Ice Multiplication by Breakup in Ice–Ice Collisions. Part II: Numerical Simulations

Vaughan T. J. Phillips Department of Physical Geography, University of Lund, Lund, Sweden

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Jun-Ichi Yano CNRM UMR3589, Météo-France, and CNRS, Toulouse, France

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Marco Formenton Department of Physical Geography, University of Lund, Lund, Sweden

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Eyal Ilotoviz Hebrew University of Jerusalem, Givat Ram, Jerusalem, Israel

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Vijay Kanawade Department of Physical Geography, University of Lund, Lund, Sweden

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Innocent Kudzotsa Department of Physical Geography, University of Lund, Lund, Sweden

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Jiming Sun Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China

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Aaron Bansemer National Center for Atmospheric Research, Boulder, Colorado

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Andrew G. Detwiler Department of Physics, South Dakota School of Mines and Technology, Rapid City, South Dakota

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Alexander Khain Hebrew University of Jerusalem, Givat Ram, Jerusalem, Israel

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Sarah A. Tessendorf National Center for Atmospheric Research, Boulder, Colorado

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Abstract

In Part I of this two-part paper, a formulation was developed to treat fragmentation in ice–ice collisions. In the present Part II, the formulation is implemented in two microphysically advanced cloud models simulating a convective line observed over the U.S. high plains. One model is 2D with a spectral bin microphysics scheme. The other has a hybrid bin–two-moment bulk microphysics scheme in 3D. The case consists of cumulonimbus cells with cold cloud bases (near 0°C) in a dry troposphere.

Only with breakup included in the simulation are aircraft observations of particles with maximum dimensions >0.2 mm in the storm adequately predicted by both models. In fact, breakup in ice–ice collisions is by far the most prolific process of ice initiation in the simulated clouds (95%–98% of all nonhomogeneous ice), apart from homogeneous freezing of droplets. Inclusion of breakup in the cloud-resolving model (CRM) simulations increased, by between about one and two orders of magnitude, the average concentration of ice between about 0° and −30°C. Most of the breakup is due to collisions of snow with graupel/hail. It is broadly consistent with the theoretical result in Part I about an explosive tendency for ice multiplication.

Breakup in collisions of snow (crystals >~1 mm and aggregates) with denser graupel/hail was the main pathway for collisional breakup and initiated about 60%–90% of all ice particles not from homogeneous freezing, in the simulations by both models. Breakup is predicted to reduce accumulated surface precipitation in the simulated storm by about 20%–40%.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

g Current affiliation: Atmospheric Modelling Group, Atmospheric Research Centre of Eastern Finland, Finnish Meteorological Institute, Kuopio, Finland.

h The National Center for Atmospheric Research is sponsored by the National Science Foundation.

Corresponding author: Vaughan T. J. Phillips, vaughan.phillips@nateko.lu.se

Abstract

In Part I of this two-part paper, a formulation was developed to treat fragmentation in ice–ice collisions. In the present Part II, the formulation is implemented in two microphysically advanced cloud models simulating a convective line observed over the U.S. high plains. One model is 2D with a spectral bin microphysics scheme. The other has a hybrid bin–two-moment bulk microphysics scheme in 3D. The case consists of cumulonimbus cells with cold cloud bases (near 0°C) in a dry troposphere.

Only with breakup included in the simulation are aircraft observations of particles with maximum dimensions >0.2 mm in the storm adequately predicted by both models. In fact, breakup in ice–ice collisions is by far the most prolific process of ice initiation in the simulated clouds (95%–98% of all nonhomogeneous ice), apart from homogeneous freezing of droplets. Inclusion of breakup in the cloud-resolving model (CRM) simulations increased, by between about one and two orders of magnitude, the average concentration of ice between about 0° and −30°C. Most of the breakup is due to collisions of snow with graupel/hail. It is broadly consistent with the theoretical result in Part I about an explosive tendency for ice multiplication.

Breakup in collisions of snow (crystals >~1 mm and aggregates) with denser graupel/hail was the main pathway for collisional breakup and initiated about 60%–90% of all ice particles not from homogeneous freezing, in the simulations by both models. Breakup is predicted to reduce accumulated surface precipitation in the simulated storm by about 20%–40%.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

g Current affiliation: Atmospheric Modelling Group, Atmospheric Research Centre of Eastern Finland, Finnish Meteorological Institute, Kuopio, Finland.

h The National Center for Atmospheric Research is sponsored by the National Science Foundation.

Corresponding author: Vaughan T. J. Phillips, vaughan.phillips@nateko.lu.se

1. Introduction

Numerical modeling is a tool for elucidating causation in nature and has revealed insights in meteorology for almost as long as computers have existed. A trend has been to include ever more detail in simulations performed at increasingly fine resolution as computers have inexorably progressed. Yet now limitations of empirical knowledge about cloud physics are hindering advances in the scope and accuracy of atmospheric models, such as the cloud models (e.g., Khain et al. 2015) now used for operational weather forecasting. One example of a cloud model used in forecasting is the Weather Research and Forecasting (WRF) Model (Skamarock et al. 2005) with nested domains of various resolutions and clouds resolved in the finest domains.

One such limitation in empirical knowledge has been uncertainty about the origin of ice seen in clouds. As noted by Phillips et al. (2017, hereafter Part I), most of the ice observed in deep clouds with tops at warm subzero temperatures (>−36°C) cannot be explained only by ice-nucleating solid aerosols [“ice nuclei” (IN)] seen in coincident measurements of the environment. Fragmentation of preexisting ice (“ice multiplication”) appears to be implicated (Pruppacher and Klett 1997, hereafter PK97, 355–360).

Cold-based (near 0°C) clouds generally tend to produce precipitation by the “ice crystal process” (Houghton 1950; Rogers and Yau 1989). Crystals grow by vapor diffusion to become snow, which may aggregate with other crystals or rime (supercooled drops freezing on impact) to become graupel (dense ice precipitation) and then melt to rain. Coldness of cloud base and abundance of aerosols make droplets too small for coalescence (<20–30-μm mean diameter). For typical continental aerosol conditions, coalescence is absent for cloud bases at about 0°C or colder, allowing the ice crystal process to prevail. In maritime aerosol conditions, the cloud base must be even colder than this to preclude coalescence (e.g., Rosenfeld et al. 2008).

Cold-based clouds provide apt natural laboratories for study of ice multiplication, because the usual mechanism that is well understood, namely the Hallett–Mossop (H–M; Hallett and Mossop 1974) process, is absent. H–M multiplication requires droplets larger than about 24 μm in diameter riming onto ice precipitation at −3° to −8°C. A cold cloud base makes the droplets too small for the H–M process. Generally if active, the H–M process can be much more prolific than other processes of multiplication because it starts sooner (Yano and Phillips 2011), obscuring them.

Recently, interest in microphysics of cold-based clouds has surged with a focus on Arctic clouds and climate (e.g., Fridlind et al. 2007; Shupe et al. 2008; Fan et al. 2011). Such studies have highlighted how morphology of ice controls cloud properties. Fridlind et al. (2007) tried to close the gap between observed and predicted concentrations of ice by including new processes of ice initiation, such as ice multiplication. One of these processes, natural fragmentation in ice–ice collisions, was observed in Arctic clouds with the cloud particle imager (CPI) probe and accounted for more than 20% of all ice particles seen (Schwarzenboeck et al. 2009). This, together with early observations that 50% of stellar or dendritic crystals collected in U.S. field studies were fragmented (Hobbs and Farber 1972; Hobbs 1969; Jiusto and Weickmann 1973; Vardiman and Grant 1972a,b; Grant 1968), suggests breakup in collisions should be revisited.

A few decades ago, Vardiman (1978) first quantified this breakup mechanism with a chamber on a mountainside during snowfall. Fragment numbers were measured by Takahashi et al. (1995), too, by colliding together a rimed–unrimed pair of ice spheres in laboratory experiments. These observations of breakup were the basis of a theory by Yano and Phillips (2011) and a numerical scheme and theoretical formulation in Part I. Yano and Phillips (2011) showed that when the H–M process is absent, a positive feedback between ice fragmentation and production of ice precipitation emerges to control storm glaciation. Lawson et al. (2015) showed another positive feedback involves shattering of freezing raindrops and freezing of supercooled drops colliding with fragments. Pathways of ice multiplication are discussed in Part I.

