Responses of Simulated Arctic Mixed-Phase Clouds to Parameterized Ice Particle Shape

Chia Rui Ong aGraduate School of Science, Department of Earth and Planetary Science, The University of Tokyo, Tokyo, Japan

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Makoto Koike aGraduate School of Science, Department of Earth and Planetary Science, The University of Tokyo, Tokyo, Japan

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Tempei Hashino bSchool of Environmental Science and Engineering, Kochi University of Technology, Kami, Japan

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Hiroaki Miura aGraduate School of Science, Department of Earth and Planetary Science, The University of Tokyo, Tokyo, Japan

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Abstract

In simulations of Arctic mixed-phase clouds, cloud persistence and the liquid water path (LWP) are sensitive to ice particle number concentrations. Here, we explore sensitivities of cloud microphysical properties to the dominant ice particle shape (dendrites, plates, columns, or spheres) using the SCALE-AMPS large-eddy simulation model. AMPS is a bin microphysics scheme that predicts particle shapes based on the inherent growth ratio (IGR) of spheroids, which determines vapor depositional growth rates along the a and c axes, and the rimed and aggregate mass fractions. We examine the impacts of various IGR values on simulations of clouds observed during the M-PACE and SHEBA experiments. Under M-PACE (SHEBA) conditions, LWP varies between 49 (1.1) and 230 (6.7) g m−2, and the ice water path (IWP) varies between 3 (0.03) and 40 (0.12) g m−2, depending on the ice shape. The lowest LWP and the highest IWP are obtained when columnar particles dominate because their low terminal velocities and large capacitance and collisional area result in large vapor deposition and riming rates, whereas the highest LWP and lowest IWP are obtained when spherical particles dominate because their vapor deposition and riming rates are low. Because ice particle shape significantly influences simulated Arctic mixed-phase clouds, reliable simulations require accurately estimated IGR values under various atmospheric conditions. Finally, comparisons between the simulation results and observations show that the size distribution larger than 2000 μm is better reproduced when the increase in rimed mass that causes ice particles to become spherical is suppressed.

Significance Statement

Atmospheric models have difficulties in reproducing Arctic mixed-phase clouds because of uncertainties in the parameterization of microphysical processes. This is the first study to use a large-eddy simulation model implemented with a habit-predicting bin microphysics scheme to demonstrate the important role of ice particle shape on the microphysical properties of both heavy-riming and no-riming mixed-phase clouds. We found the vapor deposition and riming rates to be greatly influenced by ice particle shape. By comparing the ice particle size distribution, mass–diameter relationship, and area ratio between simulation results and observations, we show that a hexagonal ice shape model and a riming model that simply converts ice crystals to graupel may not accurately reproduce actual heavy-riming clouds.

© 2024 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Publisher’s Note: This article was revised on 16 January 2024 to designate it as open access, which was mistakenly omitted when first published.

Corresponding author: Chia Rui Ong, ong.chiarui@eps.s.u-tokyo.ac.jp

Abstract

In simulations of Arctic mixed-phase clouds, cloud persistence and the liquid water path (LWP) are sensitive to ice particle number concentrations. Here, we explore sensitivities of cloud microphysical properties to the dominant ice particle shape (dendrites, plates, columns, or spheres) using the SCALE-AMPS large-eddy simulation model. AMPS is a bin microphysics scheme that predicts particle shapes based on the inherent growth ratio (IGR) of spheroids, which determines vapor depositional growth rates along the a and c axes, and the rimed and aggregate mass fractions. We examine the impacts of various IGR values on simulations of clouds observed during the M-PACE and SHEBA experiments. Under M-PACE (SHEBA) conditions, LWP varies between 49 (1.1) and 230 (6.7) g m−2, and the ice water path (IWP) varies between 3 (0.03) and 40 (0.12) g m−2, depending on the ice shape. The lowest LWP and the highest IWP are obtained when columnar particles dominate because their low terminal velocities and large capacitance and collisional area result in large vapor deposition and riming rates, whereas the highest LWP and lowest IWP are obtained when spherical particles dominate because their vapor deposition and riming rates are low. Because ice particle shape significantly influences simulated Arctic mixed-phase clouds, reliable simulations require accurately estimated IGR values under various atmospheric conditions. Finally, comparisons between the simulation results and observations show that the size distribution larger than 2000 μm is better reproduced when the increase in rimed mass that causes ice particles to become spherical is suppressed.

Significance Statement

Atmospheric models have difficulties in reproducing Arctic mixed-phase clouds because of uncertainties in the parameterization of microphysical processes. This is the first study to use a large-eddy simulation model implemented with a habit-predicting bin microphysics scheme to demonstrate the important role of ice particle shape on the microphysical properties of both heavy-riming and no-riming mixed-phase clouds. We found the vapor deposition and riming rates to be greatly influenced by ice particle shape. By comparing the ice particle size distribution, mass–diameter relationship, and area ratio between simulation results and observations, we show that a hexagonal ice shape model and a riming model that simply converts ice crystals to graupel may not accurately reproduce actual heavy-riming clouds.

© 2024 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Publisher’s Note: This article was revised on 16 January 2024 to designate it as open access, which was mistakenly omitted when first published.

Corresponding author: Chia Rui Ong, ong.chiarui@eps.s.u-tokyo.ac.jp

1. Introduction

Low-level stratiform mixed-phase clouds are frequently observed in the Arctic region (Shupe et al. 2011) where they play important roles in the radiative budget (Shupe and Intrieri 2004; Zuidema et al. 2005). However, simulation results by different regional models of Arctic mixed-phase clouds show significant discrepancies (Klein et al. 2009; Morrison et al. 2011). Although there are multiple reasons for the large discrepancies, common to all of the model calculations is the uncertainty in the representation of ice particles by cloud microphysics schemes. Inconsistent representations of ice particle shape are potentially a major source of these large discrepancies (Avramov and Harrington 2010; Sulia and Harrington 2011; Shupe et al. 2011; Sulia et al. 2014).

In contrast to liquid droplets, the shape of which is mostly determined by their diameter (though it changes slightly with temperature and pressure), ice crystals can grow to have different habits (or shapes) under different environmental conditions (Kikuchi et al. 2013) through vapor deposition. Examples of such habits include hexagonal plate, dendrite, and column habits. Ice crystals formed at temperatures lower than −20°C can even evolve into polycrystals, which have more complex shapes and irregular numbers of branches (Bailey and Hallett 2004). Moreover, ice crystals may be rimed with droplets to form graupel or collide with other ice particles to form aggregates. Rimed particles tend to become more compact and spheroidal as a result of repeated collisions with droplets, whereas aggregation tends to transform ice particles into entanglements of ice crystals that may be nonspherical. Given the existence of diverse geometrical properties of ice particles, in conventional bulk or bin microphysics schemes, these classes are often represented by different specific relationships among the largest particle dimension (D), particle mass (m), projected area (Ap), cross-sectional area (A), capacitance (C), and terminal fall velocity (TV). However, in the real atmosphere, ice particles can transform from one habit to another through depositional growth when they are immersed in changing environmental conditions. Furthermore, when riming affects a part of snow, the gradual conversion cannot be captured by a simple transition of these particles from one mD relationship to another. Furthermore, the geometry of an ice particle also changes with time under constant environmental conditions. Consequently, these conventional schemes are not ideal to capture the evolution of the shape of ice particles.

Chen and Lamb (1994) proposed a habit parameterization, called the inherent growth ratio (IGR) parameterization in this paper, to tackle the problem of the representation of diverse ice particle shapes in simulations. By assuming a spheroidal representation of an ice crystal, they derived an empirical formula for the proportionality between temperature and the growth rate of the c axis (thickness) of an ice crystal relative to its a axis (radius). This proportionality is the IGR. This formula allows models to predict the evolution of the shape of ice crystals.

The IGR parameterization was implemented into the Advanced Microphysics Prediction System (AMPS) spectral bin scheme by Hashino and Tripoli (2007). Hashino and Tripoli (2011a) further implemented a riming process in which the transformation of rimed ice particles into a more spherical shape with an increasing rimed mass is described by a power law, when the rimed mass reaches 10 times the original mass, the aspect ratio of the particles becomes 0.8. Hashino and Tripoli (2007, 2008) also showed that cloud structure and precipitation are sensitive to ice habit when riming is not considered.

Sulia and Harrington (2011) introduced the IGR parameterization for the vapor deposition growth process into a parcel model and performed calculations for mixed-phase clouds. Sulia and Harrington (2011) found a nonlinear feedback between mass growth and the evolution of the crystal aspect ratio (arc, defined as the c/a axis ratio) that affected the lifetime of mixed-phase clouds.

Sulia et al. (2014) further incorporated the IGR parameterization into a two-moment bulk scheme by adding the c- and a-axis lengths of an ice crystal as prognostic variables and then performed large-eddy simulations. They found that model-predicted ice habits affected the persistence of mixed-phase clouds by influencing the vapor deposition rates. By comparing results between simulations using the conventional fixed Dm relationship with those using the IGR parameterization, they showed that the former were not able to reproduce some important features of the evolution of mixed-phase clouds.

More recently, Jensen and Harrington (2015) introduced the riming process into their single-particle growth model (called ISHMAEL) and further modified the IGR formula by removing the need to empirically determine the vapor deposition density onto an ice crystal, which was necessary in the original IGR parameterization proposed by Chen and Lamb (1994). The change of shape due to riming is such that only the shorter axis length of an ice particle increases until the ratio of the axis lengths reaches a certain limit. The effective density of ice crystals grown from vapor deposition is in better agreement with wind tunnel data when the new formula is used (Jensen and Harrington 2015). Jensen et al. (2017) later implemented the model into a bulk scheme and then ran a series of simulations of orographic and squall-line cloud systems (Jensen et al. 2018a,b). They demonstrated that adding these new features of evolution of the shape due to vapor deposition and riming had significant impacts on the precipitation pattern. These findings indicate that a more accurate representation of ice habits in the model can improve the simulation results and our understanding of cloud physics.

Using an approach different from that of Jensen et al. (2017), Chen and Tsai (2016) developed a multimoment bulk scheme that predicts the bulk shape property without having to assume a fixed shape parameter for the gamma size distribution of ice particles. Tsai and Chen (2020) further modified the scheme by implementing riming and aggregation parameterizations under the assumption that rimed ice particles and aggregates have a fixed spherical shape, and then they performed sensitivity tests on squall-line simulations. Their results indicated that the vapor deposition growth rate, ice particle size, and precipitation flux change significantly when the parameterization of shape variation was turned on in a simulated squall-line cloud system.

