1. Introduction
Understanding the formation of ice in lower-tropospheric clouds is a topic of great importance for understanding global water balance and climate. Progress in this area, however, is quite slow because of the difficulties in characterizing the many complex interactions that lead to ice initiation and to the dynamic, non-steady-state nature of the clouds.
Primary, heterogeneous ice nucleation is induced by ice nuclei (IN), a subset of aerosol particles that nucleate ice via different pathways (Vali 1985). The action and composition of IN has been extensively studied in natural and laboratory-induced clouds using various techniques to measure these properties. Contact nucleation is the freezing of a droplet initiated by contact with an aerosol particle, whereas immersion freezing is due to freezing by an ice nuclei immersed in the droplet. Deposition nucleation is due to the formation of ice crystals directly on the surface of an ice nucleus. Many substances have different freezing thresholds when they act as contact nuclei, as opposed to when they act as deposition, condensation, or immersion nuclei, indicating that the freezing mechanism is different for the different modes. Of these three modes, immersion nucleation is the most likely candidate for ice nucleation in convective clouds. We reach this conclusion because the time scales involved in contact nucleation via Brownian motion or thermophoresis or diffusiophoresis are generally too large to allow the collection of ice nuclei via this process, whereas immersion nuclei are already immersed in the cloud droplets and drops. Ice nucleation energetics do not facilitate ice nucleation via deposition. Mineral dust from arid regions is thought to be one of the most important IN. A number of organic compounds have been identified as potential IN (Fukuta 1966). There still remain uncertainties in the processes involved in primary ice nucleation (Cantrell and Heymsfield 2005; DeMott et al. 2010).
In situ measurements in the critical temperature range from −3° to −8°C, where primary ice nuclei are relatively scarce, suggest (and laboratory experiments confirm) that a vigorous secondary ice production process is operative in clouds where graupel and small and large cloud droplets coexist. The conditions for the production of secondary ice particles in clouds in this critical temperature range are thought to involve the riming of ice particles by supercooled drops. In more than 100 small maritime cumulus clouds sampled with top temperatures of about −8°C, Mossop (1970) documented ice concentrations ~104 times larger than “primary” ice nuclei concentrations measured in a cloud chamber. Shortly thereafter, Ono (1971) showed ice concentrations that were three or four orders of magnitude above the ice nuclei concentrations expected for the temperatures sampled. In modified maritime cumuli in Australia, Mossop et al. (1972) found high concentrations of ice crystals, suggesting that a multiplication process was active, and also found rimed particles up to 4 mm in diameter. Consideration of the concentration, diameter, and fall speed of these graupel particles indicated that riming in these clouds was generally dominated by particles >l mm. The high crystal concentrations were made in clouds with a liquid water content (LWC) ~ 1 g m−3. They concluded that the riming process was usually dominated by particles >l mm in diameter. Mossop and Wishart (1978) found that, as the target velocity increases, secondary ice production during riming decreases relative to the numbers of drops accreted.
Several processes can account for or explain the high concentrations of ice particles observed at temperatures too warm to be accounted for by ice nuclei. These include the rime-splintering process [called the Hallett–Mossop (H-M) process (Hallett and Mossop 1974), discussed in more detail below]; fracturing of drops (Knight and Knight 1974; Cannon et al. 1974); fracturing of ice particles due to ice particle–ice particle or graupel–graupel collisions (Vardiman 1978; Takahashi et al. 1995); and production of multiple ice particles during the evaporation of single particles (including aggregates; Henmi 1974) or associated with vapor growth at −5°C, without the need for riming (Knight 2012). The surface temperature of a freezing drop or one undergoing appreciable riming is several degrees above the ambient temperature (Heymsfield 1983). As a result, there is a high supersaturation immediately surrounding the particle, possibly leading to the ice nucleation (Gagin and Nozyce 1984). It is apparent, though, that graupel is not needed for an ice multiplication process to operate (Gordon and Marwitz 1986; Rangno and Hobbs 2001; Knight 2012).
In late 1973, experiments were conducted to recreate the secondary ice production process in the laboratory. Mossop et al. (1974) conducted experiments in a cloud with a temperature of about −9°C, collecting supercooled droplets with sizes up to 100 μm on targets moving at velocities of 1–2 m s−1. They concluded that the number of secondary ice particles produced per unit mass of rime was far too low to account for the high concentrations of ice particles observed in the earlier Mossop cloud studies. In contrast, Bader et al. (1974) conducted laboratory experiments that generated secondary ice production during rime collection on a substrate at temperatures from −10° to −15°C. An important aspect of the splinters that Bader et al. reported was that they were submicron sized and thus difficult to detect by airborne microphysical probes, at least early in their subsequent growth. Shortly thereafter, John Hallett had the idea that the experiments of Mossop et al. (1974) be conducted at temperatures from −4° to −6°C rather than the lower temperatures used by those investigators (S. C. Mossop 1983, personal communication). Using an ice-covered rod circularly rotating through a supercooled laboratory cloud that simulated the riming of a graupel particle in a natural cloud, Hallett and Mossop (1974) indeed documented the production of secondary ice particles at temperatures from −4° to −6°C.
Others since have conducted laboratory experiments in an attempt to document the conditions under which this effect occurs and to understand the process responsible, but it is not yet certain how the accretion of rime leads to the production of secondary ice. Based on the laboratory experiments, Choularton (1978), Choularton et al. (1980), and Mossop (1980) suggest that the H-M effect operates in the following way: Occasional large drops (>25-μm diameter) are accreted in such a way that they are attached to the ice substrate by only a narrow bridge. Heat loss conditions are such that a complete ice shell forms around the drop periphery as it freezes. Pressure builds up inside the drop and is relieved by the cracking of the shell and the formation of a protruding “spike” of ice. Further pressure buildup can lead to fracture of the end of the spike and ejection of one or more fragments.
Figure 1 shows the rate of secondary ice production as a function of temperature and velocity (Vt) of the riming target, adapted from the laboratory experiments of Mossop (1976). Assuming that most cloud droplets have a negligible terminal velocity, the relative fall speed of the graupel Vt is approximately the riming target velocity. The experiments showed that a secondary ice production process occurs in the temperature range from −3° to −8°C and, as pointed out by Mossop, peaks at a temperature of −5°C and that the production rate is not a strong function of the target (graupel simulating) velocity.
Rate of secondary ice crystal production as a function of the target velocity and temperature. The data, from the experiments of Mossop (1976), have been smoothed using a three-point filter to yield relatively smooth curves.