In tackling such questions about the role of ice initiation for the microphysical properties of clouds, numerical cloud models have been applied. Cloud models have progressed in the accuracy of representing microphysics over the last few decades. Two broad methods occurred in parallel. First, in the 1960s bulk microphysics schemes were started by Kessler (1969) with a general representation of the properties of all hydrometeors in each microphysical species. Most bulk schemes solve prognostic equations for one (Orville and Kopp 1977; Lin et al. 1983) or two (Ferrier 1994) moments of the particle size distribution (PSD), and some can treat ice morphology (Morrison and Grabowski 2010). Second, bin microphysics schemes explicitly predicting concentrations near each particle size were pioneered by Takahashi (1973, 1976) and Berry and Reinhardt (1974a,b,c) and developed by Hall (1980), Kogan (1991), Khairoutdinov and Kogan (2000), and Ovtchinnikov and Kogan (2000). Khain et al. (2004) represented hail and crystal habits. Khain et al. (2015) compared qualitatively bulk and bin schemes.

Cloud models with bin microphysics have revealed the role of the H–M process in glaciation of warm-based convection. Blyth and Latham (1997) showed there are optimum updraft speeds for H–M multiplication in such clouds, with multiple thermals rich in supercooled liquid promoting it. Ovtchinnikov et al. (2000) simulated a warm-based convective cloud and the H–M process produced high concentrations of ice of 50 L−1 after about 10 min, as observed, much higher than the active IN concentration. Phillips et al. (2001, 2002) found a positive feedback between graupel production by collisional raindrop freezing and the H–M process controlling the cloud glaciation. None of these earlier studies considered multiplication in ice–ice collisions, however.

The present article quantifies the role of fragmentation in ice–ice collisions for clouds with cold bases (e.g., near 0°C) by applying the formulation of breakup from Part I. A description was provided in Part I that is universally applicable to all types of collisions of ice precipitation and to atmospheric conditions beyond those observed. In this Part II, the formulation is applied in two cloud models with explicit treatment of ice- and liquid-phase microphysics, to simulate a cold-based convective storm. Both models are independent, with fully coupled microphysics, radiation, and dynamics components. Hebrew University Cloud Model (HUCM) (2D) has a spectral bin microphysics scheme, while our aerosol–cloud model (AC) (3D) has a hybrid bin–bulk microphysics scheme.

The rationale of such a dual-pronged approach with two models is that the robustness of predictions across contrasting model architectures can be ascertained. Responses common to both models are identified when breakup is included. The aim is not to compare the behavior of contrasting models (e.g., bin vs bulk), though some differences inevitably become apparent. The primary goal of the present study is to quantify the role of this hitherto overlooked mechanism of ice initiation for the precipitation and other microphysical properties of a cold-based convective storm and to assess whether it can explain the observed concentration of ice particles.

The present paper is structured as follows. The next section provides a description of both models. In section 3 the case of a storm from the U.S. high plains in summertime is described, along with the setup of numerical simulations. Simulations of the case are compared with observations in section 4. In section 5 some sensitivity tests are done to elucidate the role of breakup in the storm. Finally, the concluding section summarizes and discusses the results.

2. Description of numerical cloud models

Two independent cloud models are applied in the present study, namely HUCM and an AC. Both models have different fortes:

  • HUCM is 2D with bin microphysics and resolves more species (e.g., hail, graupel, three crystal habits), so microphysical processes of growth are represented in more detail.

  • AC is 3D and represents the coupling of aerosol chemistry to the cloud microphysics for initiation of cloud particles, while preferential evaporation of smaller cloud droplets during homogeneous freezing is also treated.

Areas of commonality among their predictions can elucidate the role of breakup in clouds. The same scheme to treat breakup in ice–ice collisions, described in Part I, was implemented in both models for all broad types of collision, types I–III, involving crystals, snow, graupel, and hail. Type I involves collisions between only graupel and/or hail, type II involves crystals or snow colliding with graupel/hail, and type III involves collisions only among crystals or snow. This scheme involves dependencies on predicted rimed fractions of cloud ice and snow. Fragments are initiated either as cloud ice (crystals) or snow depending on size. Both models predict droplet initiation from aerosol conditions by 1) in-cloud droplet activation and 2) cloud-base droplet activation by diagnosing the unresolved peak in supersaturation.

Both models treat the H–M process (Hallett and Mossop 1974), with dependencies on droplet size such that it is inactive in the cold-based clouds simulated here. Both represent coagulation with bin microphysics. AC predicts heterogeneous ice nucleation from aerosol conditions of chemistry, size, and loading with the “empirical parameterization” (EP) (Phillips et al. 2008, 2013), while HUCM applies an empirical formula that is without aerosol dependencies (Meyers et al. 1992) and reduced by 90% to match with the AC. The EP predicts less primary ice for this case than the Meyers formula, as the EP predicts this from solid aerosol loadings, while the Meyers formula only prescribes IN. More details of the models are in the appendix.

3. Experimental setup for simulations of convective storm

a. Description of case

The case is a line (at least 50 km) of convective clouds (Tessendorf et al. 2007, Fig. 11 therein), observed near the Kansas–Colorado border during the Severe Thunderstorm Electrification and Precipitation Study (STEPS) on the evening of 19 June 2000 (Lang et al. 2004). This multicellular convective storm is on the eastern edge of a much broader mesoscale convective system (MCS) (or convective cluster) in northeastern Colorado at least about 300 km wide, as seen in infrared satellite imagery. The clouds had high cold bases near 0°C at about 4.5-km altitude above mean sea level (MSL), over 3 km above the ground. The ground was elevated at an altitude of about 1.3 km MSL. As with any multicellular storm, the line consists of many cloud types, including deep convective (e.g., cumulonimbus) cells and cirriform and stratiform clouds. The lower troposphere was very dry. STEPS included observations of cloud microphysics by the armored T-28 aircraft of South Dakota School of Mines and Technology. Reflectivity was measured by the Colorado State University–University of Chicago–Illinois State Water Survey (CSU–CHILL) S-band (10 cm) dual-polarization Doppler radar, the Weather Surveillance Radar-1988 Doppler (WSR-88D) at Goodland, Kansas, and the NCAR S-band dual-polarization Doppler radar (S-Pol) (Tessendorf et al. 2007). The CSU–CHILL radar and the NCAR S-Pol were located about 40 km to the west and northwest of Goodland, respectively.

On 19 June 2000 there was a dryline along the Kansas–Colorado border with moister air (surface dewpoints of 10°–15°C) to the east and drier air (7°C dewpoint) to the west. There was (west) southwesterly mean flow from a trough over Utah. Surface temperatures were near 30°C. By 2200 UTC the multicellular convective line developed in Colorado and propagated east-northeastward over the radars at around midnight UTC (Fig. 1). The line was temporarily weakened at 0050 UTC by an outflow boundary of a cold pool from the west (Goehring 2005). The line consisted of two clusters of cells before (“A”) and after (“B”) that time.

Fig. 1.
Fig. 1.

Radar reflectivity (dBZ) observed by radar at Goodland, Kansas (red flag symbol), at (a) 0053 UTC 20 Jun 2000 on the conical surface at a 19.5° elevation angle as plan position indicator (PPI) for the region outlined (blue rectangle) and (b) 0058 UTC 20 Jun 2000 UTC visualized in 3D and viewed from the south. Both (a) and (b) follow the same color key for shading. Domains of AC (“AC”) and HUCM are shown in (a) (black lines). In (b), the level of the box marked as “30 kft” is 10.5 km MSL altitude and its width spans about a third of the box in (a), centered on Goodland. (c) A PPI at 0058 UTC from the Goodland radar. (d) Combined swath viewed from above of maximum reflectivity (dBZ) from 2318 UTC 19 June to 0213 UTC 20 June from S-Pol, as the storm propagated eastward, plotted with axes of distance (km) relative to Goodland and a different color key (from Tessendorf et al. 2007). Lightning (cloud to ground) strike locations are superimposed (○ and ×).

Citation: Journal of the Atmospheric Sciences 74, 9; 10.1175/JAS-D-16-0223.1

The T-28 aircraft sampled the storm with several instruments (Johnson and Smith 1980). The content of liquid water was measured by the Droplet Measurement Technologies (DMT) liquid water probe (King et al. 1978; Feind et al. 2000). The aircraft measured PSDs with the Forward Scattering Spectrometer (FSSP), two-dimensional cloud (2D-C), and hail spectrometer probes. The Particle Measuring Systems (PMS) FSSP measures droplets of 1.5–67 μm in diameter. The PMS 2D-C probe measures particles from 25 μm to over 800 μm in diameter, recording their images. The hail probe (Shaw 1974; Spahn 1976) counts particles >5 mm, including snow.

Between 0045 and 0145 UTC (early evening local time), the aircraft sampled cloud properties between about −12° and −15°C. The aircraft made two passes across the earlier portion of the storm and three passes back and forth in the more vigorous later portion of the storm through convective cores. Fragments of the storm were intercepted on descent at lower altitudes. The aircraft encountered updrafts mostly from 5 to 10 m s−1, with brief peaks of 15 m s−1. The highest contents of supercooled cloud liquid exceeded 1.5 g m−3 in convective updrafts.