The IGR parameterization proposed by Chen and Lamb (1994) is now a widely accepted theory for the parameterization of the vapor deposition growth rate of ice crystals. By using the IGR parameterization, studies using the IGR parameterization have clearly revealed that feedback between ice habit and mixed-phase cloud systems is important and that accurate geometrical representation of ice particles is required for better understanding of cloud physics (Avramov and Harrington 2010; Sulia and Harrington 2011; Sulia et al. 2014; Jensen et al. 2018a,b; Tsai and Chen 2020). However, the IGR parameterization is not a complete theory that fully describes the ice crystal growth. The geometry of some ice habits is more complex than a simple hexagonal or spheroid shape (Kikuchi et al. 2013). Nevertheless, the IGR parameterization simply treats ice crystals as spheroids with two characteristic lengths (a and c axes). The feasibility of using a simple hexagonal shape to represent real ice crystals with more complex shapes is unclear.

The empirical formula for the IGR does not take into account supersaturation over ice even though laboratory results have shown that the dominant ice habit indeed changes with supersaturation (Bailey and Hallett 2004). Jensen and Harrington (2015) have also pointed out the inaccuracy of the empirical formula for vapor deposition density used in the IGR parameterization. Furthermore, the variation in shape due to riming is not treated in the same way among different models because there is no consensus or solid theory on how ice particle shape changes when riming occurs.

In this study, by performing idealized simulations of mixed-phase clouds containing rimed ice particles with complex shapes, we investigate the response of vapor deposition and riming rates, ice mass components and geometry at different sizes, and microphysical properties of the clouds to planar, spherical, and columnar ice crystals using IGR and riming parameterizations. Through these simulations, we aim to shed light on the feasibility of these parameterizations in mixed-phase clouds as well as on important feedbacks between ice physics parameterizations and clouds, which geometrical or physical factors play the most essential roles in deposition and riming processes, and the potential fluctuation range of microphysical quantities that may be introduced by uncertainties in IGR values. We use different IGR values to generate these ice habits under the constraint that the simulated number concentration of ice particles larger than 200 μm (Nice200) agrees with observations for the default IGR values.

We adopt the SCALE-AMPS model (here, SCALE stands for Scalable Computing for Advanced Library and Environment), which is a large-eddy simulation model implemented with the AMPS habit-preserving bin microphysics scheme (Nishizawa et al. 2015; Sato et al. 2015; Ong et al. 2022). AMPS predicts particle shape by using both the original IGR parameterization proposed by Chen and Lamb (1994), which determines the vapor deposition growth rate along the a and c axes, and the rimed mass fraction. We choose to use AMPS for this study because the particle size distribution is explicitly resolved in a bin microphysics scheme. Thus, we can gain explicit information on geometrical and physical particle characteristics, which include the rimed mass and crystal mass proportions of ice particles and how they respond to IGR values at different sizes. Moreover, as a large-eddy simulation model, SCALE-AMPS is a suitable tool for high-resolution idealized simulations.

We use clouds observed by the Mixed-Phase Arctic Cloud Experiment (M-PACE; Verlinde et al. 2007) campaign as our main target in this study because irregular ice particles were present, riming was active, and microphysical quantities including the liquid water path (LWP), ice water path (IWP), vertical profiles of liquid/ice particles, and ice particle size/mass distributions were measured in the persistent Arctic low-level mixed-phase stratiform clouds during the campaign. Moreover, the environmental conditions of the mixed-phase clouds stayed fairly constant, with a maximum temperature change of less than 1.5°C in the inversion and boundary layers over the 6-h observation period.

We use Arctic mixed-phase clouds observed during the Surface Heat Budget of the Arctic Ocean Experiment (SHEBA; Curry et al. 2000) campaign as a second target because, in contrast to the M-PACE clouds, rimed crystals were scarcely present and planar crystals dominated (Fridlind et al. 2012). These clouds can thus serve as an opposite case in which we can expect the IGR parameterization to produce a result in better agreement with observations. We use the tower measurement data (Persson et al. 2002) for the observed LWP values and flight data for the observed ice number concentration and ice particle size distribution (Fridlind et al. 2012). Note that the representation of the aggregation process is not analyzed in this study, although our model includes the aggregation process.

2. Model description

Our simulations used the SCALE-AMPS large-eddy simulation model with the AMPS habit-preserving bin microphysics scheme. The liquid and ice spectra are split into 40 and 20 bins, respectively. Aerosol components are subdivided into accumulation-mode and coarse-mode aerosol particles, each with a lognormal distribution (ice-nucleating chemical compounds are part of coarse-mode aerosol particles). The lognormal distribution is divided into 10 bins and only those aerosols in bins with critical supersaturations below the environmental saturation are allowed to be transferred to the liquid spectrum using the wet transfer scheme as described in Hashino et al. (2020). Further details of this microphysics scheme can be found in Hashino and Tripoli (2007, 2008, 2011a,b). Here, we describe only briefly the features that are used in the analysis performed in this study.

In AMPS, extra prognostic variables are defined in each bin to diagnose the ice particle geometry. A pristine ice crystal is assumed to have a regular hexagonal shape when temperature at which the ice crystal formed is above −20°C. Polycrystals form with a certain probability when temperature is below −20°C (Hashino and Tripoli 2008). Dendritic arms protruding from the vertices may grow under some conditions, such as when the temperature is between −16° and −12°C, as specified in Hashino and Tripoli (2007). The extra prognostic variables defined in each bin, radius (a), thickness (c), and dendritic arm length (d-axis length, d), specify the geometrical characteristics of the ice crystals. See Table 1 for a summary of all symbols used in this paper. These variables and the bulk density evolve with time according to the IGR parameterization. Because ice crystals may collide with liquid droplets or with other ice crystals and gradually turn into graupel or aggregates with an approximately ellipsoidal shape, the variables ice crystal mass, rimed mass, and aggregate mass are also stored in each bin to identify the degree of riming and aggregation. When an ice particle in a particular bin collides with liquid droplets at freezing temperatures, the liquid mass is added to the rimed mass in that bin. Similarly, the mass of collided ice particles is added as the aggregate mass. Ice particles are categorized as pristine crystals, rimed crystals, graupel, aggregates, and rimed aggregates based on these mass fractions, following the categorization method in Hashino and Tripoli (2007). For instance, an ice particle is diagnosed as a rimed crystal (graupel) when the rimed mass is larger than 10% of the total mass and smaller (larger) than the crystal mass. Aggregates and rimed aggregates do not appear in our simulations.

Table 1

List of symbols and their corresponding units used in this study.

Table 1

AMPS uses a simple ice particle geometrical model to represent rimed crystals, aggregates, rimed aggregates, and graupel. In this model, rimed crystals, aggregates, and rimed aggregates are assumed to have a cylindrical shape. Only graupel particles are assumed to be spheroids. The aspect ratio (ar) of these ice particles is defined as the ratio of the semimajor length in the c-axis direction (cs) to the semiminor length in the a-axis direction (as). It is equal to arc when the ice particle is a pristine crystal.

The relationships among D, m, Ap, A, and TV are not predefined in AMPS. Instead, the growth rates of the a, c, and d axes are explicitly calculated using the parameterization originally proposed by Chen and Lamb (1994), who used the diffusion equation to relate the vapor deposition growth rates of a and c to arc as follows:
dcda=Γ(T)ca,
where T is temperature (°C) and Γ(T) is the IGR, which because of a lack of experimental data is assumed to be dependent only on temperature. Chen and Lamb (1994) showed that the temperature dependence of Γ(T) is consistent with the results of various laboratory and field experiments at temperatures above −20°C, and Hashino and Tripoli (2008) extended Γ(T) to temperatures below −20°C. Γ is plotted against temperature in Fig. 1. When Γ > 1 and c/a > 1, the c axis grows at a faster rate than the a axis and the ice crystals tend to be columnar, whereas when Γ < 1 and c/a < 1, the ice crystals tend to be planar. In Fig. 1, Γ approximately reflects the variation of ice habit with temperature seen in the Nakaya–Kobayashi snow crystal morphology diagram (Nakaya 1954); that is, as temperature decreases, the dominant ice habit changes from platelike to columnar and then back to platelike. The ice habit in each bin can thus be diagnosed from the c/a and d/a ratios. The ice crystal shape is columnar when c > a, platelike when c < a, and dendritic when d>(2/3)a. The values of C, A and TV are subsequently calculated from the ice geometry and the degree of riming and aggregation.
Fig. 1.
Fig. 1.

Inherent growth ratio Γ in relation to temperature. At temperatures below −20°C, the dashed curve diverts from the solid black curve because hexagonal crystals can either grow into either planar or columnar shapes. The probability of each growth regime is determined by a habit frequency map as shown in Hashino and Tripoli (2008).

Citation: Journal of the Atmospheric Sciences 81, 1; 10.1175/JAS-D-23-0015.1

Rimed droplets are assumed to stick to the crystal surface along the shorter axis. By further assuming that the circumscribing volume increases with the volume of rimed droplets, the new ar of planar (columnar) rimed crystals then becomes ar=(Vs/Vc)2/3[(1+arc2)1] {ar=1/(Vs/Vc)2/3[(1+arc2)1]}, where Vs and Vc are ice particle and ice crystal circumscribing volumes, respectively. When an ice particle is diagnosed as a graupel particle, ar smoothly transitions to 0.8, which represents the typical ar value of a mature graupel particle, according to the power-law relationship with the rimed mass [see Eq. (15) in Hashino and Tripoli 2011a].

The riming efficiency is affected by the ice particle shape in AMPS. AMPS uses lookup tables constructed by interpolation of the simulation results of Lew and Pruppacher (1983), Lew et al. (1985), and Wang and Ji (2000) to calculate Erim between ice crystals (pristine or rimed) and liquid droplets. The lookup tables for the riming efficiency between graupel and liquid droplets are similarly constructed from the simulation results of Khain et al. (2001). Figure 2 shows Erim of planar (ar = 0.15), columnar (ar = 15), and dendritic (ar = 0.15, with the dendritic arm accounting for 80% of the radius) ice crystals colliding liquid droplets with a size of with 7 or 34 μm; these values approximately represent the liquid size distribution peaks in the M-PACE and SHEBA clouds, respectively (see appendix C). Columns have the largest Erim when D > 2000 μm, whereas dendrites have the lowest Erim because liquid droplets can slip through the gap between two neighboring branches of a dendrite.

Fig. 2.
Fig. 2.

Erim of columns (green), dendrites (red), and plates (blue) colliding with 7- (solid) and 34-μm (dashed) droplets. These curves are generated from the AMPS lookup table, which is a two dimensional array of Erim as a function of the Reynolds number.