Citation: Journal of the Atmospheric Sciences 71, 12; 10.1175/JAS-D-14-0093.1
The capture of the secondary ice by drops and the continued ejection of ice splinters by riming ice particles can lead to ice multiplication in natural clouds. Numerous studies have shown consistency with this hypothesis. For example, Harris-Hobbs and Cooper (1987) showed that the rate at which secondary ice was produced in the clouds they sampled was strongly correlated with the rate predicted from the laboratory studies of Hallett and Mossop (1974). Their secondary ice production rates calculated based on the droplet and ice particle size distributions were qualitatively similar to those observed. Blyth and Latham (1993) concluded that the high ice concentrations they observed in the New Mexican summertime cumulus clouds they sampled were consistent with the H-M process. Large drops of diameter D ~ 1 mm were sometimes observed just before the formation of ice. Probably the highest resolution images of what were thought to be secondary ice particles were collected in California rainbands by Gordon and Marwitz (1986). Single crystals and aggregates were the dominant ice particle forms observed, with graupel largely absent. From six flights in intense convective clouds in Oklahoma, Heymsfield and Hjelmfelt (1984) documented secondary ice production and concluded that secondary ice was much more prevalent in clouds that developed into embedded ice clouds than in those that were isolated. Concentrations of needles and aggregates of needles peaked at temperatures between −4° and −8°C and aggregates. Based on the droplet and ice particle data and model calculations of accretional growth together with the particle size distributions and habits, they concluded that the highest concentrations of secondary ice were produced by large aggregates and frozen drops and the lowest by graupel. Aggregates descending in downdrafts at temperatures of −10°C and below produced secondary ice concentrations that were comparable to or larger than those produced by the ascending particles. Stith et al. (2004) observed nearly circular images similar in size to cloud droplets in glaciated regions in concentrations up to about one-half of that of the cloud droplets in regions containing liquid cloud droplets, implying that the secondary ice concentrations were on the order of tens of cubic centimeters. However, this observation and those reported before that study were published before the shattering of large ice on the inlets of the PMS Forward Scattering Spectrometer Probe (FSSP) became a well-documented concern with FSSP observations in the presence of large ice, so caution must be applied when these observations are used to specify secondary ice concentrations. From in situ measurement in wintertime precipitation in the Pacific Northwest, Woods et al. (2008) documented needle and column habit crystal types at temperatures warmer than −10°C thought to be secondary ice particles that were produced in those clouds. Huang et al. (2011) from airborne measurements in southeast Germany and eastern France observed high concentrations of pristine and rimed columns at a temperature of about −5°C together with graupel and suggested that the H-M process of splintering during riming was responsible for the relatively high concentrations of ice particles.
What can be learned about how the secondary ice particles multiply from the in situ observations in convective clouds? Does the secondary ice production process operative in tropical maritime clouds behave similarly to the laboratory experiments? Thus, do we see a behavior similar to that plotted in Fig. 1?
The goal of this paper is to characterize the conditions where secondary ice particles, specifically identified as needle or thin columnar types, are observed. These shapes, whether they are single crystals, component crystals of aggregates, or partially rimed, often dominate temperatures where primary IN are relatively rare, and their longest dimensions grow rapidly at conditions of water saturation. When we find these crystals in this temperature range and in conditions of water saturation, then it is reasonable to assume that a vigorous secondary ice production process is active within or near to that location. Better identification of the conditions where secondary ice particles are observed may lead to a clearer understanding of the physical processes involved in their production and also provide guidance in the planning of laboratory and numerical experiments to further explore the relevant processes.
Section 2 presents an overview of the clouds sampled in this study and the instruments used to collect the data. Section 3 presents an overview of the microphysics and vertical velocities in these clouds and characterizes the properties within the regions that contain particles and particles produced by secondary processes, which we believe aid in identifying the processes leading to secondary ice production. 4 examines a case study from each field program that might provide clues to the processes involved. Section 5 discusses the development of secondary ice in updrafts. The results are summarized and conclusions are drawn in section 6.
2. Data and measurement capabilities
This study uses in situ data acquired from two field programs: the Ice in Clouds Experiment-Tropical (ICE-T), with the National Center for Atmospheric Research (NCAR) C-130 aircraft based out of St. Croix, Virgin Islands, and the National Aeronautics and Space Administration (NASA) African Monsoon Multidisciplinary Analyses (NAMMA) in 2006 sampling with the NASA DC-8 aircraft based out of Cape Verde, Africa. The Stratton Park Engineering Company (SPEC) Learjet also flew in ICE-T. The Learjet data are under analysis separately.
We focus on the 13 research flights from ICE-T and 1 from NAMMA (Table 1). They include penetrations into vigorous convective clouds, some containing dust as ascertained from an onboard lidar during both experiments, many of them isolated. The boundary layer in the 20 August 2006 NAMMA case was largely dust free, but there was a dust layer observed between 2 and 5 km that could have led to the entrainment of dust into the updrafts (Heymsfield et al. 2009). Two ICE-T flights included measurements in midlevel, supercooled clouds (RF02 and RF10).
Summary of C-130 and DC-8 flights analyzed.
In situ measurements from ICE-T include the liquid and total condensed water contents, temperatures, vertical velocities, and the properties of the particles and the particle size distributions from 0.1 to 50 μm, with detailed images. Sampling periods in supercooled cloud were appreciable (Table 2). The NAMMA flight also included penetrations into the updrafts at temperatures from −15° to below −40°C. The concentration data are averaged over 5-s intervals or about 1 km of horizontal pathlength to yield representative particle size distributions (PSD).
Sampling times in cloud.
Vertical air motions on both aircraft were acquired with accurate (±1 m s−1) wind sensing elements (see Brown et al. 1983). Temperatures were measured using Rosemount sensors. Lidars in nadir- (RF01–RF13 and N01) and upward- (RF06–RF13 and N01) viewing orientations and radars (RF07–RF13 and N01) were available on both aircraft. For ICE-T, supercooled liquid water was detected with a Rosemount icing probe (RICE), and the liquid water content was measured with a King probe (LWCK). Spectra for particles from about 1 to 50 μm were acquired with scattering instruments: a PMS FSSP (ICE-T), a Droplet Measurement Technologies (DMT) cloud and aerosol spectrometer probe nominally measuring particles in the 0.5–50-μm range (NAMMA), and a DMT cloud droplet probe (CDP; ICE-T). Because of shattering of large ice particles on the leading surfaces of the FSSP and DMT cloud and aerosol spectrometer (CAS) probes, the concentrations measured in the presence of large ice particles are anomalously high. The CDP is more immune to this ice shattering effect, although this worked only intermittently during ICE-T; thus, those data are not used. Given that typical droplet concentrations in convective elements of 50 cm−3 or larger are much higher than the concentration produced by shattering, which are generally <1 cm−3, as ascertained from the measurements when the RICE probe does not detect supercooled water, the measured concentrations of drops from all three probes are reasonably reliable when they exceed ~5 cm−3. Liquid water contents were derived from the PSD measured by the small particle probes (CAS, CDP, and FSSP; LWCPSD).