In the STEPS flight, copious graupel/hail (<1 cm) and snow were observed in the 2D-C imagery but no supercooled rain was detected, while cloud droplets were seen to have mean diameters <10–15 μm. Such cloud droplets are too small for significant coalescence (e.g., Rogers and Yau 1989), consistent with this lack of rain. Thus, the ice precipitation must have grown by the ice crystal process (section 1). This is consistent with imagery from a 2D-C optical probe of apparently heavily rimed particles (e.g., graupel or hail) at the edges of convective updrafts at the interface between high concentrations of cloud water and snow/aggregates.

The radar reflectivity observed is shown in Figs. 1a–c at 0053–0058 UTC. The multicellular convective line has radar-echo tops near 11 km MSL altitude. The 3D visualization of the radar data (Fig. 1b) shows how convective cells are tilted in the downshear direction, with anvil outflows aloft on the leading edge that are almost merged. Figure 1d shows both clusters, A and B. The convective storm lasts about 3 h. In most of the troposphere, there was a strong vertical shear of the mean flow toward the east-northeast direction, of about 3 m s−1 km−1 (Fig. 2). The shear organized the convection in a line by creating a storm-relative flow. Typically in convective lines, new cells can be triggered by flow over cold pools of older cells.

Fig. 2.
Fig. 2.

(a) M-GLASS thermodynamic sounding taken near Stratton, Colorado, at 2318 UTC 19 Jun 2000, directly from the observations (dashed–dotted and dotted lines) and after moistening the lower troposphere to initialize both models (dashed and full lines). (b) The observed profile of mean wind from the same sounding for zonal (U) and meridional (V) components and (c) hodographs for the lower, mid-, and upper troposphere.

Citation: Journal of the Atmospheric Sciences 74, 9; 10.1175/JAS-D-16-0223.1

b. Experimental setup for numerical models

The case is simulated with both models (section 2), namely AC with emulated bin microphysics in 3D (Phillips et al. 2007a, 2008, 2009, 2013, 2014, 2015a,b; Kudzotsa et al. 2016) and HUCM with spectral bin microphysics in 2D (Khain et al. 2004; Phillips et al. 2014; Ilotoviz et al. 2016). The model domains are centered near Goodland, Kansas, (39.34°, −101.71°) coinciding with the aircraft and radar observations. The simulation lasts 2.5 h (2345–0215 UTC).

Both models were initialized with the NCAR Mobile GPS Loran Atmospheric Sounding System (M-GLASS) sounding of 2318 UTC 19 June 2000, from Stratton, Colorado, about 80 km to the west of Goodland (Fig. 2). The lower troposphere was dry with a relative humidity of about 20% at the ground there, to the west of the dryline. The sounding reveals a saturated layer between 600 and 300 hPa due to the stratiform cloud deck of the broader MCS noted above. This low-level dryness caused a minimal convective available potential energy (CAPE) unrepresentative of inflow to the convective line from the east of the dryline. Hence, the sounding was modified by adding a constant amount of 1.5 g kg−1 to the environmental vertical profile of moisture up to 5 km MSL altitude.

To simulate the convective line of STEPS, the 3D domain of AC spanned a horizontal area 80 km by 80 km wide, its center moving along a track through Goodland (Fig. 1a). The 2D domain of HUCM was fixed, centered on Goodland, and zonal. The duration of both simulations was 2345 UTC 19 June–0215 UTC 20 June 2000. Features of the setup for each model were as follows.

1) AC

The grid spacing of AC is 1 km horizontally and about 0.5 km vertically, with a time step of 10 s. Boundary conditions are open at the eastern and western sides and periodic on the northern and southern sides. The convective line was observed to propagate downshear in a direction of 71° clockwise from north. Consequently, the domain and coordinate system (x and y) of AC were rotated to make the x-axis point in this direction, with the convective line parallel to the y axis. To follow it, the model domain was moved in this x direction always at 9 m s−1. There is an almost uniform vertical grid. A sponge near the tropopause absorbs gravity waves.

Convection is initialized in the model with a line, parallel to this y axis, of eight cold dry bubbles, each of 10 km in horizontal radius and spaced 10 km apart. Each cold bubble had perturbations as large as −3 K of temperature and −2 g kg−1 of moisture. Initially, the cold bubbles are superimposed on a domainwide array of many smaller warm thermal bubbles of random horizontal radius, location, and warmth (<0.1 K). All bubbles, cold and warm, were centered at 2.5-km altitude above the ground, having a depth of 5 km, slightly deeper than the boundary layer. The bubble configuration is consistent with radar observations by Goehring (2005) and Tessendorf et al. (2007) (section 4 of the present paper) (see also Phillips et al. 2001, 2007a).

The STEPS campaign made no measurements of aerosols. However, aerosol loadings were measured by the Interagency Monitoring of Protected Visual Environments (IMPROVE) at stations nearby. Initial conditions for the seven chemical species of aerosol of AC were derived from the Goddard Chemistry Aerosol Radiation and Transport (GOCART) model (Chin et al. 2000). Profiles of mass concentration (particles <2.5 μm in diameter) were scaled at all levels to match simultaneous measurements by IMPROVE averaged from the White River (3.4 km MSL) and Great Sand Dunes (2.5 km MSL) sites in Colorado. After corrections, observed concentrations were 0.3 μg m−3 for sulfate, 0.5 μg m−3 for dust, 0.02 μg m−3 for black carbon, and 0.7 and 0.2 μg m−3 for soluble and insoluble organics, respectively, assuming a water-soluble fraction of 80% for carbonaceous aerosol. Carbonaceous measurements were corrected by assuming 20% of total organic mass was misclassified as black carbon by the IMPROVE instrument (Phillips et al. 2008). Half of the insoluble organics were assumed to be biological, yielding 0.09 μg m−3 for biological organics. Sea salt was negligible. Other parameters of the PSD (modal mean diameters, standard deviation ratios, and relative numbers in various modes) are prescribed as a function of altitude for remote continental conditions (Phillips et al. 2009).

From the initial sounding and aerosol profiles, AC predicts the in-cloud size distributions of aerosol and in-cloud supersaturation. These in turn are inputs for the microphysics scheme to predict numbers of cloud droplets and crystals nucleated. The cloud condensation nucleus (CCN) activity spectrum predicted from size distributions of soluble aerosol is compared in Fig. 3 with observations at Storm Peak Laboratory (SPL) on Mount Werner, Colorado, for a similar altitude (3–4 km MSL) and month. The prediction agrees with these observations from a decade later, showing a normalized (1% supersaturation) CCN concentration of about 1000 cm−3. The normalized CCN concentration predicted near the ground (1–2 km MSL) (Fig. 3, dotted line) is twice that predicted at observational levels (3–4 km MSL), as expected from falloff with height of aerosol loadings.

Fig. 3.
Fig. 3.

The CCN activity spectrum predicted by AC for the STEPS case (19 Jun 2000, near the Colorado–Kansas border) for the environment at about 3 km MSL altitude, corresponding to the prescribed vertical profiles of size distributions of various species of aerosol (full line). Most of the CCN activity is due to sulfate, with some also due to soluble organics. This is compared with the observed CCN activity spectrum from Storm Peak Laboratory (Mount Werner, Colorado, 3.2 km MSL altitude) over a decade later, averaged over months of June and July in both 2011 and 2012 (4 months in total; crosses with error bars). No CCN observations were made in STEPS itself. Also shown is the corresponding prediction for STEPS near the ground (about 1–2 km MSL altitude) (dotted line).

Citation: Journal of the Atmospheric Sciences 74, 9; 10.1175/JAS-D-16-0223.1

2) HUCM

A cool pool was prescribed to trigger formation of convective clouds in the HUCM simulation. The rate of cooling is −0.0084 K s−1 during 1200 s. The resolution of the model is 300 m horizontally and 100 m vertically. The 2D domain is 307 km in horizontal width and 15.2 km vertically, with open lateral boundary conditions. Minimum and maximum radii of CCN are 0.003 and 0.4 μm. The aerosol size distribution (ASD) of soluble aerosols followed the activity spectrum predicted by AC near the ground (Fig. 3): N0 = 2000 cm−3 and k = 0.5. This is justified by inflow to bases of convective clouds typically originating near the ground generally (Rogers and Yau 1989). HUCM assumes a vertically uniform profile of CCN concentration in the lower troposphere.

