; Sullivan et al., 2010] since water vapor cannot be directly deposited onto the surface of the insoluble particle fraction. However, IN usually only comprise a small fraction (10−5 − 10−3) of all particles and thus the existence of a few uncoated particles cannot be fully excluded. Nevertheless, particle aging will increase the likelihood that ice formation occurs via drop formation and immersion freezing. For example, observations of strong correlations between drop size and ice content in Arctic mixed-phase clouds during ARCPAC [Lance et al., 2011] would be consistent with immersion freezing.

[72] A recent modeling study has also identified immersion freezing as the likely nucleation mode for persistent mixed-phase SHEBA cases [de Boer et al., 2010]. Their study showed that immersion freezing has a self-regulating property that follows from freezing point depression in concentrated droplets/deliquesced particles, which would help prevent complete glaciation. However, other modeling studies of this SHEBA case have shown that both deposition/condensation freezing as well as contact freezing can also reproduce persistent mixed-phase clouds [Morrison et al., 2005] so that the dominant ice nucleation mechanism remains unresolved.

4.4. Change in Liquid Water Content as a Function of the Ratio of Integral Ice Capacitance and Integral Drop Radius (Ψ)

[73] While the results discussed in section 3 suggest that there are many parameters that impact the simultaneous growth of ice and liquid and their distribution in mixed-phase clouds, it is desirable to find a quantitative description of the relative effects of these parameters on the ice/liquid partitioning. The growth of droplets and ice particles occurs by vapor deposition and the growth rate is a function of the effective size distribution of drops and ice particles. The mass increase of the liquid phase scales with the integral radius of the drops (the first moment of the drop size distribution), and ice particle growth scales with the effective length scale of ice particles, that is, with their capacitance (which is equal to the radius for spherical particles) [e.g., Korolev and Mazin, 2003].

[74] In order to sort our model results, we show in Figure 12 the ratio of the integral ice capacitance to the integral radius of droplets, Ψ, as a function of the vertical change in liquid water content (dLWC/dh). The evolution of these profiles in the updraft is marked with arrows that point to decreasing temperature. Lines that cross dLWC/dh = 0 demark situations where the ice grows at the expense of droplets in the simulated updraft. While LWC (and IWC) can decrease in downdrafts of clouds owing to the increase in temperature, in updrafts, as simulated here, the BF process is the only mechanism that can lead to a decrease in LWC. Such clouds are glaciated and it can be expected that they do not form the liquid phase in subsequent cloud cycles under adiabatic conditions [Korolev and Field, 2008].

Figure 12.

Change of LWC with height (dLWC/dh) as a function of the ratio of the integral ice capacitance and integral drop radius Ψ. (a) MPACE. (b) SHEBA. Arrows next to the same-colored symbols point to decreasing temperature. Numbers in the legend refer to the simulations in Tables 1 and 2; note that results from additional simulations are shown that are not included in Tables 1 and 2. Lines that cross the dLWC/dh = 0 show simulations where clouds are predicted to glaciate through the Bergeron-Findeisen-Process during the simulated parcel ascent.

[75] Corresponding to the results in Figures 2a and 3a, Figure 12a shows that both high N(IN) (N(IN) = 5 L−1) or low w (w = 2 cm s−1) result in glaciation of the cloud. This is in agreement with the definition of a “threshold updraft velocity” as a function of the available ice mass that needs to be exceeded to maintain a liquid phase in clouds [Korolev and Isaac, 2003; Korolev and Field, 2008]. At higher updraft velocities (w = 10 cm s−1; w = 100 cm s−1), Ψ is smaller since less ice has a shorter time period for growth (section 3.2). While initially the shape of the lines is similar to those for low w or high N(IN), it is obvious that the ice growth is not sufficient to reduce the increase in LWC and, therefore, to initiate the BF process. It should be noted that clouds with such initial conditions might glaciate in further cloud cycles if the ice mass continuously grows and reduces LWC [e.g., Korolev and Field, 2008]. It is notable that the assumption of spherical particles with bulk density leads initially to similar Ψ values for high updraft speeds (w = 100 cm s−1); however, it is obvious that the ice growth is much less efficient than in the nonspherical cases and thus the increase in LWC is not significantly reduced. Comparing the base case simulations to those for spherical particles, it can be concluded that assumptions about ice particle shape and density have a pronounced effect on the ice/liquid distribution in mixed-phase clouds which is almost comparable to that of changing N(IN). (This result is in agreement with the results of Avramov and Harrington [2010]). As shown in Figure 11a, at the higher temperature regime the nucleation mode (if freezing occurs at identical temperatures) does not have any impact on the ice/liquid distribution once a certain LWC is formed and the impact on LWC by either deposition freezing (base case) or immersion freezing is the same which might point to similar cloud longevity by either nucleation mechanism.

[76] Similar conclusions can be drawn for the colder case (SHEBA) in Figure 12b. However, while the spread in Ψ is about the same as for MPACE, the differences in dLWC/dh are more substantial and for low w or high N(IN) no liquid water (at least not apparent on the linear scale) is maintained and ice continuously grows. The results of the other simulations of deposition freezing also point to an initial increase in dLWC/dh that eventually turns and points toward a decrease in LWC together with a decrease in Ψ. Interestingly, simulations of immersion freezing show the opposite trend and show a continuous increase in Ψ. This trend can be explained with two amplifying effects: (1) relatively larger droplets freeze, as opposed to the dry aerosol particles in the deposition freezing case (see section 4.3.1), and (2) freezing droplets remove liquid water and thus the integral ice capacitance increases whereas the integral drop radius decreases.