Citation: Journal of the Atmospheric Sciences 81, 1; 10.1175/JAS-D-23-0015.1

The collection process is calculated for every combination of two separate bins. Riming is performed similarly between any two bins from the liquid and ice spectra, respectively. The calculation is based on the idea that fortunate particles exist (Chen 1992). Using a simplified statistical distribution, Chen (1992) concluded that it is plausible to assume that fortunate particles from the collector group collect just one more particle than the other unfortunate particles in the same group when the collection rate is lower than 10. Given this assumption, the mass of particles in each bin may increase by different amounts and large raindrops can be produced in a way that resembles the collision–coalescence growth predicted by a stochastic model (Chen 1992). The collection rate is proportional to the collection efficiency (or riming efficiency if the two colliding particles are a drop and an ice particle), difference in TV, and A. The geometrical properties are concentration-weighted averages when two particles collide. Parameterization of the autoconversion process is not used.

Although AMPS can track the time evolution of ice habits using the extra prognostic variables defined in each mass bin, only one spectrum is used to represent all ice habits. Under the implicit mass sorting assumption (Hashino and Tripoli 2007), a representative ice habit with averaged mass ratios, axis lengths, circumscribing volume, bulk density, terminal velocity, and cross-sectional area is assumed for each bin when calculating the growth rates. As a result, only the weighted averages of ice particle characteristics remain when ice particles of two different habits are mixed together by Eulerian advection, sedimentation, or collisions. This phenomenon is also known as ice particle property dilution (Milbrandt and Morrison 2016; Jensen et al. 2018b). Simulation results are therefore sensitive to the number of bins across the ice spectrum because the range of mass of a bin represented by a particular habit varies. A detailed discussion of this issue can be found in Hashino and Tripoli (2007).

The calculation of the radiative heating or cooling rate requires the input of the effective radius from the microphysics schemes in SCALE. We obtain the effective radius by computing the ratio of the concentration-weighted third power of the equivalent radius to the concentration-weighted second power of the equivalent radius. The equivalent radius of an ice particle is defined as the radius of a sphere with a density of 0.916 g cm−3 that has the same mass as the ice particle. The control runs were repeated without considering the radiative contribution from ice particles, and the maximum difference in LWP, IWP, and the ice particle size distribution is less than 10% (result not shown). Hence, the radiative heating or cooling effect contributed by ice particles is minor in the M-PACE and SHEBA clouds.

3. Case description and numerical setup

a. M-PACE

Intensive observations were conducted from 1700 UTC 9 October to 0500 UTC 10 October 2004 during the M-PACE campaign (Verlinde et al. 2007; Klein et al. 2009). During this period, an anticyclone caused a northeasterly cold airflow off the sea ice to the coast of Alaska where the Barrow station was located. The ocean off the Alaskan coast was free of sea ice. The cold air gathered a significant amount of water vapor and sensible heat before it reached Alaska, and single-layer mixed-phase clouds formed over the open ocean with a cloud-top temperature of about −15°C (AMPS predicts that frozen droplets grow into dendrites at this temperature). The boundary layer was about 1500 m deep with a temperature inversion of 2–3 K near the cloud top. As a result of the influx of water vapor from the open ocean, active riming and drizzle were observed (Fridlind et al. 2012). The majority of ice particles appeared to be polycrystals (see appendix A). Visual inspection of the CPI images indicated that aggregates were also scarcely present. Two flights were conducted during the observation period with the aircraft flying along the coast of Alaska between the Barrow station and Oliktok point (McFarquhar et al. 2007; Klein et al. 2009). We use the flight measurement data of McFarquhar et al. (2007) recorded between 0100 and 0200 UTC 10 October 2004, when the aircraft flew repeatedly up and down in spirals, for our comparisons with the M-PACE simulations.

For the M-PACE simulations, we use horizontal and vertical grid sizes of 50 and 20 m, respectively. The computational domain is 3.6 km × 3.6 km horizontally. We set the height to 2 km and apply Rayleigh damping to the vertical velocity at heights above 1.6 km. Because the observed cloud top and inversion layer are lower than 1.4 km, the top boundary condition does not have major impacts on our results. The lateral boundary satisfies the periodic condition. We use the balloon-sonde data collected at Barrow station (71.3°N, 156.7°W) at 2302 UTC 9 October 2004 to generate the initial vertical profiles of pressure, humidity, temperature, cloud liquid water mixing ratio, and wind speed (see the appendix B for the selected initial profiles). The calculation of radiative fluxes above the model top also uses the initial conditions of pressure, temperature, and humidity throughout the simulation. Following Klein et al. (2009), we set the surface temperature, sensible heat flux, and latent heat flux to constant values of 274.1 K, 136.5 W m−2, and 107.7 W m−2, respectively. We also follow Klein et al. (2009) for the large-scale forcing. The wind speed is nudged to the initial wind speed with a relaxation time of 1 h. The integration time is 4 h, and both ice and liquid microphysical processes are turned on from the beginning. We set the time step of the dynamical process to 0.1 s so that the Courant–Friedrichs–Lewy condition is satisfied.

The aerosol number concentration is fixed to a constant value within the model domain. The number concentration, mean radius, and standard deviation of accumulation-mode (coarse-mode) aerosols are 30 cm−3, 0.052 μm, and 2.04 (0.9 cm−3, 1.3 μm, and 2.5), respectively. Both the accumulation-mode and coarse-mode aerosols follow a lognormal distribution. The accumulation-mode aerosols are completely soluble, and their chemical form is set to ammonium bisulfate. Of the mass fraction of coarse-mode aerosols, 20% is assumed to be insoluble kaolinite, and the remaining 80% is ammonium bisulfate. Only the immersion freezing mode based on classical nucleation theory (Hashino et al. 2020) is switched on. Kaolinite with a minimum radius larger than 0.25 μm in the coarse-mode aerosols acts as an ice-nucleating particle (INP). An extra parameter Fdust is added as a tuning parameter to represent the percentage of INPs contained in droplets that may eventually freeze. In the M-PACE simulations, Fdust is set to a constant value of 0.013 so that the predicted Nice200 agrees with observations.

b. SHEBA

The ice station drifted with sea ice during the SHEBA campaign. A single-layer mixed-phase cloud deck was observed over sea ice on 7 May 1998 when the station was at 75°N, 165°W (Fridlind et al. 2012). The cloud-top temperature was about −20°C and the boundary layer was 400 m deep with a temperature inversion of about 5 K located at the height of the cloud top. The National Center for Atmospheric Research (NCAR) C-130 aircraft flew over the station during the observation period and measured ice particle distributions and ice properties.

We use the same numerical setup of SHEBA simulations as in Ong et al. (2022), except for the freezing scheme and the computational domain dimensions, as summarized below.

We employ the same immersion freezing scheme as adopted in the M-PACE simulations. Fdust is set to 0.0004 so that the predicted Nice200 agrees with observations. The dimensions of the computational domain are 3.6 km × 3.6 km × 1 km with Rayleigh damping starting at 0.8 km height. Note that the observed cloud top and inversion layer are below 0.4 km. Any influences from the top boundary condition are considered minimal. We follow Fridlind et al. (2012) for the initial and boundary conditions, large-scale subsidence, and horizontal advective tendency (see appendix B for the initial profiles). We set the surface temperature, sensible heat flux, and latent heat flux to constant values of 257.4 K, 7.98 W m−2, and 2.86 W m−2, respectively. The aerosol number concentration is fixed to a constant value within the model domain. The number concentration of accumulation-mode and coarse-mode aerosols are 350 and 1.8 cm−3, respectively. The mean radii and standard deviations remain the same as those used in the M-PACE simulations. The time step for the dynamical process is 0.2 s. We use the same time step of 2 s for the microphysical processes in both the M-PACE and SHEBA simulations.

c. Control and sensitivity calculations

As explained in section 2, in AMPS, the ice habit is diagnosed from the ratio of axis lengths. Thus, we can change the dominant habit in our simulations by adjusting the IGR Γ(T). In the control runs, the default IGR values shown in Fig. 1 are used, and the results are compared with observational data from the M-PACE and SHEBA campaigns to evaluate the model performance.

In the sensitivity calculations, we use various IGR values within the upper (Γ = 2.3) and lower (Γ = 0.27) limits of the default values to examine the sensitivity of the cloud features to IGR values and understand the influence of ice habit on mixed-phase clouds. In our simulations, we set Γ to a constant value of 0.27, 1, or 2 for a dominant habit of plates, spheres (a regular hexagonal prism with equal thickness and diameter, or equivalently an isometric ice crystal, is called a “sphere” in this study), or columns, respectively (plotted as colored straight horizontal lines in Fig. 1). In all of the sensitivity calculations, we set the dendritic arm length to zero, although dendrites form in the control run under the M-PACE conditions. The formation of polycrystals in the sensitivity calculations is switched off. In addition, we conduct another sensitivity calculation in which we inhibit the conversion of pristine ice crystals to graupel when riming takes place (i.e., an ice particle remains as a pristine ice crystal and its shape does not change when riming occurs) to examine how graupel formation affects cloud evolution. We also performed two M-PACE simulations with Erim reduced by two-thirds and to zero while keeping Γ at default values to investigate the sensitivity on the riming process. The setup of each run is summarized in Table 2. The spinup time is 1 h for all the simulations. Convection is fully developed after 1 h of integration.

Table 2

Summary of the simulations conducted in this study.

Table 2

In the sensitivity calculations, we use the same Fdust values as those chosen in the control calculations (0.013 and 0.0004 for the M-PACE and SHEBA calculations, respectively). Partly because of differences in the TV of ice particles with different shapes, Nice200 values vary in the sensitivity calculations as shown in section 4.

4. Results

a. Impact of ice habits

1) LWP and IWP

Figure 3 shows scatterplots between median LWP and IWP values of cloud grid cells in the model domain averaged after 2 h. A cell in the simulations is considered to be a cloud grid cell or a cloudy cell when the liquid mixing ratio is greater than 10−3 g kg−1 (the same criterion is applied to the measurement data). First, the results of the control runs are examined. As described in section 3, we adopted a particular Fdust value so that the predicted Nice200 in clouds agrees with observations. With this setting, we see that the predicted values of LWP, IWP, and the liquid particle number concentration (Nliq) lie within the observed maximum and minimum values in both the M-PACE and SHEBA calculations. The differences between the median LWP, IWP, and Nliq values of the M-PACE control run and the observed medians are only 4 g m−2, 0.6 g m−2, and 1.4 cm−3, respectively. The LWP (5.6 g m−2) and Nliq (256 cm−3) values of the SHEBA control run are also close to the observed values (5 g m−2 and 271 cm−3, respectively).

Fig. 3.
Fig. 3.