4. Results from control simulations of convective storm and model validation

The convective line observed in STEPS on 19 June 2000 (section 3a) has been simulated by AC and HUCM (section 2), including our scheme for breakup in ice–ice collisions (Part I) in both models (“control simulations”; Table 1). With both simulations, Fig. 4 shows the predicted snapshots of radar reflectivity, and number concentrations of snow, graupel, and cloud ice at 0055 UTC in horizontal and vertical sections. Most of the horizontal area of the storm consists of deep stratiform and cirriform cloud from the outflow of convective cells. The predicted reflectivity (Figs. 4a,b,q) resembles the radar observations (Fig. 1c), although the widespread stratiform deck of the broader MCS noted above (e.g., Tessendorf et al. 2007, their Figs. 11b,c) is missing in both simulations (HUCM and AC) of the convective line. AC predicts radar reflectivity maxima (>35 dBZ) from large rimed snow and graupel/hail above the freezing level and from rain below it, near convective cores. Maxima of reflectivity of up to 40 dBZ are predicted in vertical streaks near the ground (x = 40–50 km for AC), with 30-dBZ echo tops reaching cloud-top level (near 12 km MSL altitude) near convective cores as seen in observations (Fig. 1).

Table 1.

List of simulations performed with HUCM and AC.

Table 1.
Fig. 4.
Fig. 4.

Snapshots for 0055 UTC from the control simulation by AC of the STEPS case showing (a),(b) radar reflectivity Z (dBZ) and number concentrations (m−3) of (c),(d) graupel/hail Ng, (e),(f) snow Ns, and (g),(h) cloud-ice Ni particles and (i),(j) liquid water content (LWC; g m−3). Horizontal sections (left) at about −17°C (7.2 km MSL altitude) across the entire domain are shown, as well as vertical slices (center) at y = 56 km oriented almost zonally. (k),(l) Cloud-ice concentration, (m),(n) LWC, and (o),(p) snow concentration are shown in the no-breakup case on the same sections. Comparison of (g) and (k) reveals the role of breakup. Almost all (>95%) of the ice particles marked in colors from medium blue to dark orange (>1 L−1) in (g) were from mechanical fragmentation. Note that the color scale differs between (g),(h), and (t) and between (k), (l), and (v). Also shown are the corresponding vertical sections from (right) HUCM for (q)–(u) the control run and (v)–(x) the no-breakup case. Comparison of (s) and (x) reveals breakup in HUCM. The simultaneous observations from the Goodland radar corresponding to (a),(b), and (q) are shown in Fig. 1.

Citation: Journal of the Atmospheric Sciences 74, 9; 10.1175/JAS-D-16-0223.1

Graupel is predicted to be widespread throughout the layer cloud (x = 50–70 km for AC) of the convective line, albeit with lower concentrations (about 0.1–1 L−1) than in the convective cores (x = 40–50 km for AC), being most prolific near edges of convective updrafts (Figs. 4c,d,r), as in the aircraft observations (section 3a). Concentrations of snow are similarly distributed (Figs. 4e,f,s), arising from growth of fragments, especially in convective updrafts, with riming of snow as the only source of graupel. Fragments of ice are generated in or near the cores (Figs. 4g,h,s) and advected downshear. Supercooled liquid (Figs. 4i,j,u) coincides with convective ascent.

To identify convective updrafts in aircraft data, vertical velocities > 5 m s−1 were selected, owing to errors of up to 3 m s−1 from flight maneuvers. Observations of cloud droplet concentrations (FSSP) were filtered to include only times when ice was minimal (<0.5 L−1), in view of biases from ice shattering on the probe. Errors in aircraft observations of vertical velocity are about 30%. Radar observations were computed on a domain moving with the convection. Errors in conditionally averaged (where >−20 dBZ) radar reflectivity arise because most convective cores of high reflectivity (>40 dBZ) are missed if too near the radars, which would then oversample the stratiform cloud (~20 dBZ), implying a sampling error of about 5–10 dBZ aloft. “Clutter” increases this error below cloud. “Cloud fraction” is the fraction by horizontal area in (i) the simulation with cloud condensate paths >0.01 g m−2 and (ii) the observations (fixed domain, 80 km × 80 km) with “raw satellite counts” (GOES-8, NOAA) in the visible channel exceeding a threshold (3000 until 45 min before sunset, then decreasing linearly to 2000 at sunset). Errors in observed cloud fraction arise partly from a 30% error in this threshold. To minimize effects from shattering of ice on the aircraft optical (2D-C) probe, only particles >0.2 mm in maximum dimension were included in the plotted concentrations, both in simulations and observations, in any comparison with the 2D-C data (see Part I). Raw data from these probes were corrected further (Field et al. 2006). Errors in filtered ice concentration data are from measurements of shattering bias for the 2D-C probe (Korolev et al. 2011, their Fig. 8) and from sampling uncertainty of the aircraft guided by reflectivity (bias of about 10 dBZ) for the hail probe. The initial hour was omitted from the averaging of predicted profiles because of the times of aircraft traverses.

Figure 5 shows a comparison of both control simulations (AC, HUCM) of the storm against aircraft, ground-based, and satellite observations of the case. The models agree with the observations, insofar as differences between each model and the observations are generally less than or comparable to the errors in the observations and/or differences among observations. The predicted average of the concentration of ice particles with maximum dimensions >0.2 mm in cloudy convective updrafts (>5 m s−1) is on the order of 10 L−1 at observational levels, the same order of magnitude as in the aircraft data (Fig. 5d). It varies by at least three orders of magnitude over the depth of the cloud. The filtered ice concentration in Fig. 5d is predicted to have contributions from large crystals (e.g., 50% for AC), snow (25%), and graupel (25%), but with very little supercooled rain (<0.02%). No supercooled rain was observed in the flight (2D-C).

Fig. 5.
Fig. 5.

Comparison of the control simulations by AC (full line; “A–C”) and HUCM (full lines with filled squares) of the STEPS case with aircraft, radar, and satellite observations (filled circles), 2345 UTC 19 Jun–0215 UTC 20 Jun 2000 (except without the first hour in simulated vertical profiles), for (a) number concentration and (b) average size of cloud droplets (<20 μm), conditionally averaged over convective cloudy updrafts (>5 m s−1) with little ice (<500 m−3), with aircraft observations from the FSSP; (c) the liquid water content in such updrafts, comparing with the hot-wire probe; (d) ice number concentration for all particles > 0.2 mm in maximum dimension of all microphysical species (cloud ice, graupel/hail, snow), similarly averaged over convective updrafts (>5 m s−1), both simulated and observed by the 2D-C probe on the aircraft; (e) vertical profile of radar reflectivity [dB(Z)], conditionally averaged over all regions of significant reflectivity (>−20 dBZ) at each level, simulated and observed with the ground-based radars; (f) the simulated cloud-cover fraction, compared that from satellite (GOES-8) data in the visible channel before sunset for the simulated area when centered near Goodland (80 km by 80 km); (g) the histogram of vertical velocity in fast convective updrafts (>5 m s−1) compared with aircraft data and ground-based Doppler radar data; and (h) predicted surface accumulation (mm) of precipitation compared with observations from the Goodland radar averaged over the same area as in (f). Error bars are standard errors of observational samples for (a)–(c). Also shown in all panels are corresponding predictions from the no-breakup case by both models [thin dashed lines without (AC) and with (HUCM) × symbols].

Citation: Journal of the Atmospheric Sciences 74, 9; 10.1175/JAS-D-16-0223.1

The two models differ in predictions and details of design. Yet errors in predicted cloud cover and surface precipitation from both models (Figs. 5f,h) arise partly from the idealized nature of the experimental setup of both simulations. The lack of observations to prescribe either the large-scale advection of heat, moisture, and condensate into the model domains, their 3D initial fields, or the thermal bubbles all introduce errors into prediction of such thermodynamically constrained quantities. Inevitably the models were not initialized to represent either the dryline or the widespread stratiform cloud deck (about 20 dBZ) of the broad MCS 300 km wide (section 3b). The deck was seen in the radar observations (Tessendorf et al. 2007, their Fig. 11c). This missed deck caused a low bias of predicted cloud fractions in the first hour (Fig. 5f).

The predicted concentration and size of cloud droplets, conditionally averaged over fast convective updrafts, differ by less than about 50% and 20%, respectively, from observations (−6° to −15°C) (Figs. 5a,b). Predicted average values of liquid water content in such updrafts agree with observations (Fig. 5c). There is good agreement insofar as differences between each model and observations are less than the differences among observations at similar levels. Biases in predictions partly arise from lack of observations of ASDs aloft, while those in observations arise from instrumental and sampling biases of the aircraft.