Imaging probe data are used to derive the PSDs for maximum dimensions of about 50 μm to at least 5 or 10 mm, depending on the concentration of the largest particles. A PMS 2D probe with fast electronics (fast 2D) provided excellent imagery of particles >50 μm (ICE-T). A DMT cloud imaging probe (CIP) and a SPEC 2D-S probe provided imagery and size distributions for particles beginning at sizes above about 25 or 50 μm (NAMMA). The fast 2D and 2D-S probes readily detected needle and columnar crystals and shattered drops (Fig. 2). A SPEC three-view cloud particle imager (3VCIP) also measured particles from the C-130 during ICE-T (RF03, RF06, and RF10). A PMS 2D precipitation probe measured PSDs and imagery from about 200 μm to 1 cm for both experiments.
Examples of needles and columns: (a) frozen drops and (b) a shattered drop from the fast 2D-C probe from ICE-T, and (c) needles and columns together with graupel from the CIP probe during NAMMA. The distance between horizontal lines in the figures are about 1 mm. (a) RF12: 1511:07 UTC 28 Jul 2011, with temperature of −10.2°C; (b) RF05: 1900:43 UTC 12 Jul 2011, with temperature of −15.3°C; and (c) 1722:45 UTC 20 Aug 2006, with temperature of −7.7°C.
Citation: Journal of the Atmospheric Sciences 71, 12; 10.1175/JAS-D-14-0093.1
We used two methods to reduce the concentrations of particles that might have been caused by shattering of large ice particles or splashing of drops on the leading edges of the imaging probes. One method rejected particles using the particle interarrival times (Field et al. 2006). The second method used only those particles that were 125 μm and larger. The latter method also reduced uncertainties in the concentrations because of sizing and depth of field uncertainties. It is unlikely that there were significant concentrations of needles that would have been below the detection threshold of 125 μm (see the appendix), although we are not completely ruling out the possibility that artifacts may have still been included in the dataset.
Condensed water contents in particles 50 μm and above were derived from the imaging probe PSDs, assuming that all particles were liquid drops (LWCPSD2D) at all temperatures and all particles were ice particles below 0°C using a mass–diameter relationship developed for clouds sampled during NAMMA (A. J. Heymsfield et al. 2010). The 2D concentrations, however, included only those particles >125 μm. It was not possible to differentiate liquid from ice particles at sizes < 125 μm.
3. Synthesis of data
The ICE-T cases analyzed were mostly smaller fairly isolated convective clouds with a deep layer of well-developed warm rain below the freezing level. The NAMMA case was a much more complex mesoscale convective complex forming in a sheared environment in the vicinity of the intertropical convergence zone (ITCZ).
a. Overview
Based on the examples of particle images shown in Fig. 2, it is reasonable to expect that we can detect small columns with high fidelity with the fast 2D and 2D-S probes and with somewhat lower fidelity with the CIP. In the appendix, the growth time required for the imaging probes to first detect ice columnar, needle, and planar crystals is estimated. We should be able to detect columns or hexagonal plates that originate as particles from 10 μm in diameter, a rough estimate of their size at the time of their production, after between 150 and 300 s of growth.
b. Liquid water observations
Trends noted in the ICE-T cloud LWC with temperature, as derived in small particles from the FSSP and the King probe and in the larger particles from the 2D probes at temperatures 0°C and above, for all sizes and temperatures measured directly by the CVI total condensed water content (TWC), are shown in Figs. 3a–d. Because we do not know the mix of liquid and ice water contents below 0°C, we have not plotted these water contents in Fig. 3c. The LWC trends with temperature from the FSSP PSDs and those from the King probe are remarkably similar, as they should be given that both probes are sensitive to about the same particle sizes. The FSSP and King probe LWCs are highly correlated: LWC (King probe) = 0.01 + 0.99 × LWC (FSSP), with a correlation coefficient of 0.94, with the LWC in grams per cubic meter.
Temperature dependence of the liquid water content as derived from several different probes during ICE-T: (a) FSSP, (b) King, (c) 2D, and (d) CVI TWC. Note that the data shown in Fig. 3, for updrafts only, use colored symbols to show vertical velocities in different ranges.
Citation: Journal of the Atmospheric Sciences 71, 12; 10.1175/JAS-D-14-0093.1
This adds credibility to the droplet spectra deduced from the FSSP. The liquid water contents are subadiabatic, and entrainment of ice nuclei in these subadiabatic parcels can have a major effect on the ingestion of ice nuclei into the updrafts.
The LWCs from the FSSP and King probes increase from cloud base to about the 10°C level, presumably reflecting diffusional and coalescence growth to this level (Figs. 3a,b). This interpretation is corroborated from the 2D probe data, which also indicates an increase in LWC with altitude. Note that the data shown in Fig. 3 are for the updraft regions only. The CVI TWC is relatively constant with height (Figs. 3c,d). Between +10° and 0°C, the LWCs in cloud droplet sizes continue to decrease, while in 2D sizes they continue to increase with the CVI TWC remaining about constant, again indicating coalescence growth. From 0° to −10°C, the LWCs in cloud droplet sizes decrease only slightly while the TWC for all sizes continues to increase, suggesting primarily collection of the droplets and growth of the larger droplets and now ice particles. Note that the CVI saturates at a CWC of about 2 g m−3, but this amount was infrequently approached.
Assuming a cloud-base temperature of +24°C as suggested by the data, the saturation vapor density with respect to water at cloud base would be about 22 g m−3. A parcel moving adiabatically upward to the 0°C level would contain about 15 g m−3 of liquid water. Thus, there is substantial fallout and/or entrainment in the updrafts. The latter is more likely given the vertical distribution of equivalent potential temperature in the updrafts.