Model median LWP, IWP, Nliq, and Nice200 in clouds in the (a),(b) M-PACE and (c),(d) SHEBA simulations. The gray zones and error bars represent the observation ranges, and the black dots indicate the observed median (McFarquhar et al. 2007) in the M-PACE clouds. The observed range of LWP is derived from the maximum (10 g m−2) and minimum LWP (5 g m−2) values of the SHEBA clouds measured at the ground station (Persson et al. 2002). Because there are no reliable measurement data of IWP during the SHEBA campaign, the gray zone in (c) extends from zero to infinity. The observed median and range of Nliq in the SHEBA clouds are derived from the flight measurement data (Fridlind et al. 2012). The data for the upper (1.7 L−1, not shown) and lower limits (0.3 L−1) of observed Nice200 are from Morrison et al. (2011) and Fridlind et al. (2012), respectively. According to Fridlind et al. (2012), the real in-cloud ice number concentration is thought to be nearer to 0.3 L−1. Therefore, the error bar is plotted at Nice200 = 0.3 L−1.

Citation: Journal of the Atmospheric Sciences 81, 1; 10.1175/JAS-D-23-0015.1

Results from the sensitivity runs show that in both the M-PACE and SHEBA calculations, LWP and IWP vary considerably by up to one order of magnitude when different IGR values are adopted. When the IGR value is set to 0.27 and 2, the dominant ice habit is columnar and platelike, respectively. The maximum difference in the LWP or IWP between the results for the control runs, which use the default IGR, and those for the plate run and sphere run results is less than 20% in both the M-PACE and SHEBA simulations. This result is obtained because the default IGR value at temperatures between −12° and −17°C is about 0.3 (M-PACE) and that between −19° and −21°C (SHEBA) is about 0.7, and these values are close to the IGR values in both the plate and sphere sensitivity runs.

The simulated mixed-phase cloud system with dominant columnar ice crystals tends to have a smaller LWP (49 and 1.1 g m−2 in M-PACE and SHEBA, respectively) and a larger IWP (40 and 0.97 g m−2, respectively). In contrast, mixed-phase clouds tend to have a larger LWP (230 and 6.7 g m−2 in M-PACE and SHEBA, respectively) and a smaller IWP (2.8 and 0.03 g m−2, respectively) when spheres are forced as the dominant ice habit. In the simulated system with dominant platelike ice crystals, LWP (158 and 2.3 g m−2, respectively) and IWP (7.7 and 0.12 g m−2, respectively) lie between these two cases, because the mass-weighted C and A of plates are larger (smaller) than those of spheres (columns). These two parameters are the most important factors in the vapor deposition and riming rates, respectively (see section 4b), which are the source terms for ice water, and simultaneously the sink term for liquid water: the larger the value of C (A), the higher the vapor deposition (riming) rate. The IWP fraction in the total water path (TWP = LWP + IWP) increases from 1.2% (0.45%) to 45% (48%) when the dominant ice habit switches from spheres to columns under M-PACE (SHEBA) conditions.

Changes in Nice200 are less pronounced than those in LWP and IWP with different ice habits. There is a less than 15% difference in median Nice200 between the plate and sphere runs in both M-PACE and SHEBA simulations. In the column run, median Nice200 is about twice the median value in the plate and sphere runs. The different responses between Nice200 and LWP/IWP to the ice habit result from the different geometrical properties and ice particle size distributions, as described later in sections 4a(4) and 4b.

Notably, LWP and IWP levels differ by one or two orders of magnitude between M-PACE and SHEBA simulations. These large differences is because the M-PACE clouds formed over the open ocean, where the sensible and latent heat fluxes were large, whereas the SHEBA clouds formed over sea ice, where these fluxes were smaller (Morrison et al. 2011). Morrison et al. (2011) also reported that riming was observed during the M-PACE campaign. Despite these differences in the environmental conditions, the calculated LWP and IWP levels in both the M-PACE and SHEBA simulations are quite sensitive to the ice habit.

2) Vertical profiles

In the previous section [section 4a(1)], we have seen that the LWP, IWP, Nliq, and Nice200 of the M-PACE control run are consistent with observations, and that they vary considerably when the ice habit changes. Comparisons of the simulated liquid and ice water contents (LWC and IWC, respectively) and number concentrations for flight data points at different heights in both clear sky and cloudy conditions can partly reveal the cloud physics that affects the LWP, IWP, Nliq, and Nice200.

Figure 4 compares vertical profiles of cloud microphysical parameters and temperature between the simulations and observations collected during the M-PACE aircraft experiment (McFarquhar et al. 2007). First, we see that the median LWC, IWC, Nliq, and Nice200 in the control run fall within the observational ranges from the cloud top to cloud bottom. When the dominant ice habits are spheres or columns, however, there are obvious discrepancies between the simulated and observed values of LWC and IWC, and these results are consistent with the discrepancies between simulated and observed values of median LWP and IWP (Fig. 3). Note that the simulated mean cloud thickness in the control run is 581 m, which is less than the observed mean value of 639 m. The simulated cloud layer also shifts 200 m higher because the simulated inversion layer is higher and stronger (Fig. 4e). The stronger simulated inversion layer also leads to the temperature being 1°C lower than observations and an overestimation of LWC, Nice200, and Nliq near the cloud top. Because the strength of the inversion layer is also associated with large-scale forcing and cloud-top entrainment and detrainment processes, unrealistically strong large-scale forcing and weak cloud-top turbulent mixing are a possible cause of the sharp inversion layer in the simulations, even though the initial temperature profile agrees with the flight data (see appendix B).

Fig. 4.
Fig. 4.

Vertical profiles of model simulation results (colors) and observations (black dots) collected during the M-PACE campaign (McFarquhar et al. 2007). (a)–(e) Control run (red). (f)–(j) Sphere run (orange). (k)–(o) Column run (green). (p)–(t) Plate run (blue). The lower and upper limits of the shaded regions are the 5th- and 95th-percentile values, respectively. The solid colored lines represent the model median. The simulation results and data are from all grids. The simulation results are averaged over the final 2 h.

Citation: Journal of the Atmospheric Sciences 81, 1; 10.1175/JAS-D-23-0015.1

Further explanation about the vertical profiles of IWC and Nice200 is given in appendix E.

3) Ice types

Figure 5 shows vertical profiles of the median number concentration of pristine crystals, rimed crystals, graupel, and aggregates averaged over the final 2 h in the M-PACE simulations. Although aggregates and rimed aggregates (rimed mass larger than 10% of the total mass and smaller than the aggregate mass) are also calculated in AMPS, the contributions from these categories are negligible. In these simulations, the number concentration of graupel increases with decreasing altitude from the cloud top to the cloud middle in the control, sphere, and plate runs (in Fig. 5, the thickness of the purple shading in the cloud layer increases from the top toward the middle of the cloud layer even though the total number concentration decreases). This pattern occurs because ice particles capture supercooled droplets as they fall through the upper portion of the clouds, whereas this process is less efficient in the lower portion where the liquid droplets are smaller and the LWC is lower. In the column run, graupel shows a similar tendency, although its fraction is lower because TV and A of pristine crystals are small compared to those of dendrites of the same size (see section 4b). Only ice particles larger than 2000 μm efficiently collide with droplets (Fig. 6c). Ice particles with a sweeping volume (A multiplied by TV) larger than about 10−2 cm3 s−1 increase their mass by riming more efficiently than by vapor deposition. Efficient riming of these ice particles explains the increase in the IWC with decreasing altitude (Fig. 4). In the M-PACE simulations, the riming process is already efficient just below the cloud top: in the control run, more than 80% of the ice particles at the cloud top are rimed crystals or graupel. The geometrical characteristics of pristine crystals of any size are the same in both the M-PACE and SHEBA sensitivity calculations. The active riming process in the M-PACE setup is owing to the fact that the LWP in the M-PACE control run is about 30 times larger than that in the SHEBA control run. Moreover, Erim is larger in the M-PACE calculations because the average droplet size is 34 (7) μm in the M-PACE (SHEBA) control run (see Fig. 2 and appendix C).

Fig. 5.
Fig. 5.

Median vertical profiles of the number concentration of all ice particle types averaged over the final 2 h in the M-PACE simulations. (a) Control run. (b) Sphere run. (c) Column run. (d) Plate run. The two horizontal dashed lines in each panel represent the cloud top and the cloud bottom. The thickness of the color shading along the x axis represents the number concentration, and the different colors stack along the x axis. For example, the number concentration of a particular ice type is 0.1 L−1 when its color shading extends from 0.05 to 0.15 L−1.

Citation: Journal of the Atmospheric Sciences 81, 1; 10.1175/JAS-D-23-0015.1

Fig. 6.
Fig. 6.

Mean number concentrations of pristine crystals (blue bars), rimed crystals (yellow bars), aggregate (green bars; they are not present in the simulations), rimed aggregate (red bars), and graupel (purple) in cloudy grids at 2 h as a function of D in the M-PACE (a) control run, (b) sphere run, (c) column run, and (d) plate run. The sweeping volume, defined as A multiplied by TV, is also plotted (black curve). Unlike in Fig. 5, the colors represent the normalized proportion of each ice type at a value of D (e.g., if 50% of the total bar length is yellow, then half of the ice particles are rimed crystals).

Citation: Journal of the Atmospheric Sciences 81, 1; 10.1175/JAS-D-23-0015.1

In the SHEBA simulations, more than 99% of the ice particles are pristine crystals throughout the cloud layer because riming activity is low. This lack of riming is consistent with observations (Morrison et al. 2011).

4) Ice particle size distributions

Figure 7 shows the simulated ice particle size distributions in and below the clouds at an integration time of 3 h in the M-PACE and SHEBA calculations, along with the size distributions measured by one-dimensional cloud (1D-C) and two-dimensional cloud (2D-C) array probes on the research aircraft during the M-PACE (McFarquhar et al. 2007) and SHEBA experiments (Fridlind et al. 2012). For particle sizes smaller than 2000 μm, the mean particle size distribution of the control runs differs from observations by less than one order of magnitude. Although the number of ice particles with D < 400 μm in the M-PACE control run is approximately half the observed number, the overestimation of the number of ice particles over the range between 500 and 1000 μm eventually results in an overestimated median Nice200 (Fig. 3). Although the mean size distribution in the sphere (column) run is close to the observed value when D < 300 μm (D is between 600 and 2000 μm), otherwise the discrepancy between the simulation results and the observed values is often larger by several orders of magnitude. Note that the size distributions in the M-PACE plate and control runs are similar because the default IGR values are close to 0.27 at the temperature of about −16°C.

Fig. 7.
Fig. 7.

Ice particle size distributions averaged over (a),(b) all cloudy cells and (c),(d) cells below clouds at 3 h in the (left) M-PACE and (right) SHEBA simulations. The observation data collected from the 1D-C and 2D-C probes (gray curves) during the M-PACE campaign are from McFarquhar et al. (2007). In (a), the black dashed line labeled “1dc mean” is the mean of the 1D-C data and the black dotted line labeled “2dc mean” is the mean of the 2D-C data. The observed below-cloud means collected by the 2D-C probe during the SHEBA campaign (black dotted line) are from Fridlind et al. (2012). Note that the units of Nice200 are set to cm−3 only in this figure for comparisons with the flight data.