The trend of simulated average reflectivity for radar as a function of height agrees with observations, differing from them by less than about 5 dBZ at most subzero levels observed (Fig. 5e). Such differences are comparable to errors in the observed profile from limited sampling of the storm. Equally, Fig. 5f shows both predicted cloud fractions (AC, HUCM) agree with observations during the entire simulated period in view of plotted errors, except for the first hour. During the final hour, the trend of decreasing cloud fraction seems better reproduced by HUCM than AC. The predicted distribution of updraft speeds >5 m s−1 (Fig. 5g) differs by less than about 10% from ground-based Doppler radar and aircraft observations. The models differ from observed updraft speeds by as much as both sets of observations differ from each other. Figure 5h shows domain-averaged precipitation at the ground: predictions differ from the radar-derived observations (Fulton et al. 1998) by less than about 10% and a factor of 2 for the control runs by AC and HUCM, respectively, at most times while nonzero.

For AC, extra analysis was performed with budgets of total particle numbers. About 80% of all fragments arose from collisions in convective clouds (|w| > 1 m s−1), since these have higher values of liquid water content than stratiform clouds and intensified production of graupel by the riming of snow. Most (99.7%) of all graupel particles generated in the control run are from riming of snow particles, with practically no graupel from raindrop freezing and almost no supercooled rain. Precipitation was produced by the ice crystal process (section 1) due to the cold cloud base (near 0°C) and continental aerosol conditions, without coalescence. A budget of total numbers of droplets initiated revealed that about 85% of droplets were from cloud-base activation and only 15% were from in-cloud droplet activation in this STEPS case. High updraft speeds at cloud base of up to 5 m s−1 (peak supersaturation of about 1%) and a the smallest aerosols active at supersaturations >1% (Fig. 3) in inhibited in-cloud droplet activation, which usually tends to prevail in droplet generation. Most (about 70% for AC) of all droplets eliminated were lost by evaporation, with the rest accreted by precipitation (almost 30%; e.g., riming) or lost by other types of freezing (1%; e.g., homogeneous).

Figure 6 shows the PSD for all hydrometeors, observed (0045–0145 UTC) and predicted for in-cloud conditions of temperature (−12° to −16°C) and ascent in fast convective updrafts (5–8 m s−1). Probes measured the PSD on the aircraft (FSSP, 2D-C, and the hail probe). Both models predict the correct order of magnitude of the size distribution function at almost all sizes, though they predict particle concentrations between 0.1 and 1 mm correctly for different reasons (mostly cloud–ice for AC and snow for the HUCM). At the largest sizes near 1 cm, both models predict that rimed snow dominates the PSD while large hail (fall speeds of up to 40 m s−1) is much scarcer, as expected for updrafts <8 m s−1. This prevalence of rimed snow also extends down to millimeter sizes or smaller, consistent with the qualitative interpretation of 2DC probe images.

Fig. 6.
Fig. 6.

The size distribution for all hydrometeors predicted in the control simulation of the STEPS case by (a) AC and (b) HUCM, conditionally averaged for fast convective updrafts (5–8 m s−1) between −12° and −16°C (full lines, medium width). Contributions from all microphysical species predicted are displayed (thin lines in various styles). Also shown are the T-28 aircraft observations (three short thick lines) from three probes [FSSP (full), 2D-C (dashed), hail spectrometer probe (dotted–dashed)]. Finally, the no-breakup case is also displayed (dotted lines, medium width).

Citation: Journal of the Atmospheric Sciences 74, 9; 10.1175/JAS-D-16-0223.1

A number budget of ice initiated is shown in Fig. 7 for both control simulations. Fragmentation in all ice–ice collisions generated 50 and 20 times more particles than heterogeneous ice nucleation for AC and HUCM, respectively. It corresponds to an ice enhancement (IE) ratio of about 20–50 during most of the storm. For both models, fragmentation in collisions of snow with graupel/hail is by far the most prolific of all mechanisms of ice initiation represented (60%–80% of all nonhomogeneous ice), except for homogeneous freezing of cloud droplets at −36°C. Fragmentation in all other types of ice–ice collision produces several times more ice than heterogeneous ice nucleation. Snow–snow collisions and collisions only involving graupel/hail have appreciable impacts on the budget (1%–10% of nonhomogeneous ice for each). Heterogeneous ice nucleation is 2%–5% of nonhomogeneous ice initiated. The H–M process is absent because of cold cloud bases. As deep clouds reached above the −36°C level, homogeneous freezing is the most prolific of initiation processes. Pie charts in Fig. 7 may be viewed as applying to clouds with tops warmer than −36°C.

Fig. 7.
Fig. 7.

(a) Percentage of number of ice crystals from processes of primary and secondary initiation in the control simulation of the AC. These are (left)–(right) homogeneous freezing of (i) aerosols and (ii) supercooled cloud droplets; (iii) H–M process of multiplication (“H–M”); (iv) breakup in collisions of graupel with either graupel (“G–G”) or hail (“G–H”); (v) breakup in hail–hail collisions (“H–H”); breakup in collisions with graupel/hail (“GH”) of (vi) dendritic (“dS”) and (vii) nondendritic (“nS”) snow, and of (viii) dendritic (“dC”) and (ix) nondendritic (“nC”) cloud ice crystals; breakup in (x) snow–snow (“S–S”) collisions and (xi) collisions of cloud ice with snow (“C–S”); heterogeneous ice nucleation (condensation–freezing/deposition) at (xii) warm (>−30°C) and (xiii) cold (<−30°C) temperatures; and (xiv) outside-in and (xv) inside-out contact freezing [not included in (xii) and (xiii)]. Triangles denote breakup in ice–ice collisions [“Br.”; for (iv)–(xi)]. Circles and squares denote homogeneous freezing (“homog.”) and heterogeneous (“het.”) ice nucleation, respectively. The same information is shown as pie charts for (b) AC and (c) HUCM, not including homogeneous freezing, for the most prolific of the above processes: (iv) (dark blue), (vi) (blue), (vii) (lighter blue), (viii) (cyan), (ix) (green), (x) (yellow), (xi) (orange), and (xii)–(xv) (dark red/brown).

Citation: Journal of the Atmospheric Sciences 74, 9; 10.1175/JAS-D-16-0223.1

5. Role of breakup in clouds from sensitivity tests

To evaluate the role of fragmentation in ice–ice collisions for the partial glaciation of cold-based clouds, sensitivity tests were performed by comparing each control run (AC, HUCM) of the convective line with the simulation redone by prohibiting all breakup (the “no-breakup case”). The control runs include the breakup scheme [all types (I–III) of collisions; section 2] and were validated above (section 4). For AC, a simulation was done by including only breakup in collisions between graupel/hail (type I) (“graupel-splintering case”). Simulations are listed in Table 1.

In the no-breakup case, the filtered (>0.2 mm) ice concentration in convective updrafts is predicted to be too low by one to two orders of magnitude, both compared to aircraft observations (Fig. 5d) and compared to the control run at all levels below 9 km MSL. Consequently, breakup in ice–ice collisions of paramount importance in the storm, as the observations of ice concentration can only be simulated when it is represented.

Moreover, in both models, the domainwide cloud fraction is perturbed by almost 0.1 in the final 30–60 min by inclusion of breakup (Fig. 5f). Another robust feature of both models is that eventual accumulated surface precipitation is reduced by about 20%–40% when breakup is included (Fig. 5h). Ice particles are smaller on average from more competition for vapor and liquid among the numerous ice fragments growing by diffusion of vapor (“vapor growth”) and then by riming. This intensified competition causes more subsaturation in the layer cloud and evaporation of its liquid, which must increase the extent of ice-only cloud (no supercooled liquid). Generally the low humidities of ice-only cloud inhibit any vapor growth of ice fragments.

Number concentrations of cloud ice/snow and cloud droplets are shown in Figs. 8 and 9 for all three cases, averaged in various ways. First, cloud ice/snow is conditionally averaged over fast (w > 5 m s−1) convective updrafts with warm cloud tops (>−36°C) without cloud above them at levels (<−36°C) of homogeneous freezing (“warm-topped fast convective updrafts”) (Fig. 8a). This removes the influence of homogeneous freezing. Second, cloud ice/snow is also conditionally averaged over all regions where it exists (Fig. 8b). Figure 8a corresponds to historical observations of ice multiplication in warm-topped clouds (Hobbs et al. 1980).

Fig. 8.
Fig. 8.

The number concentration of all crystals and snow particles in the convective line, from AC (full line; A–C) and HUCM (full line with squares), conditionally averaged over (a) fast convective updrafts (>5 m s−1) in the mixed-phase region without significant ice above them at levels of homogeneous freezing (average between the −36°C level and model top of ice concentration < 0.1 cm−3) and (b) all regions where there is cloud ice. In both plots, the control simulation with the mechanical breakup scheme (“CONTROL,” full lines) is shown as well as perturbation simulations without it (the no-breakup case, dashed lines). Also shown is the run involving breakup in collisions of graupel/hail only (“graupel-splintering case,” dotted–dashed lines).