There is a direct correlation between the LWC and the vertical velocity (w) (Figs. 4a,b). The relationship between the LWC and w is about the same for the temperature intervals 0° to −5°C and −5° to −10°C. Assuming that the FSSP LWCs are approximately correct, a 1 m s−1 updraft in each of these temperature intervals is associated with an LWC ~ 0.2 g m−3, and a 2 m s−1 is associated with an LWC ~ 0.3 g m−3 (see specific values shown in Fig. 4a).
Liquid water content as a function of vertical velocity from ICE-T: (a) FSSP and (b) King probes. Vertical green and yellow lines are for reference, for constant LWCs of 0.1 and 0.2
Citation: Journal of the Atmospheric Sciences 71, 12; 10.1175/JAS-D-14-0093.1
The mean number-weighted mean droplet diameter (DMN) and volume-weighted mean droplet diameter (DMV) are shown as a function of temperature in Fig. 5. The two diameters both increase with decreasing temperature and their magnitudes are typical of maritime tropical convection (e.g., see Zipser and LeMone 1980).
Mean and median volume diameters as a function of temperature from ICE-T.
Citation: Journal of the Atmospheric Sciences 71, 12; 10.1175/JAS-D-14-0093.1
The H-M effect is shown in the laboratory to be dependent on the coexistence of drops that are <12 and >25 μm, although, in the laboratory and field observations of Mossop (1985a,b), a much reduced role of the small drops is noted. Nonetheless, we have examined the properties of the small and large modes of the droplet populations (where the concentration is 0.1 cm−3 and above defining any cloudiness, although this is arbitrary and we could have set it to any value) as a function of vertical velocity and temperature. The total concentration is directly proportional to the vertical velocity (Fig. 6a). The median concentrations in key temperature intervals identified in the figure tend to be quite low as a result of near 0 m s−1 average vertical velocities for the clouds investigated and also of how we decided to define a cloud.
Droplet concentrations as a function of vertical velocity as derived from the FSSP during ICE-T: (a) total concentration and concentration of drops of (b) <12 and (c) >25 μm.
Citation: Journal of the Atmospheric Sciences 71, 12; 10.1175/JAS-D-14-0093.1
In Figs. 6b,c, we examine how frequently and how many droplets that are <12 μm, encompassing most of the lower range of sizes for the H-M effect, and >25 μm, for the larger sizes, appear in the ICE-T clouds. There is a weak dependence of the concentration of these smaller size droplets on the updraft velocity (Fig. 6b). Although the concentrations obviously increase with the vertical velocity, the median values do not show this effect. Therefore, reasonably high concentrations of small drops are present in both weak and strong updrafts; relatively high LWCs are not needed to produce the small drops. For the 25–50-μm droplets, higher droplet concentrations are correlated with stronger updrafts: that is, strong updrafts are needed to produce high concentrations of these large droplets. For both size ranges, from the median concentrations in various temperature intervals shown in Figs. 6b and 6c, we can expect concentrations ~5 cm−3 in the temperature intervals where the H-M effect is thought to occur. Also indicated in Fig. 6 is the fraction of in-cloud time intervals when drops that are <12 and >25 μm are present in concentrations exceeding 1 cm−3. Roughly one-third of the time in cloud the conditions needed for the H-M effect to operate are satisfied.
In Table 3, we show the properties of the droplet population measured in clouds the −3° to −8°C temperature range as a function of the vertical velocity. In downdrafts and in updrafts below 1 m s−1, there is virtually no liquid water. Water is present but concentrations are relatively low where updrafts are in the 1–2 m s−1 range. Liquid water contents, the total concentration, and concentrations of droplets of <12 and >25 μm ramp up considerably where updrafts exceed 2 m s−1. Examining the properties of the droplet population in this way suggests that updrafts of 2 m s−1 and above have the requisite droplet sizes needed for the H-M effect to operate.
Cloud droplets (FSSP) in the −3° to −8°C temperature range: mean values.
The NAMMA liquid water regions contain droplet concentrations on the order of 100 cm−3 in the critical temperature range −3° to −8°C, the concurrent presence of drops of <12 and >25 μm, and the presence of significant liquid water when the updrafts exceed about 1 m s−1 (Figs. 7a–d). Droplet concentrations are lower in the warm rain region than at temperatures below 0°C. Insufficient in-cloud sampling precludes an interpretation of the properties of the liquid phase at temperatures above 0°C.
Observations from the CAS probe on the NASA DC-8 aircraft on 20 Aug 2006 as a function of (a)–(c) temperature and (d) vertical velocity from NAMMA: (a) total concentration; (b) concentrations of drops <10 μm as a function of drops >25 μm ; (c) liquid water content; and (d) LWC as a function of vertical velocity.
Citation: Journal of the Atmospheric Sciences 71, 12; 10.1175/JAS-D-14-0093.1
c. Column and needle occurrence
The locations where columnar and needle crystals are observed have been identified by reviewing all of the fast 2D-C and 2D-P probe images from ICE-T and the 2D-S probe images from the 20 August 2006 NAMMA case. These identifications were done qualitatively by noting those times when two or more of these particles were present in a sample from each second of data. Identification by quantitative descriptors was not possible because the particles are oriented randomly in the horizontal and the appearance is affected by the airflow around the probes.
4. Case studies
a. ICE-T and RF05
We have examined in detail a unique case, RF05, on 11 July 2011, when four constant-altitude penetrations were conducted at successively lower temperatures as a single “chimney” cloud developed upward from +10° to −7°C (Fig. 8 and Table 4). A chimney cloud is a cumulus cloud that has much greater vertical than horizontal extent. These clouds were largely isolated and dynamically active so that the primary ice particles could be identified as the cloud developed upward.
Photograph of chimney cloud penetrated at 1849:49 UTC 11 Jul during ICE-T. The temperature was −1.7°C, peak vertical velocity reached 3.5 m s−1, and the cloud was 600 m across.
Citation: Journal of the Atmospheric Sciences 71, 12; 10.1175/JAS-D-14-0093.1
Summary of chimney cloud penetrations.
An FSSP (<50 μm) was used to characterize the droplet size distribution and liquid water content, and the NCAR fast 2D-C and 2D-P were used to characterize the particle size distributions and to identify the early ice. Four penetrations into the chimney cloud, at approximate temperatures of +7°, −4°, −6°, and −7°C, were found to be suitable for analysis (Fig. 9a). Eventually, by the time of the fourth penetration, this chimney cloud had merged aloft with several other cells. Vertical velocity peaked at 6, 4, 13 and 15 m s−1 (Fig. 9b). Weak, compensating downdrafts were noted on the edges of the clouds. Peak droplet concentrations fell in the range of 100–200 cm−3 (Fig. 9c).