Citation: Journal of the Atmospheric Sciences 81, 1; 10.1175/JAS-D-23-0015.1

Figure 7 also shows the impact of ice habit on the peak of the ice particle size distributions. The in-cloud particle size distribution peak shifts from 800 μm in the plate run to between 2000 and 3000 μm in the column run, and in the sphere run, it is located at just 200 μm. It is not surprising that spheres have the smallest mean size because the vapor density gradient is weaker for a spherical particle than for particles with other shapes (Sulia and Harrington 2011); thus, the growth rates of the a and c axes are lower.

In the SHEBA calculation results, only the mean below-cloud ice particle distribution in the control run follows the mean observed distribution (Fridlind et al. 2012) and there are no particles larger than 2000 μm, whereas the maximum D of spheres, plates, and columns deviate from observations. Consequently, the SHEBA calculations also indicate that even when riming is absent, the ice habit assumption is important in simulations.

Notably, median Nice200 varies by a factor of only about 3 among the control, sphere, and plate runs (see Fig. 3). However, because of the mean size differences described above, the maximum median IWC value varies by a factor of 40 among these runs. Recall that we adopted a particular value for the tuning parameter Fdust, which determines the INP number concentration, such that the predicted Nice200 agrees with observations in the control run. The results presented here indicate that even when the simulated Nice200 agrees with observations, the IWC can be different when an inappropriate ice habit is assumed in simulations. Systematic differences in the mean particle size result in large variations in the IWP in spite of the relatively small variations in Nice200.

5) Mass–diameter relationship

Figure 8 shows the mean mass–diameter (or maximum dimension) (mD) relationships derived from our simulations. The mD relationship differs among the different ice habits in both the M-PACE (Fig. 8a) and SHEBA (Fig. 8b) calculations. The particle mass varies by more than two orders of magnitude when particles with the same D are compared among the sensitivity calculations. The mass of an ice particle at any specific D increases when the ice habit changes from columns to plates to spheres. Conventional single-moment (Lin et al. 1983; Tomita 2008) and double-moment (Seifert and Beheng 2006; Morrison and Gettelman 2008) bulk schemes often use a fixed or environment-dependent mD relationship (as well as fixed AD and TV–D relationships). Our results show that LWP and IWP values depend on the choice of mD (and A–TV–D) relationship if a fixed relationship is adopted, which is determined by the growth rate of ice particles. Consequently, the use of an appropriate mD relationship is essential for reliable simulation of Arctic mixed-phase clouds.

Fig. 8.
Fig. 8.

Mass–diameter (mD) relationships in the (a) M-PACE and (b) SHEBA simulations, and (c) rimed mass fraction in the M-PACE calculations. All simulation results are values averaged over the final 2 h. Black curves are calculated by the method in Heymsfield et al. (2007). Gray curves are plotted according to the data in Mitchell (1996). Densely rimed dendrites and crystals with sector-like branches are categorized as R2b and P1b, respectively, by the categorization method of Magono and Lee (1966).

Citation: Journal of the Atmospheric Sciences 81, 1; 10.1175/JAS-D-23-0015.1

As described in section 2, the mD relationship is not predetermined in AMPS but is dynamically determined by the mass composition and the ar that result from the vapor deposition and riming process calculations. In the vapor deposition process, the temperature-dependent IGR values determine ar of ice particles [Eq. (1)]. In the riming (aggregation) process, the rimed (aggregate) mass fraction is used to estimate ar. The vapor deposition process is generally dominant in the SHEBA calculations, but in M-PACE, although ice particles smaller than about 200 μm grow by vapor deposition, larger ice particles undergo active riming and more than 80% of the particles are rimed crystals in the control, plate, and sphere runs. The monotonic increase in the mean rimed mass fraction to 0.8 in the control and all sensitivity runs as shown in Fig. 8c is evidence of the active riming process in the M-PACE calculations. Slopes of the mD relationship tend to be steeper when riming occurs, compared with those in the SHEBA simulations, in which vapor deposition dominates. Furthermore, the mD relationship for ice particles larger than 200 μm in the M-PACE control, sphere, and plate runs also approximately satisfies a power law.

In the M-PACE column run, a distinctive concave cusp can be seen at about 2000 μm, because the riming mass starts to build up at this particular size (see Figs. 6c and 8c). The particle size at which the slope steepens depends on the ice habit, because the riming rate, which is determined by A, TV, and Erim, differs among different ice habits. The steeper slope for D > 2000 μm in the column run, as compared with the other runs, is due to the efficient riming process, which causes ar and bulk sphere density (ρs) of these particles to decrease and increase tenfold, respectively, as D increases from 2000 to 7000 μm (Figs. 9a,e). The mD curve of the column run is expected to approach the extrapolated mD curves of the control and plate runs. These results clearly demonstrate that mD relationships are dynamically controlled in cloud systems. Our results also show that the applicable range of ice, snow, and graupel categories in bulk microphysics schemes must be carefully chosen because the particle size at which riming becomes active is different for different ice habits.

Fig. 9.
Fig. 9.

Distributions of the concentration-weighted aspect ratio (ar^), terminal velocity (TV^), bulk sphere density (ρs^), capacitance (C^), and cross-sectional area (A^) in relation to maximum particle dimension averaged over the final 2 h of the (left) M-PACE and (right) SHEBA simulations.

Citation: Journal of the Atmospheric Sciences 81, 1; 10.1175/JAS-D-23-0015.1

It is interesting to note that even though ar varies with ice particle size in the SHEBA calculations, the mD relationship in the control and plate runs is approximately linear on a logarithmic scale (Fig. 8b). These results suggest that the power law is adequate for representing the mD relationship of pristine spherical, columnar, or planar ice crystals in mixed-phase clouds when riming is absent, with the coefficient and exponent of the power law depending on the ice habit. The abrupt change in the slope at D = 1000 μm in the column run does not violate this finding because the maximum ar in AMPS is restricted to 20. Ice crystals larger than 1000 μm reach this limit and then grow with a fixed ar. This restriction of AMPS also causes the slope of the mD curve to be steeper in the column run than in the plate and control runs because the ice crystals in the plate and control runs become thinner as they grow by vapor deposition (their ar decreases with D). Nevertheless, the mean ice particle mass in the column run is still the smallest.

We compare the simulated mD relationships in the M-PACE calculations with power-law parameterizations (m = αDβ) based on aircraft measurements or theoretical models for ice clouds to examine whether our results are within the physically reasonable ranges of observed mD relationships. In Fig. 8a, the observed mD relationship derived from the in situ observations during the M-PACE campaign (McFarquhar et al. 2007) is presented as a gray curve with plus signs and the mD power laws for typical rimed crystals and graupel are plotted as gray curves with circles, stars, and diamonds, respectively. We use β and α values from Mitchell (1996) for densely rimed dendrites, categorized as R2b in Magono and Lee (1966); rimed long columns; and graupel as follows: β = 2.3 (α = 0.003), 1.8 (0.001 45), and 2.8 (0.049), respectively.

For the SHEBA calculations (black solid curves in Fig. 8b), a constant β is chosen to represent typical ice crystals: hexagonal plates (β = 2.45); hexagonal columns (1.75); crystals with sector-like branches (2.05), categorized as P1d in Magono and Lee (1966); and ice spheres (3), following Mitchell (1996). The value of α is calculated by assuming that ice crystals with a diameter less than 10 μm are spherical following the method in Heymsfield et al. (2007).

The simulated mass of ice particles in the plate and control runs under the M-PACE conditions (Fig. 8a) approaches the graupel curve (gray diamonds) because of the heavy riming that converts rimed crystals to graupel in the model (Figs. 5a,d). Hence, the simulated mD relationship of rimed dendrites and graupel in the control run under the M-PACE conditions (the red curve in Fig. 8a) deviates from the observed power law for densely rimed dendrites, with the slope of the simulated curve being larger than the observed slope. In fact, the mean ice particle mass with D > 500 μm in the control run is overestimated. The simulated ice particle mass with D > 1000 μm even exceeds the observed particle mass by more than one order of magnitude. A probable cause is an overestimation of the riming mass rate for these ice particles in the control run.

The mD relationship obtained by assuming that ice crystals are spherical at all sizes is also shown (black diamonds in Fig. 8a). This curve represents the upper bound of mass for an ice crystal with any maximum dimension. The mass of ice particles in the sphere run is closest to this limit because the initial aspect ratio of the particles is 1.0, and they increase their mass mainly by riming with supercooled droplets.

Under the SHEBA conditions where riming is absent, the mass of individual ice particles in the simulations falls within the regions bounded by the observed power laws for hexagonal plates and columns and crystals with sector-like branches (P1b). The mD curves of the control and sphere runs are closest to the mD relationship for hexagonal plates, whereas the mD curve of the plate run is closest to the mD relationship for P1b. Note that gradient of the mD curve in the plate run is lower than those of the simulated mD curves in the control and column runs. This lower gradient is because ar decreases by an order of magnitude from 0.2 to 0.02 as D increases from 200 to 2000 μm (Fig. 9b). Nevertheless, the mD relationship in the plate run can still be well approximated by a power law for crystals with sector-like branches.

b. Mechanisms of ice habit impacts

1) Controlling parameters

To understand how different ice habits influence the various cloud parameters presented in the previous sections, we analyze the controlling parameters (see Table 1 for abbreviations), namely, ar, TV, ρs (bulk sphere density), C, and A of ice particles averaged over the final 2 h in both the M-PACE and SHEBA simulations. Figure 9 shows these parameters as a function of D.

In all runs, AMPS diagnoses the ice habit from ar, which is determined by Γ (IGR values) and the rimed mass fraction. The upper limit of ar in AMPS is 20, and in fact, the ar^ value of pristine crystals in column runs approaches this upper limit when D > 1000 μm (700 μm) in the M-PACE (SHEBA) calculations. Under the M-PACE conditions, ar^ values of columns larger than 2000 μm decrease to values close to unity because riming tends to reduce ar to a constant value of 0.8, which corresponds to the steeper mD relationship slope in the column run (Fig. 8a). The value of ar^ is still greater than unity, however, because the rimed mass fraction is only 80% (Fig. 8c). In AMPS, a 90% rimed mass fraction is required for the ar value of a graupel particle to become less than unity when ar of the pristine columnar crystal inside the graupel is 20. Similarly, under the M-PACE conditions, ar^ tends to approach 0.8 from about 0.2 (1) in the plate and control (sphere) runs as they increase in size as a result of the riming process. In contrast, under the SHEBA conditions, plates become thinner as their maximum dimension increases through vapor deposition because riming is negligible and Γ is less than 1.0.