Citation: Journal of the Atmospheric Sciences 74, 9; 10.1175/JAS-D-16-0223.1

Fig. 9.
Fig. 9.

The number concentration of all cloud droplets, conditionally averaged over all cloudy convective updrafts > 5 m s−1 with significant droplet concentrations (>5 cm−3), simulated by both models and plotted as in Fig. 8.

Citation: Journal of the Atmospheric Sciences 74, 9; 10.1175/JAS-D-16-0223.1

a. Breakup in collisions between graupel/hail particles

Comparing the no-breakup and graupel-splintering cases of AC (Table 1), the effect from inclusion of this type of fragmentation is to increase the average ice concentration by up to about 300% in all cloudy regions, near 4.5–8 km MSL altitude (0° to −24°C) (Fig. 8). There is little impact on either the ice in warm-topped cloudy updrafts or supercooled droplet concentrations in fast convective updrafts (Fig. 9).

b. Breakup of snow/cloud ice

The average concentration of ice is increased by about one to two orders of magnitude at most levels in warm-topped fast convective updrafts, comparing the control run and graupel-splintering cases (Table 1) of AC (Fig. 8a). This is consistent with historical observations of IE ratios for ice concentrations boosted by multiplication (e.g., Hobbs et al. 1980). In the storm, the average ice concentration is increased by about an order of magnitude at most levels in the mixed-phase region (0° to −36°C) below about 10 km MSL altitude (Fig. 8b), in simulations by the AC. There is little impact near levels of homogeneous freezing (<−36°C).

Most ice particles in the storm are from homogeneous freezing of cloud droplets near −36°C (about 10 km MSL). This major source is not altered greatly by breakup. Supercooled droplet concentrations are perturbed by up to about 10% in the upper half of the mixed-phase region in the AC. Inclusion of breakup alters amounts of snow and graupel, altering riming of droplets.

c. Breakup in all ice–ice collisions

Combined effects on the simulated storm from all breakups are similar to those for collisions of snow with graupel/hail noted above, as this breakup type predominates. Comparing the no-breakup case and control run (Table 1), the ice concentration is increased by about one and one to two orders of magnitude in simulations by HUCM and AC, respectively, in warm-topped fast convective updrafts when breakup is included. The corresponding changes in all cloudy regions are about one to two orders of magnitude below about 8 km MSL altitude, with less sensitivity above this level because of homogeneous freezing of droplets.

From a 3D perspective, the occurrence of fragments is illustrated in Figs. 4g and 4h for the control run of AC, compared with Figs. 4k and 4l from the no-breakup case. High concentrations of crystals of up to about 50 L−1 arose from fragmentation at 6–10 km MSL altitude in the control run (blue to green in Fig. 4h; see also Fig. 5d), compared with up to 1 L−1 in the no-breakup case (Fig. 4l). Active IN concentrations from heterogeneous ice nucleation of 0.1–5 L−1 at 7–8 km MSL (black carbon IN and dust IN) were predicted. Coincident maxima in snow concentration of up to 10 L−1 are predicted associated with the fragments (Figs. 4e,f). Fragments cause evaporation of cloud liquid, as seen by comparing Figs. 4j and 4n: most of the mixed-phase cloud in weak ascent (x = 40–50 km) near a convective updraft becomes ice-only when breakup is included. In the 2D runs, HUCM classifies new fragments mostly as snow: Figs. 4s,x show the snow concentration boosted by breakup, reducing supercooled cloud liquid in the convective updraft (Figs. 4u,w).

The observed PSD in Fig. 6 is predicted adequately only with breakup included. Moreover, Fig. 10 shows time series of average concentrations at 6–7 km MSL altitude for cloud ice, snow, and graupel, with and without breakup. About 25 min after first ice, an explosion (positive feedback) of concentration of cloud ice starts owing mostly to fragmentation in snow–graupel collisions in both models when snow and graupel exceed 0.1 L−1. The explosion continues for a further 30–60 min, reaching a domainwide average IE ratio of about 50 and 10 in AC and HUCM, respectively, at 80–100 min into the simulations, after an overshoot to 100 for 30 min in HUCM. This IE ratio then remains steady at 10–50 until the end of the simulation. While the IE ratio is increasing initially, snow concentrations are boosted by an order of magnitude by breakup in both models, while graupel concentrations are boosted by a factor of up to 3–10. The steady state occurs when the positive feedback of multiplication by graupel (growth of crystals to snow, riming to graupel that fragments snow) is severed by depletion of liquid (e.g., evaporation) in weak ascent with copious ice. Vapor growth of ice and riming cease when cloud becomes ice-only. During IE ratios >10 at steady state (80–150 min), contents of supercooled liquid averaged in clouds are reduced by up to one-half to one order of magnitude by breakup (Fig. 10).

Fig. 10.
Fig. 10.

Number concentrations between 6 and 7 km MSL altitude of (top) cloud ice, (top middle) snow , and (bottom middle) graupel/hail , conditionally averaged over regions of nonzero concentration of each species, in the control simulations of STEPS by AC (full line) and HUCM (line with squares). The no-breakup cases are shown (dashed and line with × symbols). (bottom) The liquid water content conditionally averaged over all regions with cloud ice (>10−8 m−3), including both mixed-phase and ice-only cloud at those altitudes.

Citation: Journal of the Atmospheric Sciences 74, 9; 10.1175/JAS-D-16-0223.1

Finally, total numbers of graupel particles generated in the entire simulation are increased by a factor of 3 when all breakup is included in AC, owing to riming of extra snow. Regarding the budget for numbers of crystals initiated (e.g., Fig. 7), inclusion of fragmentation in AC altered most ice-initiation processes. Total crystal generation is reduced by 60% as a result of fewer supercooled droplets for homogeneous freezing. Homogeneous aerosol freezing is rendered active (higher humidities at levels of cirrus) being inactive otherwise. Heterogeneous ice nucleation is reduced by 40%, because some mixed-phase clouds with weak ascent become ice-only with low humidity. Including extra breakup processes, from the graupel-splintering case to the control run, boosts breakup involving only graupel/hail by about 50%. Multiplication mechanisms cooperate synergistically with each other, fragments from one growing to become precipitation for another, but may compete with nonmultiplicative initiation. Losses of droplets by evaporation and accretion are increased by 7% and 20% when breakup is included.

6. Discussion

Both models show a boost by about one to two orders of magnitude of the ice concentration above the heterogeneous ice concentrations. A problem with the observed storm case is that there were no IN measurements during STEPS with which to validate the predicted heterogeneous ice concentrations. It could be argued that if the primary ice concentrations were inaccurate then the role of breakup would be exaggerated in the simulations. Yet such a bias is unlikely since the loadings of solid aerosol (<2.5-μm diameter) species were observed in Colorado by IMPROVE during the campaign, the basis of AC’s prediction of IN (section 3b). The EP is a physically fundamental representation of ice nucleation in terms of the loadings, sizes, and chemistry of solid aerosol species. The EP was based on coincident aerosol and IN observations in Colorado and was comprehensively validated by Phillips et al. (2008, 2013), especially against field observations of thin wave clouds from the Ice in Clouds Experiment–Layer Clouds (ICE-L). These wave clouds were used as natural IN counters and the EP predicted the observed ice concentrations from coincident observed ASDs of each aerosol species for a wide range of aerosol conditions (Phillips et al. 2013, Figs. 1–3 therein). Consequently, the predicted concentrations of primary ice in the present paper are expected to be accurate.

There are some quantitative differences between both simulations. Generally, except for the initial half-hour, the ice enhancement is less prolific in the HUCM simulation than for AC since both models differ in treatment of microphysical processes. There are slight differences in the PSDs (Fig. 6), such as with more crystals in AC than HUCM partly owing to fragments being initiated as snow in HUCM and different classification criteria for snow and cloud ice. Errors arise from different assumptions about the morphology of snow and graupel. Bulk density determines cross-sectional area for accretion, while fall speeds govern fragmentation. There are numerical errors too, with positive feedbacks of multiplication amplifying them. HUCM predicts ice concentrations in each size range (full bin microphysics), treating growth better with more accurate times for conversion of fragments to snow or graupel. Its positive feedbacks may be more accurate. HUCM may have more realistic reflectivity and cloud fraction (Fig. 5), with better sedimentation. Such differences typify bin-versus-bulk comparisons (Khain et al. 2015).

Yet, equally, AC has more accuracy in treatment of both heterogeneous ice nucleation and the 3D storm dynamics with multiple cells of convection throughout its domain, which can influence the ice microphysics. For example, in AC heterogeneous ice nucleation is realistically shut down by humidities well below water saturation (EP) at warm subzero temperatures and fragments from one convective cell can collide with graupel from another cell to yield more fragments.