Data summary for the four penetrations into chimney clouds during RF05. (a),(b) The times of the passes are shown, with the durations of the penetrations (s) at the top of each panel, and the dotted vertical lines are the breakpoints between penetrations: (a) temperatures; (b) vertical velocities; and (c) FSSP concentration and liquid water content. In (c), the numbers shown along the lower axis are the relative time and are shown for reference.
Citation: Journal of the Atmospheric Sciences 71, 12; 10.1175/JAS-D-14-0093.1
Examples of 2D-C probe images from the supercooled cloud regions sampled illustrate important points related to ice production (Fig. 10). Along the cloud edges, in the weaker updrafts (indicated in each panel), there is strong evidence of droplet freezing and fallout of the particles (Figs. 10b,d). The drops are relatively small in the strong updraft cores (Fig. 10c) and, over the temperature ranges considered (−3° to −7°C), there is little evidence for secondary ice production. Penetrations 1–3 were made directly at cloud top.
Example 2D-C images from three of the penetrations into chimney clouds: Cloud (a) 2, (b) and (c) 3, and (d) 4. The title for each panel shows the penetration number and the range of times considered. Within each panel, each strip represents images obtained within the second noted at the left of the panel, with the span between the top and the bottom equal to 800 μm. The associated temperature and vertical velocity is also listed.
Citation: Journal of the Atmospheric Sciences 71, 12; 10.1175/JAS-D-14-0093.1
The median values of the concentrations of particles 50 μm and above in the updrafts are 2.5, 1.3, 3.5, and 2.7 L−1 for penetrations 1–4, respectively (not shown). Higher concentrations of particles of these sizes are found in the downdrafts, about 8 L−1. The generation of these concentrations required ~32 min.
Given that the ice diffusional growth rates are on the order of 3–5 μm s−1 (observed in laboratory experiments at these temperatures), needle crystals marking secondary ice production should be rapidly detectable from the 2D-C imagery. We conclude that secondary ice production has not yet begun or is weak. The spherical ice that is readily observed—500 μm and above—must be the result of drop freezing. The concentration of the large drops in the +7°C penetration is about one-half of the concentrations of the 500-μm and larger drops and ice observed in penetrations 3 and 4 at about −6°C, and, although we did not resample the same chimney cloud, growth of the smaller frozen drops through accretion following freezing into the >500-μm range can readily account for this increase.
b. NAMMA
The NAMMA case analyzed herein was a mesoscale convective complex forming in a sheared environment in the vicinity of the ITCZ. The freshest updrafts were observed on the upshear side of the cloud. The updrafts were long lived, as observed from successive DC-8 penetrations and the onboard downward-viewing, two-wavelength Doppler radar. The updraft persistence facilitated the interchange and interaction between the individual convective elements. The trajectories of frozen drops and graupel, as well as any secondary ice produced, could propagate downshear through the much-longer-lasting cloud system.
Multiple convective cells form and interact in the N1 case. Vertical radar profiles of the N1 cloud system clearly showed the shear-imposed organization of the cloud system: upshear to the north and downshear spreading of the anvil and buoyancy spent cells to the south (Fig. 11).
Time plot of the radar imagery obtained from the two-wavelength Jet Propulsion Laboratory (JPL) Airborne Second Generation Precipitation Radar (APR2) during penetration into cloud system sampled on 20 Aug 2006 during NAMMA. The distance flown in each panel is about 50 km. Shown are the reflectivities at (a) Ku and (b) Ka bands, (c) the linear depolarization ratio at Ku band, and (d) the Doppler velocity at Ku band. Figure courtesy of Simone Tanelli, JPL.
Citation: Journal of the Atmospheric Sciences 71, 12; 10.1175/JAS-D-14-0093.1
To illustrate the locations and conditions in the cloud where secondary ice was observed, we have chosen a cloud transect that includes the important temperature range around −7.5°C (Fig. 12a). Even though the transect did not sample the absolutely strongest updraft core, it illustrates the salient features of secondary ice evolution in the context of the vertical velocity structure (Fig. 12a). The transect includes 152 s in cloud, covering a distance of 28 km. The distribution of LWC derived from the CAS PSDs across the transect are plotted in Fig. 12b.
Observations during penetration at a temperature of about −7°C into cloud system sampled during NAMMA. (a) Vertical velocity (left ordinate) and temperature (right ordinate), (b) the LWC from the CAS, and (c) number of needles and columns per second (see text) as a function of time. (d) Number of needles and columns per second as a function of the vertical velocity.
Citation: Journal of the Atmospheric Sciences 71, 12; 10.1175/JAS-D-14-0093.1
Beginning with the entry into this cloud complex, small to medium graupel are ubiquitous, probably lofted and transported from an updraft feature. There were distinct regions of particles >500 μm, almost all graupel, interspersed between, distinct from, and in close proximity to the regions of high concentrations of needles and/or columns (presumably secondary ice), as identified by eye using a size threshold of approximately 100 μm in maximum dimension and an aspect (length to width) ratio of at least 2. We counted all such images for each second of data (Fig. 12c). These were done independently by both authors, and then the results were compared. The results of each of the authors were rarely needed to be modified. Examples of these images are shown later. The graupel size in these regions is generally large (>1 mm). The imaged graupel often exhibit bumps on their surfaces. Some of the most prolific occurrences of secondary ice are at a CAS LWC > 1 g m−3 (Figs. 12b,c).
Figure 12d shows the vertical winds measured where the secondary ice was observed on this cloud transect. In this figure, the number of secondary ice images observed in a sample of image data for each second is plotted as a function of updraft velocity on the abscissa. There are a few observations at w > 4 m s−1, but the preponderance of the observations of high secondary ice particles is found at <4 m s−1, mostly at <2 m s−1 and into the downdraft.
5. Discussion
In this section, we describe the early and developing stages of ice during ICE-T. The horizontal extent and duration of the NAMMA cloud system sampled, as well as the sampling direction along the direction of shear, allows us to evaluate secondary ice production from initial through late stages in updraft parcels. We further document where the secondary ice of at least 50 μm is found in these clouds.