The ar^ values are closely related to ρs^ values (Fig. 9). Spherical particles, whose ar is unity, have a compact particle shape and therefore the highest ρs, whereas columns and plates, whose ar is far from unity (about 10 or 0.1, respectively), have low ρs. The ar^ and ρs^ values directly affect TV^: spherical particles (highest ρs) have the highest TV, whereas columns (lowest ρs) have the lowest TV. The ρs and TV values of plates are intermediate between those of spheres and columns.

Because Nice200 is affected by the precipitation flux gradient in the advection equation, a larger TV^ value reduces Nice200 because ice particles fall at a faster rate to the surface. In contrast, a smaller TV^ value implies that Nice200 increases because the precipitation flux is smaller. As a result, median Nice200 is lowest in the sphere run (highest TV^) and highest in the column run (lowest TV^) (Fig. 3). IWC is also affected by TV^: IWC is lowest and highest in the sphere and column runs, respectively, due to their lowest and highest Nice200 values as well as the difference in their size distributions. In summary, ar^, ρs^, TV^, Nice200, and IWC are all closely related.

Plates have higher C and A values than spheres at any particle sizes because of their extremely small ar values, far below unity. Setting Γ = 2 causes pristine crystals to have extremely large ar values in the column run. These ice crystals have a long needle shape, and thus, their A values are smallest. Columns also have the lowest C values because they are assumed to be equivalent to prolate spheroids in the calculation of the vapor deposition growth rate. The capacitance of a prolate spheroid decreases as its ar increases. C and A are also key parameters for both depositional growth and riming growth rates, which are higher for particles with larger C and A values, as is discussed in the next section.

We further observe that, in the M-PACE simulations, no particles with TV larger than 2–3 m s−1 exist (the curve is cut off when the ice particle size distribution is smaller than 10−6 cm−3 μ−1, see also Fig. 7). There is a lack of ice particles larger than the cutoff diameter because the absolute vertical gridscale wind speed of more than 98% of the cloud grids is less than 2 m s−1. As a result, particles with TV larger than 2 m s−1 fall to the surface. In the SHEBA simulations, the mixing motion is milder: more than 98% of the cloud grids have a vertical gridscale wind speed of less than about 1 m s−1 because the surface is assumed to be sea ice, which causes heat exchange with the air to be smaller. Therefore, the average size of ice crystals is smaller in the SHEBA simulations.

The above analysis suggests that ice particle geometry and the calculation of the dynamical processes in models are closely connected and that their correct representation is essential for accurate prediction of Arctic mixed-phase clouds. In large-eddy simulations, the boundary layer dynamics and radiative cooling at the cloud top partly determine the distribution of vertical mixing in clouds. In turn, the vertical wind speed limits the maximum TV of ice particles. Because TV at a particular size is determined by the ice habit, how well the observed ice particle distribution is reproduced in simulations is also affected by how well dynamical processes are represented in the model.

2) Riming and deposition rates

The riming and vapor deposition processes directly control how fast the liquid content and water vapor are depleted or refilled, either via a Wegener–Bergeron–Findeisen mechanism or particle–particle collection. The rate at which these processes occur depends on the ice particle geometry. In this section, we elaborate on how the controlling parameters investigated previously affect the riming and vapor deposition rates to evaluate the impacts of different ice habits on cloud parameters such as IWC and LWC.

We first define the vapor deposition rate Rvap (g cm−3 s−1) as
Rvap=NiceCK(T,p,Si),
where K(T, p, S) = 4πG(T, p)fυ, with G(T, p) and fυ being the thermodynamic function and ventilation factor (Pruppacher and Klett 1997), respectively; K(T, p, Si) is a parameter that depends on the temperature (T), pressure (p) and the supersaturation over ice (Si). However, because the temperature changes by less than about 1 K in the calculations, we ignore the effect of K(T, p, Si) in our analysis. We also define the riming rate Rrim (g cm−3 s−1) as
Rrim=ErimNiceATVLWC,
where Erim is the riming efficiency, and we assume that the terminal velocity of collected droplets is negligible. Because LWC and LWP vary with different ice habits (see Figs. 3, 4, and D1d,i), we also define the liquid-normalized riming mass rate (R˜rim) as R¯rim/LWC to study how Nice, A, and TV of each ice habit affect R¯rim. Because the vapor and riming rates are dependent on the ice particle mass, we use the mass-weighted variables in Eqs. (2) and (3). The mass-weighted mean capacitance (C¯), cross-sectional area (A¯), terminal velocity (TV¯), total Nice integrated over all cloud grid cells (N¯ice), and R¯rim and R¯vap averaged over the period from 2 to 4 h (2 to 3 h) in the M-PACE (SHEBA) simulations are shown in Fig. 10 (Fig. 11). The averages are not calculated over the final 2 h in the SHEBA simulations because clouds dissipate almost completely in the column and plate run in the final hour.
Fig. 10.
Fig. 10.

(a) Total Nice (N¯ice), (b) mass-weighted capacitance (C¯), (c) mass-weighted terminal velocity (TV¯), (d) mass-weighted cross-sectional area (A¯), (e) vapor deposition rate in clouds (R¯vap), and (f) riming rate (R¯rim) normalized by the LWC (denoted as R˜rim), in clouds averaged over the final 2 h of the M-PACE simulations. “Control,” “Sphere,” “Column,” “Plate,” and “Crystal” denote the control, sphere, column, plate, and crystal runs, respectively.

Citation: Journal of the Atmospheric Sciences 81, 1; 10.1175/JAS-D-23-0015.1

Fig. 11.
Fig. 11.

(a) Total Nice (N¯ice), (b) C¯, (c) TV¯, (d) A¯, (e) R¯vap, and (f) R˜rim of different ice habits in clouds averaged from 2 to 3 h of the SHEBA simulations. “Control,” “Sphere,” “Column,” and “Plate” denote the control, sphere, column, and plate runs, respectively.

Citation: Journal of the Atmospheric Sciences 81, 1; 10.1175/JAS-D-23-0015.1

As described by Eq. (2), R¯vap depends on N¯ice and C¯. We see that relative differences in R¯vap closely follow relative differences in C¯ in both the M-PACE and SHEBA simulations (Figs. 10 and 11) indicating that C¯ is the primary controlling factor for the vapor deposition process. Exceptions are found in the M-PACE crystal and SHEBA plate runs. We see different trends in R¯vap and C¯ in the plate run under the SHEBA conditions because there is no riming; thus, plates under the SHEBA conditions can grow to a size of 3000 μm (Fig. 7). Inefficient riming under SHEBA conditions is due to the low LWC and the fact that the mean droplet diameter is only less than 10 μm, whereas under the M-PACE conditions, it is about 30 μm (Fig. C1). In contrast, there exist no ice particles larger than 2000 μm in the M-PACE plate run because riming is the main growth mode. These ice particles become graupel (see, e.g., Fig. 6d for the number concentration of all ice types at 2 h) and fall out of the clouds. Consequently, the plate run has the largest C¯ under the SHEBA conditions. Because the TV¯ of the plate run is similar to that of the sphere run and the clouds dissipate over time (Fig. D1i in appendix D), N¯ice is smallest in the plate run. Hence, the total vapor deposition rate in cloud grids becomes smaller (for the same reasons, the crystal run has low R¯vap). In the M-PACE control and sensitivity calculations, C¯ is highest in the column run1 because of the elongated particle shape. Spheres, which have a more compact shape, have the smallest C¯, and plates have a moderate C¯. Note that in the sphere run, N¯ice is similar to that in the plate run in the M-PACE calculations even though the higher TV¯ of spheres implies that N¯ice should be smaller in the sphere run. This similarity is because there are more cloudy grids in the sphere run. Moreover, a larger LWP in the sphere run leads to greater radiative cooling and a colder cloud-top temperature (more than 0.1°C colder than in the other runs). A colder temperature and a higher number of cloudy grids cause the immersion freezing rate to become higher (Fig. D1c in appendix D), and thus, more ice crystals are generated. These factors partly offset the reduction of N¯ice caused by the higher TV¯ of spheres.

Examination of Eq. (3) shows that the relative differences in R˜rim among different ice habits are generally consistent with the relative differences in A¯ in both the M-PACE and SHEBA calculations (Figs. 10 and 11). Because a slower (faster) TV¯ of ice particles implies a larger (smaller) N¯ice, the difference in the product of these two terms is not as great as the difference in A¯ among the different ice habits. Therefore, A¯ is the key factor controlling how much liquid water is collected by ice particles in clouds.

In the control and sensitivity runs under both M-PACE and SHEBA conditions, R˜rim is smallest in the sphere run because spheres have the smallest A¯. The value of R˜rim is highest in the M-PACE column run and in the SHEBA plate run, in each case the ice habit with the highest A¯. In the SHEBA calculations, columns have a smaller A¯ than plates because efficient vapor deposition in the column run dissipates the clouds (Fig. D1i in appendix D) before ice particles can grow to larger sizes (Fig. 7). Note that A of a columnar crystal is only comparable to the maximum A of a planar crystal in the SHEBA plate run if D is on the order of 104 μm (Fig. 9j). Larger values of Erim and LWC under the M-PACE conditions allow columns to grow to sizes larger than 4000 μm, and those large particles are mostly rimed crystals or graupel with larger A because riming tends to cause ice particles to become more spherical (Figs. 8a and 9a) (ice particles of 5000 μm have the maximum riming mass rate). In fact, A¯ in the column run is only comparable to those in the control and plate runs before 1.5 h when the maximum ice particle size is between 4000 and 5000 μm (not shown, but see Fig. D1 for the time series of the riming rate and LWP). Therefore, R˜rim of the plate (column) run under the M-PACE (SHEBA) conditions is lower than that of the column (plate) run.