Nevertheless, robustness of the modeling analysis is sufficient for comparison with our earlier theory. A 0D analytical model with three species of ice (crystals and small and large graupel) was created by Yano and Phillips (2011), in which breakup in collisions between the two larger species was a source of crystals. A positive feedback occurred as fragments would grow to become ice precipitation that further fragments, if a “multiplication efficiency,” [ is the primary ice generation rate, is the breakup rate, while and are time scales (see Table 2)], exceeded unity. In the present paper, graupel–snow collisions cause most of the simulated fragmentation. Our 0D analytical model applies also to this fragmentation in graupel–snow collisions, as its species can be redefined as cloud ice, snow, and graupel/hail by slight changes in time scales of conversion in the standard case. The theory is otherwise unchanged.

Table 2.

List of symbols.

Table 2.

In simulations of the present paper, cloud ice converts to snow in only about 5 min because of vapor growth to about 0.3 mm in mixed-phase clouds. Snow converts to graupel in a further τg ≈ 15 min in convective cores. The breakup rate is about three fragments per graupel–snow collision, so that now for graupel–snow collisions. Thus, the multiplication efficiency is reduced to (from about 300 originally for graupel–graupel collisions). Since it exceeds unity, this value of for breakup implies explosive breakup for any initial snow concentration with an increase of the cloud ice concentration by a factor of 10 over a time scale of about an hour (Yano and Phillips 2011, Fig. 3 therein). The cloud simulation predicts similar rates of ice enhancement. In summary, the ice multiplication predicted is consistent with the 0D theory, modified to treat breakup in graupel–snow collisions.

7. Conclusions

Strong nonlinearity characterizes the evolution of microphysical systems in nature, especially regarding cloud glaciation (Yano and Phillips 2011). For the process examined here, the ice-multiplication rate is proportional to (i) the number of fragments per collision and (ii) the number densities of the two ice types that collide each other. Nonlinearity arises from dependency (ii), with the possibility of a positive feedback controlling ice particle numbers.

In this article, a theory of fragmentation in ice–ice collisions was created from an energy conservation principle and applied in two validated cloud models to evaluate the role of this ice multiplication in an observed convective storm. A far-reaching substantial effect from breakup on the partial glaciation and precipitation production of the convective line was predicted:

  1. Our representation of breakup was essential for correct simulation of the storm; without it, the ice concentration predicted by both models was about one to two orders of magnitude too low compared to aircraft observations.

  2. Breakup in ice–ice collisions generated about 20–50 times more ice particles in the storm than heterogeneous ice nucleation by IN aerosols for both models. Most (95%–98%) of all ice particles not from homogeneous freezing were these fragments.

  3. The vast majority of these fragments were formed in collisions of snow with graupel/hail. The snow consists of large crystals (>~1 mm) and aggregates.

  4. In the fast convective updrafts (>5 m s−1) simulated, with tops too warm for homogeneous freezing and clear skies above them, inclusion of breakup in ice–ice collisions boosted predicted ice concentrations by about one to two orders of magnitude throughout the mixed-phase region (4–10 km MSL) owing mostly to fragmentation of snow. This corresponded to predicted IE ratios of 10–100. It is consistent with historic observations of typical IE ratios between 10 and 104 in such warm-topped convection, depending on the cloud type (Hobbs et al. 1980).

  5. Ice enhancement by breakup in ice–ice collisions was more pronounced in convective updrafts than in stratiform/cirriform clouds owing to more graupel/hail.

  6. The indirect impact from breakup on numbers of ice particles initiated is stronger than its direct effect and occurs via perturbation of other ice-initiation processes. In deep convection with cloud tops colder than −36°C (about 10 km MSL), breakup intensifies the ice crystal process of precipitation, depleting supercooled droplets (e.g., by more riming) and diminishing homogeneous freezing (20% less), which produces most of the ice in the entire storm. Amounts of supercooled cloud liquid decline earlier (e.g., by more evaporation) when breakup is included.

  7. Numerous fragments of ice converted some of the mixed-phase clouds to ice-only in weaker ascent. More snow particles are produced, competing more intensely for the available liquid and riming less. With smaller ice particles, breakup reduced surface precipitation in simulations of both models by 20%–40%. They predicted alteration of the cloud-cover fraction by breakup (by up to about 0.1).

Consequently, breakup would be expected to influence noninductive charging in ice–ice collisions and lightning. Moreover, there was a wide range of cloud-top heights (5–15 km MSL), as in any mesoscale convective storm. For clouds with tops below 10 km MSL altitude (near −36°C), too warm for homogeneous freezing, breakup in ice–ice collisions must have been their greatest source of ice. Breakup is of paramount importance for their ice initiation.

The results presented provide full modeling support for the explosive ice-multiplication tendency of the ice-breakup process theoretically predicted (Yano and Phillips 2011; Yano et al. 2016). The modified theory predicts a multiplication efficiency for the STEPS case of about 10, so multiplication is expected to increase the cloud ice concentration by a factor of 10 over a time scale of about an hour. The cloud simulation predicts similar rates of ice enhancement, consistent with the positive feedback of our theory (section 6): fragments grow to form snow that rimes to form graupel/hail, which then collides with snow to yield more fragments and so forth.

Indeed, such a role for multiplication in ice–ice collisions in natural clouds was envisaged by Vardiman (1978) and, regarding graupel/snow collisions, by Vidaurre and Hallett (2009). High concentrations of ice, observed in convective clouds with cold bases near Japan, were explained in terms of this breakup (Takahashi et al. 1995). In the STEPS case, the coldness of the cloud base causes ice precipitation to form by the ice crystal process, with vapor growth of crystals followed by lengthy riming of some of the snow to form graupel. Hence, the snow particles are far more numerous than the graupel. Any graupel particle is far more likely to collide with snow than with other graupel. This explains why collisions with snow were more prolific in generating fragments than those only involving graupel/hail in simulations here.

A natural implication for future model development is that ice morphology (e.g., bulk density) is crucial to the overall ice concentrations. Density of accreted rime in nature has various dependencies and determines the fragility and fall speeds of graupel and snow, which in turn control the collision kinetic energy (CKE) and fragment numbers in ice–ice collisions. Currently most cloud models prescribe ice morphology in a simple way. Moreover, future modeling studies will examine the sensitivity of cold clouds with respect to IN concentrations. On the one hand, eventual ice concentrations from explosive breakup may be limited by thermodynamics (temperature, ascent) governing onset of subsaturation and evaporation of liquid (Yano and Phillips 2011), minimizing this sensitivity. On the other hand, multiplication may amplify impacts from scarce active IN (e.g., at warmer temperatures), boosting the sensitivity.

To conclude, ice production in the simulated mixed-phase clouds proceeds partly by a positive feedback of explosive multiplication in a microphysical “chain reaction,” with fragments growing to become snow that then fragments further in collisions with graupel. There is a strong case for quantifying this feedback in more cloud cases and for more elucidation of fragment numbers in laboratory and field observations of realistic collisions, especially for various types of snow.

Acknowledgments

The work was funded by an award to Phillips (VTJP) from the U.S. National Science Foundation (NSF) (ATM-0427128, which later became ATM-0852620) and by a subaward from BER/DoE to VTJP and Professor A. Khain at the Hebrew University of Jerusalem (DE-S0006788). VTJP directed the study. Development of AC and its simulations were performed by Formenton, Kanawade, Kudzotsa, Sun, and VTJP. HUCM was developed by Khain and Ilotoviz. Observations for STEPS were provided by Detwiler, Tessendorf, and Bansemer. VTJP acknowledges advice from Axel Seifert, Andrew Heymsfield, and Charles Knight. Comments from three anonymous reviewers enhanced the manuscript.

APPENDIX

Details of Model Description

a. Description of aerosol–cloud model

The aerosol–cloud model (AC) has representations of clouds and aerosols with a hybrid spectral bin–two-moment bulk microphysics, interactive radiation, and semiprognostic aerosol schemes. These schemes were created in the WRF framework and validated (Phillips et al. 2007a, 2008, 2009, 2013, 2015a; Kudzotsa 2014; Kudzotsa et al. 2016), with extension of the two-moment bulk scheme to include precipitation in the present paper. Other schemes are from WRF (Skamarock et al. 2005), for dynamics, subgrid-scale mixing, the planetary boundary layer, and surface layer. The model can be run as a cloud-system-resolving (CSRM) or cloud-resolving model (CRM) with a mesoscale domain and a resolution resolving clouds (e.g., a horizontal grid spacing of only 1 or 2 km).