The number of seconds of in-cloud sampling where the updrafts were greater than 2 m s−1 for ICE-T and NAMMA are listed in Table 5. At a temperature of 0°C and pressure of 500 hPa, the 2–4 m s−1 range can suspend 0.4–0.8-mm drops; the 4–6 m s−1 range, 0.8–1.1-mm drops; and the 6–8 m s−1 range, 1.1–1.5-mm drops. Therefore, the ICE-T and NAMMA updrafts were fully capable of lofting or suspending 0.5- and 1-mm drops to the H-M zone. However, Table 5 suggests that lofting or suspending of drops larger than about 1.5 mm would have been unlikely, at least for the updrafts we sampled.
Summary of updraft regions penetrated within or just above Hallett–Mossop zone.
To further evaluate whether lofting of large drops was possible, we derived the maximum diameter Dmax of each 1-s PSD from the combination of the fast 2D probe and the wide-head 2D-P probe for ICE-T and the CIP and narrow-head PIP probes for NAMMA. Postprocessing removed obvious artifacts where there were fewer than three particles in a size bin, and there were no particles in several smaller size bins; but these criteria or the probe sample volumes themselves may have limited our detection of the largest particles. In the >2 m s−1 updrafts and at temperatures 0°C and above, almost no >1-mm drops were observed, but some were observed for NAMMA (Figs. 13a,b,f). The factor of 5 larger sample volume of the large particle probe for ICE-T compared to that for NAMMA makes us question the latter results, but it could either be the result of particles falling through the updrafts or collisional breakup and regrowth in the much longer lasting NAMMA clouds. In the ICE-T updrafts >2 m s−1 and where the temperatures were between 0° and −5°C, the largest particles, mostly drops, were primarily 1 mm or smaller (Fig. 13c). The drops in the updrafts at temperatures colder than −5°C (Figs. 13d,f) presumably had frozen and developed into graupel and rimed particles, and the needles produced larger aggregates.
Frequency distributions of the largest particle size observed for each 1-s PSD, grouped into temperature categories listed at the top of each panel for (a)–(d) ICE-T and (e),(f) NAMMA. In each panel, the distribution of points for all vertical velocities and for vertical velocities > 2 m s−1 are plotted.
Citation: Journal of the Atmospheric Sciences 71, 12; 10.1175/JAS-D-14-0093.1
Let us assume that the ice nucleation process is via immersion freezing, given the long time scales for contact nucleation. There are few 1–1.5-mm drops relative to 0.5–1-mm drops; at temperatures above 0°C and in the updrafts with velocities 4 m s−1 and above, the median ratio of the concentration of 0.5–1-mm drops is 2.2 and of 0.5–1.5-mm drops is 3.4. The volume of a 0.5-mm drop is only 12% of the volume of a 1-mm drop. Thus, the most likely combination of drop concentration and drop volume would peak at some size between 0.5 and 1.0 mm. Future studies should examine where the peak in the distribution of total drop volume with size at temperatures near −5°C is found.
The initial ice particles are therefore likely to be 0.5–1-mm frozen drops. There is considerable evidence from the 2D probe (fast 2D and 2D-S) images that many of these frozen raindrops shatter upon freezing. These images display flat (cleaved) edges and/or a semicircular shape. Most experiments on freezing drops do not find fracturing upon freezing. Obviously, this could not have occurred in the H-M secondary ice experiments, as the rotating rods replicating the frozen drops (graupel) certainly could not have fractured upon freezing. Similar experiments but for freely falling, suspended drops are clearly needed.
The freezing and frozen drops are carried upward into the H-M zone and eventually become graupel capable of producing secondary ice. The time required for the frozen drops to fully freeze and the resultant latent heat release from their riming delay their immediate production of secondary ice. The surface temperature of the frozen drops must reach −3°C or below for secondary ice production to commence (Heymsfield and Mossop 1984). These factors, which depend on the specifics of the sizes of the frozen drops, the liquid water content, and updraft velocity, together with the time required for a secondary ice particle to reach a size detectable by the aircraft instrumentation, imply that the temperature in an updraft probably must reach several degrees below −3°C before we would detect secondary ice particles. Furthermore, this all takes place in a layer encompassing the H-M zone (−3° to −8°C). Thus, in these important convective clouds that are ubiquitous in tropical and near-tropical ocean bands of the globe, the secondary ice process is operating, since the lengthy process of nucleation and vapor growth of an ice crystal to a size of several hundred micrometers, at which it can rime efficiently is instantaneously circumvented. At temperatures −5°C and below, the largest particles in the updrafts are several millimeters or larger and are almost all graupel or aggregates of needles, mostly rimed.
Figure 14 shows the difference in the velocity of the updraft (for w > 2 m s−1) and velocity of a particle of diameter Dmax (ΔV) as a function of the observation temperature, using the Dmax values (Fig. 13) and assuming that all particles are liquid drops and are falling at the temperatures and pressures of the observation. This is an obvious overestimate for any of the particles which are ice but it serves as a first approximation to the particle fall speeds. Also shown are the ΔV for drops of 0.5-mm diameter. The horizontal lines in Fig. 14 show examples of the range of ΔV experienced by particles from 0.5-mm diameter to Dmax in two example size distributions. What this shows is that, for typical PSDs, many of the larger particles remain at a constant temperature or altitude in the updrafts, in the H-M zone.
Differences between the air vertical velocity (when >2 m s−1) and the velocity of a drop of the maximum diameter of each PSD for the temperature and pressure level of the observation (blue symbols): (a) ICE-T; (b) NAMMA. Also shown are the differences for drops with diameters of 500 μm. The horizontal line in each panel is used to illustrate the range of differences for drops with diameters of 500 μm to the largest observed.
Citation: Journal of the Atmospheric Sciences 71, 12; 10.1175/JAS-D-14-0093.1
We now examine the residence time of these rising raindrops and freezing and frozen drops in updrafts from −2° to −11°C. This entire layer is about 1500 m (ΔZ) thick in parcels rising in unmixed regions, and the secondary ice layer from −3° to −8°C is a layer of about 1000 m deep contained within this layer. For the sake of argument, we will examine the time (t) required for the range of raindrop sizes to traverse (rise through) a 1000-m layer at a velocity of the updraft velocity w and for a drop of diameter Dmax with a terminal velocity Vt, given by t (s) = (ΔZ /[w (m s−1) − Vt (m s−1)]: that is, the residence time of rain drops in the layer. Of course this assumes a steady state w or at least a quasi-steady updraft structure, which is not strictly true because the cloud is a very active, dynamic changing entity. Even though the structure is not steady state the w distributions are quasi stable, and the lifetime of the updrafts vertically transporting the raindrops probably have a lifetime on the order of at least 600 s (10 min). Thus, when w approximately equals the raindrop terminal velocity (Vt), the vertical motion is very slow (essentially stationary with height) but the particles move laterally downshear, and those sizes of hydrometeors have a very long residence time in the layer. The median residence times using the measured updraft velocities from the −2°C transect are 133 s for 0.3-mm drops and 500 s for 1.8-mm drops. The data of this study show that this is probably a very common occurrence in this cloud. The same basic scenario undoubtedly occurs in nearly all tropical maritime convective clouds. Note that raindrops are moving up only in the active convective updraft regions of the cloud. Also note that the collisions of the large hydrometeors with smaller cloud particles (riming, or accretion) continues as a function of Vt, even though the large hydrometeors are stationary in space.