5. Conclusions

[77] A parcel model has been developed that includes a detailed description of ice nucleation by immersion and deposition freezing. It includes probabilistic prediction of freezing for particles of identical size and composition. Vapor depositional growth is based on ice particle shapes (habits), which are calculated as a function of temperature on the basis of mass redistribution theory.

[78] Sensitivity studies were performed in order to explore the effects of (1) updraft velocity w, (2) ice nucleus number concentration N(IN), (3) nucleation mode (deposition or immersion freezing), (4) CCN properties (concentration, composition), and (5) assumptions on particle shape (habits versus spheres) on the ice/liquid partitioning in the updraft of Arctic mixed-phase clouds. Model simulations were performed for temperature ranges −12.8°C < T < −9.1°C, and −22°C < T < −17.8°C as observed for mixed-phase clouds during the MPACE and SHEBA experiments. Model simulations for these two cases differed only in their initial temperature where RH = 95%; all other parameters were kept identical in order to quantify the impact of individual parameters on cloud properties for these two scenarios. The following main conclusions emerge.

[79] 1. High updraft and low IN concentrations bolster the liquid phase against depletion by ice. These conditions might lead to longer-lived clouds; however, since our simulations are restricted to one ascent the consequences for cloud longevity cannot be fully assessed.

[80] 2. The role of nucleation modes has been investigated for the (colder) SHEBA case. It is shown that immersion freezing forms less ice than deposition freezing since the temperature of the onset of freezing is lower than for deposition freezing and thus ice particles have less time to grow.

[81] 3. Since the physicochemical parameters that determine a particle's freezing ability carry significant uncertainties, additional simulations were performed with identical temperatures of the onset of freezing for the two different nucleation modes. In the case of deposition freezing in the warmer regime, the results point to freezing temperature, and time available for growth as being more important than the nucleation mode for the ice/liquid distribution. However, owing to large uncertainties in the parameters that control immersion freezing (contact angle or fraction of active sites), it is difficult to draw firm conclusions. If immersion freezing is forced to start at the same temperature as deposition freezing, it will form more ice owing to prior drop formation as opposed to deposition freezing which occurs on dry particles and only comprises ice mass due to vapor deposition in the ice nuclei.

[82] 4. In agreement with previous studies, it has been shown that the assumption of spherical particles leads to a significant underestimate of ice mass given an identical size of the initially nucleated aerosol particles. The predicted ice particle number is the same as in simulations with nonspherical particles, which shows that effects of ice particle growth on the supersaturation are minor, but the reduced growth rates for spherical particles are responsible for this difference. Nonsphericity is in some cases at least as important as IN number concentration and updraft velocity in determining ice/liquid, in particular if high (bulk) density for spherical particles is assumed.

[83] 5. Because sedimentation is not simulated, the model results likely represent an overestimate of IWC/LWC ratios (note that even higher IWC could form, e.g., by riming, not simulated in this study). Sensitivity studies that enforce the removal of those ice particles whose terminal fall velocities exceed the updraft velocity of the air parcel show that all ice particles are likely to reach this threshold. Spherical particles are removed even faster owing to their higher density and smaller surface area projected to the flow.

[84] 6. Most of the simulations predict simultaneous growth of ice and liquid water in the parcel updraft and a dominance of the liquid phase. While our model studies do not allow comprehensive conclusions on cloud stability, which would require simulations over longer time scales (cloud cycles), the identified parameters are likely to affect ice/liquid distribution in longer-lived clouds to a similar extent and thus might eventually impact cloud stability by initiation of the Bergeron-Findeisen process. Aspects of these effects on cloud longevity and maintenance warrant further studies.

[85] Our conclusions are not restricted to Arctic clouds and can likely be extended to other mixed-phase cloud systems. However, relatively high aerosol concentrations at lower latitudes might not be comparable to the low concentrations in Arctic clouds and thus different sensitivities might emerge. Finally it is clear that mixed-phase clouds represent a case where we are still severely limited by our knowledge of the physicochemical properties of ice nuclei and until these are better quantified much uncertainty will remain.


[86] B.E. and G.F. acknowledge support from NOAA's Climate Goal and from the Office of Science (BER), U.S. Department of Energy, grants DE-FG02-08ER64539 and DE-SC0002037. J.H. and K.S. were supported by NSF grants ATM-0639542 and AGS-0951807. J.H. received partial support for this work through the Office of Biological and Environmental Research of the U.S. Department of Energy grant DE-FG02-05ER64058 as part of the Atmospheric System Research Program. K.S. was supported in part by an award from the Department of Energy (DOE) Office of Science Graduate Fellowship Program (DOE SCGF). The DOE SCGF Program was made possible in part by the American Recovery and Reinvestment Act of 2009. The DOE SCGF program is administered by the Oak Ridge Institute for Science and Education for the DOE. ORISE is managed by Oak Ridge Associated Universities (ORAU) under DOE contract DE-AC05-06OR23100. All opinions expressed in this paper are the authors' and do not necessarily reflect the policies and views of DOE, ORAU, or ORISE.