There are five microphysical species: cloud liquid, cloud ice, rain, graupel/hail, and snow. (Here, “snow” is defined to consist of ice particles larger than about 0.3 mm, not sufficiently rimed to be graupel or hail, and including both large pristine crystals and aggregates.) Prognostic bulk variables are the mixing ratios of total number and mass of all particles in each species. Other prognostic variables are rime-mass mixing ratios for snow and cloud ice and liquid-mass mixing ratio for graupel/hail. The known mechanisms of initiation of cloud droplets and ice particles are all treated in terms of dependencies on the chemistry, size, and loading of seven chemical species of aerosols. Preferential evaporation of smaller cloud droplets during homogeneous freezing at temperatures colder than −36°C is represented (Phillips et al. 2007a). Homogeneous freezing of each aerosol species is treated. The EP predicts IN activity from four of the seven aerosol species: dust, soot, soluble organics, and primary biological aerosol particles (PBAPs) (Phillips et al. 2008). An improved EP was validated offline against aircraft observations of thin wave clouds and coincident ASDs (Phillips et al. 2013). Heterogeneous ice nucleation is predicted from components of each solid aerosol species that are interstitial and immersed in drops, including all known modes of IN activity (deposition and condensation/immersion freezing, outside-in and inside-out contact freezing), with the EP. Components of ASDs of solid aerosol immersed in supercooled rain are predicted, allowing heterogeneous raindrop freezing to be predicted with the EP for initiation of graupel/hail, in addition to collisional raindrop freezing.

A semiprognostic aerosol scheme allows in-cloud ASDs of seven chemical species of aerosols to be predicted (Phillips et al. 2009). ASDs of components of each aerosol species that are interstitial, and immersed in cloud and in precipitation, are predicted. Two-moment bulk variables define each sulfate mode (Kudzotsa et al. 2016). Two modes of operation are possible: either aerosol species in the cloud-free environment are prescribed (no feedback) or these are predicted with bulk prognostic variables nudged toward observations (feedback from cloud to environment). In this paper, the latter mode was used.

Recent developments are schemes for wet growth (Phillips et al. 2014), sticking efficiency that depends on size (Phillips et al. 2015a), and size-dependent ice morphology. Average shape and bulk density of snow are prescribed as functions of size, from aircraft [density ∝D−0.508 (Heymsfield et al. 2002)] and ground-based observations [aspect ratios of 0.65 and 0.3 for snow <1 and >10 mm, linearly interpolated in between (Korolev and Isaac 2003; Garrett et al. 2015; Mitra et al. 1990)]. The bulk density of graupel(<0.5 cm)/hail(>0.5 cm) is prescribed as a function of size (230 kg m−3 for graupel <1 mm, 900 kg m−3 for hail >0.5 cm, and linearly interpolated in between), with similar treatment of its particle shape. Fall speeds of graupel/hail are from empirical formulae for hail (>0.5 cm) and graupel <1 mm (Heymsfield and Kajikawa 1987; PK97) and linearly interpolated at sizes in between.

To implement the wet-growth scheme (Phillips et al. 2014, 2015b) in the hybrid bin–bulk scheme, the liquid fraction was assumed to have the form beyond the size for onset of wet growth, , evaluated in the wet-growth scheme. An iterative numerical scheme (secant method) solves for so to match the total liquid mass of all temporary size bins with the bulk liquid-mass mixing ratio of graupel/hail (mass of its liquid per kilogram of air).

“Emulated bin microphysics” techniques treat all coagulation processes for the five microphysical species [except for autoconversion of cloud droplets to rain from Khairoutdinov and Kogan (2000)]. Temporary equidistant mass grids of bins are created anew in every grid box in the microphysics routine to represent the PSD and are populated from the two-moment bulk variables (total mass and number). The grids are used only in the microphysics routine. The continuous collection equation is solved with the grids for each permutation of bin pairs. In the rest of the model, advection, sedimentation, and diffusion are all done with the two-moment bulk variables. Shape parameters of the PSDs are prescribed for cloud droplets (about 3), cloud–ice (unity), and rain [2.5 from Willis (1984)], and evaluated for graupel and snow (as a function of average snow mass per particle, using lookup tables). Self-collection of graupel, rain, and snow are treated, with an average size of raindrop embryos from field observations (Willis 1984). Cloud ice is converted to snow when its mean diameter exceeds about 0.3 mm (Ferrier 1994).

To implement the breakup scheme described in Part I, it was necessary to include extra prognostic bulk variables. These were the mass mixing ratios of rime on snow and cloud ice, each incremented with the mass of supercooled liquid rimed and sedimenting at the same fall speed as the snow or cloud ice. From these bulk variables, the rimed fraction Ψ is diagnosed in each bin of the temporary grid for snow and cloud ice as an exponential function of size, . Here, while is a constant determined numerically (secant method again). For each permutation of bin pairs in the emulated bin treatment of ice–ice collisions, the breakup scheme initiated extra fragments. Each bin of snow is emptied to form graupel/hail if its rime fraction exceeds 50%. More details of implementation of the breakup scheme are in Part I (section 5 therein). Finally, prediction of radar reflectivity for liquid-, ice-, and mixed-phase particles follows Battan (1973) and Bader et al. (1987), as described by Phillips et al. (2003).

b. Description of Hebrew University Cloud Model

The Hebrew University Cloud Model (HUCM) is a 2D nonhydrostatic model using spectral bin microphysics. Recent description of the model is presented by Ilotoviz et al. (2016). PSDs for eight hydrometeor types are predicted [drops, platelike, columnar, and branch-type (dendrites) ice crystals, snow (aggregates), graupel, hail, and freezing drops]. The PSDs are defined on the logarithmic equidistant mass grid containing 43 mass-doubling bins for each microphysical species. The mass corresponding to the smallest bin is equal to that of a liquid droplet with a radius of 2 μm. The cloud–aerosol interaction is described by means of a size distribution of aerosol particles (AP) playing the role of CCN. The ASD is treated with 43 bins. The radius of dry AP ranges from 0.005 to 2 μm. The initial (t = 0) CCN ASD is calculated using the empirical dependence , where is supersaturation with respect to water and and k are the measured constants. The prognostic equation for the ASD of nonactivated AP is solved for t > 0. Using the value of calculated at each time step, the critical radius of CCN is determined according to the Köhler theory. The CCN with radii exceeding the critical value are activated, and droplets are initiated. Corresponding bins of the CCN ASD become empty. The supersaturation maximum near cloud base is from an analytical solution by Pinsky et al. (2012).

The properties of cloud particles (aspect ratio, densities, fall velocities) are determined using the empirical power-law relationships (PK97; Khain et al. 2004). Diffusional growth of all particles is calculated by solving analytically the equation system for particle size and supersaturations with respect to water and ice, so that the supersaturation values change during the model time step in the course of the diffusional growth. Collisions between particles are calculated by solving stochastic kinetic equations for collisions (Bott 1998). Height-dependent, gravitational collision kernels for drop–drop and drop–graupel interactions and for collisions between ice crystals, following Khain et al. (2004, and references therein).

Sticking efficiency between ice particles follows Phillips et al. (2015a), depending on temperature and type (habit) of colliding ice particles. Collisional breakup of drops follows Seifert et al. (2005). Spontaneous breakup of rain drops larger than ~6.5 mm in diameter is included according to Srivastava (1971). Effects of turbulence on collisions between cloud drops are included, following Benmoshe et al. (2012). The primary ice nucleation is described using the empirical expression of Meyers et al. (1992). The number concentration of IN lost by activation is approximated by that of actual ice crystals. The habit of ice crystals depends on temperature. The H–M process is treated (Hallett and Mossop 1974). Time-dependent melting of snow, graupel, and hail as well as shedding of water from hail follows Phillips et al. (2007b).

HUCM describes also time-dependent freezing (Phillips et al. 2014, 2015b). Nucleation freezing of raindrops leads to formation of freezing drops (FD) containing liquid water fraction. Total freezing of liquid in FD leads to formation of hail. Two regimes of hail growth, dry and wet, are described. The rate of freezing of liquid water within FD and hail is determined by solving the corresponding heat balance equations at the particle surface and at the ice–liquid interfaces. The balanced equations are written in the most general form that takes into account thermodynamic effects of accretion of drops and ice crystals, as well as of shedding. One of the specific features of wet growth is shedding of water film and the production of new raindrops. The shedding takes place if both the mass of exterior liquid water and the mass of hail particles exceed their critical values. The size of raindrops forming as a result of shedding depends on the Reynolds number.

Rimed fraction of snow is calculated for each mass bin. Riming increases bulk density of snow. If the bulk density of snow exceeds 0.2 g cm−3, then the rimed snow is converted to graupel. Graupel is converted to hail in two cases: if graupel starts growing by wet growth or if graupel reaches 1 cm in diameter. Masses of water within ice particles, as well as rimed mass in snow, are advected and sedimented similarly to PSDs of corresponding hydrometeors.

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