We now summarize the cloud updraft velocities and microphysics where secondary ice particles were observed. For ICE-T, there is a preference for needles to be observed at temperatures from −6° to −8°C, but they are found throughout the range −3° to −14°C (Fig. 15a). The red curve in the figure indicates that there was no preferential sampling temperatures to bias this interpretation. Quite surprisingly, needles were observed predominantly where the vertical velocities were in the range from −1 to 1 m s−1 (Fig. 15b). It is not likely that the sample size in the figure biased this interpretation as there would have been an ample number of periods when sampling was conducted in each vertical velocity interval (red curve). It is interesting to note that needles are observed primarily in weak downdrafts in the warmest temperature intervals and in weak updrafts at the lowest ones, suggesting that they are transported from the primary zones of secondary ice production (Fig. 15c). The LWCs in the regions where secondary ice particles are observed are dominantly below 0.10 g m−3, even though sampling occurred throughout a wide range of LWCs (as indicated by the number of samples per interval; not plotted) (Fig. 16a). Median LWCs in these regions are only about 0.03 g m−3 with no obvious dependence on the temperature (Fig. 16b). The average droplet concentration is consistent with the low LWCs, averaging only a few per cubic centimeter (Fig. 16c). These are very surprising results given that the H-M effect is thought to involve droplet accretion. Within regions of secondary ice, ice concentrations are generally tens per liter (Fig. 16d).
Summary of general features of regions penetrated during periods when needles were observed during ICE-T. For those periods when needles are observed, the distribution of fractional occurrences observed within (a) a 1°C temperature range and (b) a 1 m s−1 vertical velocity range. (c) In regions where needles are observed, the vertical velocity as a function of temperature. For reference, the terminal velocities of drops of different diameters are shown as a function of temperature, with temperature and pressure derived from the U.S. Standard Atmosphere, 1976.
Citation: Journal of the Atmospheric Sciences 71, 12; 10.1175/JAS-D-14-0093.1
Summary of microphysics during sampling of needle regions: (a) distribution of the LWC and (b) LWC dependence on temperature. Note that 0.01 g m−3 has been added to the LWC to enable plotting on a log scale. (c) FSSP concentration as a function of temperature and (d) 2D probe concentration of particles >125 μm as a function of temperature. Median values are shown in each panel.
Citation: Journal of the Atmospheric Sciences 71, 12; 10.1175/JAS-D-14-0093.1
The limited number of periods where secondary ice particles are observed for NAMMA precludes an analysis similar to ICE-T, but meaningful results are nevertheless obtained. For temperatures with appreciable number of needles and columns, as defined where there were at least five such particles in the CIP data per second, the average concentration was high, about 100 L−1 (Fig. 17a). Vertical velocities were primarily in the range −2 to +2 m s−1, with a median value of 0.5 m s−1 (Fig. 17b). The liquid water contents and droplet concentration are higher than for ICE-T, averaging about 0.4 g m−3 and 120 cm−3 (Figs. 17c,d).
Summary of observations of secondary ice occurrence during NAMMA. Concentration of CIP particles >125 μ as a function of (a) temperature, (b) vertical velocity, (c) the CAS LWC, and (d) the CAS concentration.
Citation: Journal of the Atmospheric Sciences 71, 12; 10.1175/JAS-D-14-0093.1
6. Conclusions
In both the ICE-T clouds and the NAMMA cloud system, initial ice production is likely through the freezing of 0.5–1-mm raindrops. These are the drop sizes that can be carried upward to the H-M zone by the updrafts in these clouds. All large raindrops are either frozen by the time parcels traverse the layer from −2° to −11°C, or they do not make it through the layer because the updrafts are not strong enough to carry them through that temperature range. The concentrations of this primary ice are on the order of 1–2 L−1, close to the likely concentration of raindrops with D > 0.5 mm arriving at the freezing level in the stronger updrafts of an average of 1.2 L−1. There is evidence of fracturing of the drops upon freezing. Although these probable one to two satellite ice particles do not explain the observed (presumably secondary) high ice concentrations in more aged cloud parcels, it is a topic needing further investigation. From the observations, it is extremely difficult to identify which processes other than the H-M process can explain the observations. It is very likely that one or more processes are active, but the H-M process can account for much of the secondary ice. Realistic laboratory experiments of the freezing of millimeter raindrops are clearly needed to make further progress on identifying the dominant mechanisms.
Many cloud parcels observed between −2° and −11°C in the ICE-T clouds and in the NAMMA cloud system display evidence of secondary ice. Almost all of the updrafts >2 m s−1 observed in both experiments met the conditions required for production of secondary ice by the H-M riming–splintering mechanism.
In both experiments, but particularly in ICE-T, the observations of high concentrations of secondary ice particles occur in cloud parcels with low measured updraft speeds, low liquid water contents, and low concentrations of supercooled cloud droplets. These cloud vertical and microphysical conditions await further clarification in future laboratory and modeling studies.
The observations of high concentrations of secondary ice are nearly always in close spatial proximity to more active parcels with significant concentrations of medium to large graupel, but they are not precisely in these parcels. A possible explanation for these important observations comes from the laboratory experiments of Mossop and Wishart (1978). They found that, as the target velocity increases, secondary ice production during riming decreases relative to the numbers of drops accreted. They explained this by suggesting that a drop that impacts onto an ice surface at a high velocity is more likely to spread out on this substrate and thus not create a fractured shell than if the droplet lands lightly on the substrate. Thus, as we found here, the low liquid water content–low vertical velocity regions, with drops of 0.5–1 mm, may be the most favored regions for ice multiplication. Laboratory experiments on suspended frozen drops are needed to further examine why the most copious secondary ice particles are observed in the weaker updraft–low LWC–low droplet concentration regions.