In our simulations, we use only three values of Γ from the literature and initial and boundary conditions based on the M-PACE and SHEBA experiments. According to our analysis, we expect that for any other values of Γ, LWP/IWP would fall between the values shown in Fig. 3. For instance, mass-weighted A should decrease if Γ is set to some a value between 1.0 and 0.27, and the mass-weighted C would also decrease. As a result, LWP (IWP) would increase (decrease). The same reasoning applies if Γ is set to a value between 1.0 and 2.0. The peak of the ice particle distribution occurs at a smaller size. Hence, these results present a general picture of the impacts of ice habit (hexagonal shape model) on low-level stratiform mixed-phase clouds in the Arctic.

c. Shape variation due to riming

In the M-PACE control run, the number concentration of particles larger than about 2000 μm is significantly less than the observed mean number concentration (Fig. 7). We know that a rimed snow crystal is assumed to be converted either abruptly or smoothly to other types such as a graupel particle, or to remain a snow crystal, and this conversion affects the number concentration of these large particles. Although the model median Nice200 in the control run agrees well with the observed value, the underestimation of small amounts of these large particles can have a significant impact on the cloud liquid and ice contents. We performed an extra M-PACE simulation to explore the sensitivity of large ice particles and cloud properties to the conversion of snow crystals to graupel by restricting the conversion of collided frozen water mass to rimed mass. In this simulation, the added rimed mass is converted to crystal mass whenever riming occurs (crystal run in Table 2). Moreover, we assume that the aspect ratio of the ice crystals remains the same after they collide with supercooled droplets. LWP/IWP, Nliq/Nice, and the ice particle distribution in this extra simulation are shown in Figs. 3 and 7 along with the control and sensitivity results.

The ice particle size distribution in the crystal run agrees better with the observed mean than with the control run mean at sizes larger than 2000 μm, with the discrepancy of less than an order of magnitude (Fig. 7). Hence, it is possible that the absence of large particles may be partly due to the assumed variation in the aspect ratio when ice particles are rimed with droplets. In AMPS, the ice particle shape only becomes more ellipsoidal and the aspect ratio is assumed to approach 0.8, according to the power-law function for added riming mass (Hashino and Tripoli 2011a), but the change in the aspect ratio and shape of ice particles may be more complicated such that it cannot be fully represented by a power law. Indeed, field observations have shown that riming tends to occur at the edges of ice crystals (Zikmunda and Vali 1972). Furthermore, Magono and Aburakawa (1969) have found experimentally that rimed droplets smaller than 30 μm can start a new crystalline axis and form polycrystals, which have lower terminal velocity than graupel of the same size, when the temperature is below −15°C (in the upper portion of the observed M-PACE clouds, the temperature was below −15°C).

Owing to the inhibition of the conversion of pristine crystals to graupel, ice crystals tend to grow to a larger size in the crystal run than they do in the control run. Hence, the cross-sectional area becomes larger (Fig. 10d). Similar to what is observed in the column run, the larger collisional area triggers the rapid removal of supercooled droplets by the riming process and causes the LWP of the crystal run to be lower than the observed value (Figs. 3a and D1d). This result implies that shape variation due to riming can have an impact on the LWP and LWC that is as considerable as the impacts due to the use of different IGR values. For a better model representation of mixed-phase clouds, the need for a precise reconstruction of shape variation due to riming should not be neglected.

This result also implies that the actual ice particle shape may resemble columnar polycrystals instead of hexagonal dendritic crystals because the former have a lower cross-sectional area and riming efficiency than dendrites. Hence, the cloud is not consumed by the riming process as quickly in the crystal run and control run, in which most of the ice particles rapidly become graupel near the cloud top (Fig. 5). In fact, CPI images obtained during the M-PACE campaign show that most of the ice crystals may be side planes (Magono and Lee 1966) and sea gulls (Kikuchi et al. 2013), both of which have an elongated shape with two to four branches (they might also be dendrites with broken branches), and only a minority are dendrites (see appendix A for selected images). In AMPS, polycrystals including side planes form only when the temperature is below −20°C. The observed habits of side planes and sea gulls with a more complex shape than hexagonal ice crystals are not predicted in AMPS under M-PACE conditions when the temperature is above −20°C. Moreover, visual inspection of the images shows that graupel are hardly present, although rimed crystals are indeed common. The lack of aggregates in the control run agrees with observations based on our visual inspection of the CPI images.

As we saw earlier (Fig. 8), the mD curve in the control run is steeper than the observed mD power-law relationship of densely rimed dendrites. Even by artificially reducing the riming efficiency by two-thirds and completely switching off the riming process, the model still cannot reproduce both the observed size distribution of particles larger than 2000 μm and LWP. These results further strengthen our conclusion that a simple hexagonal ice model may not be able to reproduce the ice particle size distribution and LWP/IWP under heavy riming conditions such as those observed during the M-PACE experiment (or the error may be due to the dynamical part of the model not being realistic).

Although we do not know how accurately the actual mixing process is represented in the model and the accuracy of the riming efficiency coefficient is unclear, our simulation results show the importance of correct ice habit representation over the entire ice spectrum, from small pristine crystals to large graupel, for the accurate prediction of the evolution of mixed-phase clouds by models.

d. Projected area

McFarquhar et al. (2007) measured the area ratio AR, which is defined as Ap/Ac, where Ac is the circumscribing area of each ice particle detected by the 2D-C probe deployed on board the research aircraft during the M-PACE experiment. Because AMPS predicts the evolution of the ice geometry, here, we calculate AR values based on our simulation results and compare with the observed values. Because an ice particle generally falls with a random orientation, its AR varies as it falls through the clouds (McFarquhar et al. 1999). We do not know how turbulence or wind may affect the preferred ice particle orientation. Therefore, we adopt the mean AR of ice particles viewed from the side (a-axis direction) and top (c-axis direction) for comparisons with the measurement data. The observed AR should fall within a range between the simulated side-view and top-view AR if the real ice particle shape is accurately represented by the model. The side-view AR of pristine crystals and rimed crystals in the simulations is approximated by the area of a rectangle, whose length and width are equal to the semimajor and semiminor axis lengths, respectively, over the circumscribing area. To calculate the AR of graupel, Eq. (15) from Hashino and Tripoli (2011a) is used, with α being replaced by AR and αlmt = 0.8 in the equation (this equation is also used for calculating the porosity for terminal velocity in AMPS). Figure 12 compares the observed AR values with model-calculated mean AR values, as well as the side-view and top-view AR values, in relation to D. The observed AR is more or less constant at about 0.4, irrespective of the particle diameter. Interestingly, the mean control run and plate run values do not reproduce the observed AR value of 0.4, even though they reproduce the observed LWP/IWP, Nice200, and particle size distribution reasonably well. The mean AR of the column run, which is nearly constant, is closest to the observed value, even though there is a large difference between the side-view and top-view AR values. Dendrites (i.e., control), plates, and spheres with a diameter of 200–300 μm have mean AR values of 0.3, 0.5, and 0.7, respectively, and they sharply increase toward values of 0.7, 0.6, and 0.9, respectively, with increasing D because the rimed mass fraction increases with D and the ice particles become more spherical by riming. This inconsistent increasing trend of AR compared with that of the observed AR possibly may suggest that either the riming rate is overestimated or that the parameterization of the variation in shape due to riming is incorrect in the control and plate runs. The mean AR of the crystal run is the smallest because the ice particles are pristine crystals. It also decreases with ice particle size because riming is assumed not to change the aspect ratio in the crystal run.

Fig. 12.
Fig. 12.

Ratio of the projected area to the circumscribing area, AR, in relation to the maximum particle dimension in clouds averaged over the final 2 h of the M-PACE simulations. Dashed curves are measured from the side view (c-axis direction), Dotted curves are measured from the top view (a-axis direction) in the simulations, and colored curves are the mean of the side-view and top-view AR values. The black curve shows the observed mean based on the data of McFarquhar et al. (2007).

Citation: Journal of the Atmospheric Sciences 81, 1; 10.1175/JAS-D-23-0015.1

It is surprising that the observed AR value is approximately constant regardless of ice particle size, even though riming was observed during the M-PACE campaign. However, in the simulations, riming simply causes ar and AR to increase sharply with size. Real ice particles may rotate and tumble as they fall, whereas in the simulations AR calculated only from the side and top views. A quantitative comparison of AR values between the simulation results and observations may not be appropriate. Nevertheless, the sharp increase in simulated AR does not change whether our calculations are based on the side or top view. Therefore, this comparison result further suggests that a more sophisticated ice particle model for rimed particles or a more complex model for the growth of dendritic arms is needed to capture the complicated geometry of real ice particles.

5. Conclusions

To investigate the performance of the inherent growth ratio (IGR) and riming parameterizations, and the role of ice particle shape (plates, columns, or spheres) in Arctic mixed-phase clouds, the SCALE-AMPS large-eddy simulation model is developed. AMPS is a bin microphysics scheme that can predict the evolution of geometrical properties and the degree of riming and aggregation of ice particles. Particle shapes are predicted both by the IGR of spheroids, which determines the vapor deposition growth rate along the a and c axes, and by the fraction of rimed mass. We simulate two typical examples of mixed-phase clouds, one under M-PACE conditions, where heavy riming occurred, and another under SHEBA conditions, where riming was negligible.

In the control runs, we use the temperature-dependent IGR values reported in the literature. We adopt a particular value for Fdust, which is a tuning parameter for the ice-nucleating particle number concentration, such that the predicted Nice200 agree with observations. We find a good agreement is found for both LWP and IWP. In contrast, we find that LWP and IWP vary by a factor of more than 4 and 10, respectively, in both the M-PACE and SHEBA simulations, in response to the typical ice habits of spheres, plates, and columns, which are formed in the simulations by assuming different IGR values. These differences result both from the vapor deposition and riming processes. Capacitance and terminal fall velocity play an important role in the vapor deposition of ice particles, whereas cross-sectional area is a key parameter for the riming rate. The lowest LWP and highest IWP are obtained when columnar particles dominate because of their low terminal fall velocities and large capacitance and collisional area. The highest LWP and lowest IWP are obtained when spherical particles dominate because of their low vapor deposition and riming rates. Furthermore, although this study does not discuss the stability of mixed-phase clouds, the SHEBA column and plate runs show that the clouds dissipate within 4 h of the calculation due to enhanced precipitation (Fig. D1). These results clearly demonstrate the importance of ice particle shape in simulations of Arctic mixed-phase clouds.

Although Nice200 varies by a factor of only about 3 among the control and sensitivity simulations, maximum median IWP varies by a factor of 40 within these runs. The large IWP differences reflect differences in ice particle size distributions. In the M-PACE simulations, the peak of the ice particle size distribution appears around 200, 800, and between 2000 and 3000 μm in the sphere, plate, and column runs, respectively. The differences in these size distributions are resulted from the vapor deposition and riming processes described above. The results presented here indicate that even when the simulated Nice200 agrees with observations, IWC can be different if an inappropriate ice habit is assumed in simulations.

When ice particle size distributions of plate runs are compared, a quick falloff is found around 2000 μm under M-PACE conditions, whereas plates grow to 3000–4000 μm under SHEBA conditions. The difference is caused by the riming process, which is far more frequent in the M-PACE clouds which form over the open ocean and TV of rimed particles is generally higher. We also find that the maximum ice particle size is related to the maximum vertical wind speed. Because TV is a function of the ice habit, which changes by two orders of magnitude from spheres to columns in the M-PACE and SHEBA simulations, the simulated ice particle size distribution is closely connected to the ice habit and vertical wind speed. These results indicate that accurate calculations of ice habit and both the riming process (microphysical processes) and vertical wind speed (dynamical processes) are necessary for good predictions of mixed-phase clouds.

Our simulations show that the simulated mD relationship when riming is active may not follow a power law, because riming tends to make the ice particle shape more spherical. When riming is negligible, the simulated mD relationship follows a power law even if the aspect ratio changes by an order of magnitude, although this may not be the case in other cloud systems, particularly those containing multiple temperature-growth regimes, and more tests will be required to confirm the applicability of the power-law mD relationship in the absence of riming. Nevertheless, these results show that the mD relationship is dynamically controlled by microphysical processes and riming is key to changes in this relationship.

Finally, although the control run under the M-PACE conditions reproduced the observed LWP, IWP, Nice200, and Nliq, ice particles larger than 2000 μm are underestimated and the increasing trend of the area ratio (AR) does not agree with observations. The ice particle size distributions obtained from sensitivity tests in which the riming efficiency is reduced are also not consistent with observations. When the added rimed mass is forced to increase the crystal mass, the ice particle size distribution is well reproduced, but not the observed LWP and IWP. If we assume that the dynamics of the simulated clouds properly reflects the dynamics of true clouds, then a simple hexagonal shape model may not adequately represent real ice particles in the temperature range encountered during the M-PACE campaign. More complex polycrystals, including side planes and sea gulls, are not simulated in AMPS because the cloud-top temperature is >−20°C. It is also possible that the main culprit is the riming efficiency lookup table or the assumption that the aspect ratio changes according to a power law. These results demonstrate the importance of correct representation of ice particles in models and the need for physical experiments to develop more accurate parameterizations of IGR and rimed particles.

This study considers only immersion freezing as the primary nucleation mode active in the cloud. The M-PACE case is likely affected by secondary ice processes (Korolev and Leisner 2020), which is not considered here and further research on their role in mixed-phase clouds is warranted.

1

Because only the results of the control and sensitivity runs with different IGR values are considered in this section, the column run has the highest C¯ and A¯. The results of the crystal run are discussed later in section 4c.

2

Our comparisons of the spreads between the simulations and observations are physically meaningful because the measurement data were obtained during the spiral flight at about the same longitude and latitude.

Acknowledgments.

This study was performed as part of the Ministry of Education, Culture, Sports, Science, and Technology (MEXT) of Japan for the Arctic Challenge for Sustainability II (ArCS II, JPMXD1420318865) project and was supported by a Grant-in-Aid for Scientific Research on Innovative Areas 6102 (KAKENHI Grant JP19H05699) and KAKENHI Grant JP22H01294 from the Japan Society for the Promotion Science. This research was also supported by the Environment Research and Technology Development Fund (JPMEERF20202003 and JPMEERF20232001) of the Environmental Restoration and Conservation Agency of Japan.

Data availability statement.

Please contact the authors for the original data presented in this paper. The model, setup files, analysis codes, and processed data are available for download at https://doi.org/10.5281/zenodo.8359899. All the M-PACE data, including the raw CPI image data, can be downloaded from the Atmospheric Radiation Measurement (ARM) website at https://adc.arm.gov/discovery/#/results/iopShortName::nsa2004arcticcld. The authors thank Dr. Fridlind for her data on observed ice particle size distributions during the SHEBA campaign. The authors also sincerely thank three anonymous reviewers for their constructive comments that helped improve the quality of this paper.

APPENDIX A

CPI Images Obtained during the M-PACE Campaign

Selected representative CPI images (Verlinde et al. 2007) are shown in Fig. A1. Visual qualitative inspection of the CPI images indicates that most of the ice crystals are columns and polycrystals including side planes and sea gulls. Some pristine or rimed dendrites can be observed as well as some heavily rimed elongated particles.

Fig. A1.
Fig. A1.

Selected CPI images collected on a research flight on 10 Oct 2008 during the M-PACE campaign.

Citation: Journal of the Atmospheric Sciences 81, 1; 10.1175/JAS-D-23-0015.1

APPENDIX B

Initial Conditions for the M-PACE Simulations

Figures B1 and B2 show the initial vertical profiles of temperature, LWC, Nliq, and absolute horizontal wind velocity (U) used in the M-PACE and SHEBA simulations, respectively.

Fig. B1.
Fig. B1.

Initial profiles used in the M-PACE simulations.

Citation: Journal of the Atmospheric Sciences 81, 1; 10.1175/JAS-D-23-0015.1

Fig. B2.
Fig. B2.

Initial profiles used in the SHEBA simulations.

Citation: Journal of the Atmospheric Sciences 81, 1; 10.1175/JAS-D-23-0015.1

APPENDIX C

Liquid Particle Size Distributions

Figure C1 shows the mean liquid particle size distributions of the control, sphere, column, and plate runs after 3 h of integration in both the M-PACE and SHEBA simulations. The liquid particle sizes are larger in the M-PACE simulations because of larger moisture input from the open-sea surface. The peaks are located approximately at 34 and 7 μm in the M-PACE and SHEBA simulations, respectively.

Fig. C1.
Fig. C1.

Mean liquid particle size distributions of the control, sphere, column, and plate runs in both the M-PACE and SHEBA simulations at 3 h of the integration. Dashed lines represent SHEBA runs and solid lines represent M-PACE runs.

Citation: Journal of the Atmospheric Sciences 81, 1; 10.1175/JAS-D-23-0015.1

APPENDIX D

Time Series

Figure D1 shows time series of Rimm, Rrim, and Rvap integrated over all cloud grid cells, denoted as R¯rim,R¯vap, and R¯imm (g s−1), respectively, and of the mean LWP and IWP values. We see that clouds dissipate over time in the SHEBA column and plate runs.

Fig. D1.
Fig. D1.

Time series of R¯rim, R¯vap, R¯imm, LWP, and IWP in the (left) M-PACE and (right) SHEBA simulations. See Fig. 9 in the main text for the meaning of the colored curves.

Citation: Journal of the Atmospheric Sciences 81, 1; 10.1175/JAS-D-23-0015.1

In addition, there is a sudden increase in the riming rate over within about 15 min in the M-PACE column and crystal runs. Because, explained in section 4b(2), A¯ is a critical factor for the riming rate, it is easy to understand the sudden increase in R¯rim at about 2 h in the column run under M-PACE conditions (Fig. D1d). Because IGR is 2 in the column run, the aspect ratio and C¯ increase with time as ice crystals grow by vapor deposition. As a result, TV¯ gradually becomes slower and Nice increases as new ice crystals continue to form by freezing (Fig. D1c). Hence, R¯vap increases between the simulation times of 1 and 2 h. The mean effective diameter of the ice crystals in the column run increases from 1000 to 2800 μm between 1 and 2 h and remains approximately constant afterward (not shown). At about 2 h, the gradual increase in R¯vap is followed by a sudden increase in R¯rim, because A¯ of the ice crystals is large enough to trigger rapid riming. Similar reasoning applies to the crystal run.

APPENDIX E

Further Explanation about the Vertical Profiles of IWC and Nice200

We explain the influences of riming on the simulated IWC profiles in more detail and give possible causes of discrepancies between the simulated and observed spreads of the IWC and Nice200 in this appendix.

In all four simulations (control and three sensitivity runs), IWC increases with decreasing altitude, and the rate of increase is greater in the upper portion of the profiles. Furthermore, the rate of increase is larger (smaller) in the column (sphere) run, because the riming mass growth, which is larger than the vapor depositional mass growth in the M-PACE calculations, increases as the altitude decreases in the upper portions of the profiles. The maximum riming mass growth rate is found roughly in the middle of the cloud layer regardless of the ice habit (not shown). As described in section 4b, ice particles in the column (sphere) run have the largest (smallest) mass-weighted A, which results in the highest (lowest) collision efficiency and riming mass growth rate in the column (sphere) run. LWC and LWP are therefore smaller (larger) because of the larger (smaller) riming mass growth in the column (sphere) run. Consequently, the vertical IWC/LWC profiles and IWP/LWP are consistent with the vapor deposition and riming processes.

The spread (defined as the range between the 5th and 95th percentiles) of the simulated IWC is dependent on the ice habit; the spread is largest in the column run and smallest in the sphere run. Although the spread of the vertical LWC profile in the control run is similar to the spread of the observations, the spread of the vertical IWC profile is greater in the simulation than in the observations,2 especially in the middle of the profiles. The large IWC spread in the lower portion is caused by the nonuniformly distributed graupel, which mainly grow by riming in the cloud region. Note that the observed IWC is obtained by using a single mD relationship (McFarquhar et al. 2007). In the simulations, different types of ice particles dominate over different diameter ranges. For example, more than 50% of the ice particles larger than 600 μm in the control run are graupel, whereas the smaller ice particles are rimed or pristine ice crystals. Thus, they have different mD relationships. The use of a single mD relationship may have caused underestimation of the actual IWC spread when there are multiple types of ice particles in the clouds (Avramov and Harrington 2010). Therefore, the use of a single mD relationship is a possible reason of the overestimated IWC spread in the control run. Nevertheless, we cannot rule out the possibility of inaccurate representation of the riming process and boundary convection in the simulations.

It is also clear from Fig. 4 that ice habit may have influenced the vertical distribution of Nice200. In the column run, Nice200 is larger than the observed values throughout the clouds because of the low TV of ice particles in this size range. In the control and plate runs, model-calculated Nice200 in clouds changes little with altitude. Unlike the results in the control and plate runs, the model-calculated median Nice200 in the sphere run increases with decreasing altitude. The spread of Nice200 in our simulations is smaller than that in the observations, and it does not change substantially, irrespective of whether the ice habit is spherical or platelike. Only in the column run does Nice200 show a larger variance, possibly because the different ice types are nonuniformly distributed and some grids contain only graupel, which account for less than 10% of the total amount of ice (see Figs. 5 and 6), falling from the cloud top. The reasons for these inconsistent results are unclear. We suspect that the nucleation properties of aerosols in the actual clouds may have varied more substantially than is consistent with our simple assumption that coarse-mode aerosols all have the same chemical composition. The ice shattering problem of the probe may also be the underlying reason (Korolev and Isaac 2005). Note that only the Hallett–Mossop secondary ice production process (Hallett and Mossop 1974; Cotton et al. 1986) is installed in AMPS. The cloud temperature (Fig. 4e) is outside the temperature range of −4° and −8°C in which the Hallett–Mossop process is active. The smaller variance of simulated Nice200 may imply the existence of other modes of secondary ice production in the observed clouds (Field et al. 2017) that are not implemented in AMPS. Furthermore, the assumption of a uniform aerosol concentration everywhere in the computational domain may be another potential cause of the smaller variance in the simulations.

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