Another very important component of the generation of secondary ice from growth on the surfaces of the graupel or lightly rimed particles, in particular rimed aggregates, must be considered in laboratory experiments. At the surface of the graupel, growing through accretion and/or diffusion in the updrafts, the temperature is above the ambient temperature, because of latent heat release upon freezing (Heymsfield 1983). When any spicule forming on the surface grows out of the particle’s boundary layer, it can grow very rapidly—much faster than those in the Ryan et al. (1976) experiments of ~0.15 μm s−1 [and perhaps even approaching those observed in the Knight (2012) laboratory experiments of ~2 μm s−1]—because its growth rate is enhanced by ventilation owing to the 5+ m s−1 fall speed of the graupel. This spicule can then dislodge from the parent moderate to heavily rimed ice particles, because of either the mechanical force on it or ice particle–ice particle collisions or because the junction of the graupel and feature sublimates because the surface temperature of the graupel is subsaturated with respect to ice. This calls into question whether secondary ice particle production is directly related to the concentrations of small and large droplets that are accreted on an ice particle or whether the process is most prolific with intermediate concentrations of these droplets. Laboratory studies that take this possibility into account are needed to guide future parameterizations of the process in models.
A key finding in this study is that the frozen drops and graupel can loiter within the secondary ice production zone for considerable periods because their net fall speeds up or down through the layer are very low, allowing for a long residence time. This process has been suggested in an earlier study (Lamb et al. 1981). We found this to be the case for the NAMMA sampling, and it is likely to be a feature of tropical maritime convection in general. This conjecture is supported by G. M. Heymsfield et al. (2010), who presented airborne Ku-band Doppler radar–based observations of the vertical motions in tropical and subtropical deep convection. The storms used in that analysis had to reach a height of at least 12 km and a reflectivity at those levels of at least 20 dBZ or, alternatively, the updrafts anywhere in the vertical column as deduced from the Doppler radar measurements had to reach 10 m s−1 or greater. For each updraft crossing, the maximum updraft velocity and radar reflectivity were derived. From the original dataset kindly provided by G. Heymsfield, Fig. 18 plots the vertical distributions of vertical velocity for oceanic deep convection. Also shown in Fig. 18 are updraft velocities measured by the University of North Dakota Citation aircraft in convective clouds sampled from Kwajalein, Marshall Islands, during the Kwajalein Experiment (KWAJEX). Because these clouds tended to be shallower than the more intense convective clouds measured by the radar, mean and maximum updrafts were weaker. These observations indicate that, in the H-M zone, between about 5 and 7 km, mean updraft velocities are below 8 m s−1, enough to slowly loft or suspend a 1.5-mm raindrop. Once frozen, the particle will slow down somewhat because its cross section changes from oblate to conical or more spherical but its terminal velocity will only slightly decrease and increase again because of its riming. Radar reflectivity data, also reported in the G. M. Heymsfield et al. (2010) study, support the view of a graupel “accumulation zone” just above the 0°C level in updrafts suggestive of the location of suspended frozen drops.
Mean and standard deviations of (a),(b) the vertical velocity and (c),(d) reflectivity based on the nadir-viewing Doppler radar observations of G. M. Heymsfield et al. (2010), for tropical and subtropical (left) land- and (right) ocean-based convection. The radar beamwidth is approximately 0.7 km at about the 5-km (~0°C temperature) level. The shaded regions show the standard deviations. Also shown are the mean and maximum updraft velocities (for w > 2 m s−1) observed during the KWAJEX field program [data kindly provided by Nickolas Anderson of the National Science Foundation (NSF), based on Anderson et al. (2005)].
Citation: Journal of the Atmospheric Sciences 71, 12; 10.1175/JAS-D-14-0093.1
Acknowledgments
We particularly wish to acknowledge Aaron Bansemer for processing the C-130 aircraft data and the NCAR Aviation Facility and the National Science Foundation for supporting the aircraft measurements. The authors wish to thank Gerry Heymsfield, Nick Anderson, Simone Tanelli, and Paul Lawson for use of their original data. The comments by anonymous reviewer 2 greatly improved this manuscript. Technical editing by Meg Miller is greatly appreciated.
APPENDIX
Estimates of the Growth Times from Initiation Required for Detection by the Imaging Probes
It is important to address the question of what particle sizes we are capable of measuring with our imaging probes and what growth times are associated with those sizes. We have performed calculations of these times as a function of growth temperature. We assume that the critical dimensions for detection of columns and needles is 100 μm long and 50 μm wide or 200 μm long and 50 μm wide. For hexagonal plates, these dimensions are 100 μm wide and 50 μm thick or 200 μm wide and 100 μm thick. For simplicity, we will also assume growth is at water saturation, by diffusion and not accretion, and that growth is at a constant temperature. Although this is an overly simplistic estimate given that the updrafts of 10 m s−1 for 200 s corresponds roughly to a change in temperature of 12°C, by calculating growth over a wide range of temperatures we can provide some estimate of this error. We further assume that the growth rates, aspect ratios, and densities of Ryan et al. (1976) can be applied to our situation by enhancing the growth according to the ratio of the water vapor diffusivity at 500 hPa to that at 1000 hPa, as suggested by ice particle growth rate theory. Our more detailed calculations, based on theory as in Westbrook and Heymsfield (2011), produce approximately this enhancement. Also, as suggested by those authors, the ventilation coefficient (enhanced growth due to ventilation) is approximately 1. If anything, this coefficient is underestimated, which would in reality reduce these times. As shown in Fig. A1, for crystals that are growing primarily in the −3° to −8°C range, critical growth times are somewhere between 100 and 200 s. Of course, since many various scenarios are possible—a range of vertical velocities, liquid water contents, relative humidities, crystal shapes, sizes of the frozen drops, fallout, transport through varying vertical velocities, and liquid water contents—we acknowledge that these simple calculations provide only a rough guide.
Calculated dimension of ice crystals growing at a constant temperature [between −3.7° (top left) and −12.2°C (bottom middle)] and pressure (500 hPa) as a function of growth time. (a)–(e) The width and length are shown, along with symbols indicating the time where the crystals reach a minimum and maximum dimensions of 50 and 100 μm and of 100 and 200 μm. (f) The time required to reach those sizes is plotted as a function of the growth temperature.
Citation: Journal of the Atmospheric Sciences 71, 12; 10.1175/JAS-D-14-0093.1
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