The impact of ice clouds on weather and climate is a function of ice particle shape through light scattering properties and cloud lifetime through ice particle sedimentation rates. Many weather forecast and climate models use two categories to represent ice cloud particles: cloud ice and snow, though the distinction between particle categories is generally without observational justification. Improved characterization of cloud ice and snow as well as the transition between them will make models more realistic. An analysis of particle imagery data from high-resolution aircraft particle imaging probes indicates that atmospheric ice particles can easily be separated by particle complexity. In this work, a technique is described which enables the clear separation of vapor grown particles from aggregates of particles. When applied to two example data sets, the technique shows that the separation between these categories occurs at 150 and 250 microns, for two example data sets.
Many weather forecast and General Circulation Models (GCMs) categorize most ice particles in clouds as either “cloud ice” or “snow.” Cloud ice is characterized by small particle sizes and pristine hexagonal shapes which have an assumed terminal velocity of zero. Snow consists of larger particles, often complex aggregates, which are modeled to have a terminal velocity, enabling them to gravitationally settle. Morrison and Grabowski  stated that the transition between different modeled particle types is difficult to identify in natural clouds. Waliser et al.  point out that though cloud processes in GCMs have become more sophisticated in recent years in their treatment of ice particles, these improvements have been largely independent of measurements. This study aims to demonstrate a method to more accurately categorizing the transition between cloud ice and snow using aircraft particle observations in a way that will be useful to the modeling community.
To understand the separation of cloud ice and snow, it is important to understand how cloud particles grow in the atmosphere. Early laboratory studies have shown that ice crystals grow at predictable rates under controlled temperature and humidity conditions [Ryan et al., 1976]. In natural clouds, once ice particles have formed, they can sediment or be transported by vertical winds through wide temperature and humidity changes. As vapor grown particles possibly of pristine shapes, these particles would be considered to be cloud ice. Once cloud ice particles grow to a sufficient size, differential sedimentation rates lead to particle aggregation and riming (in mixed phase clouds) which can produce highly irregular shapes [Ono, 1969] that would be classified as snow. Though the processes leading to these complex shapes are fairly well understood, most cloud modeling techniques have not advanced sufficiently to include these growth processes. The technique of autoconversion is used to transition cloud ice into snow in models.
Observations in natural clouds indicate that complex particle shapes are common. Korolev et al. , using high-resolution imagery from the SPEC Inc. Cloud Particle Imager (CPI) probe [Lawson et al., 2001], found that only 3% of Arctic ice cloud particles were pristine. In contrast, Stoelinga et al.  pointed out that aggregates of ice crystals often included components that can be readily classified using the Mogono and Lee  classification scheme. The reader is cautioned that “pristine,” the terminology used in the Korolev et al. paper, and “readily identifiable,” the terminology used by Stoelinga et al., are not synonymous. The Mogono and Lee  classification scheme referenced by Stoelinga et al.  contains 80 particle types, yet many of those types are quite complex, while Korolev et al.  only classify four vapor grown habits (plates, columns, needles, and dendrites).
Cloud ice and snow have substantially different dimensional characteristics which lead to different radiative and fall speed behaviors. The dimensional characteristics of pristine crystals can be characterized by the relationships presented in Ryan et al.  as well as characteristics implied by the capacitance model [Westbrook et al., 2008]. As particles grow by vapor, their densities are generally low, given that either one or the other axis of the hexagonal crystal is dominant in growth, leading to either thin plates or long columns. Here, density is defined as the ratio of the mass of the particle to the mass of a spherical water droplet with the same maximum dimension. The low density of these shapes leads to terminal velocities low enough to be considered negligible for modeling studies. As cloud ice transitions to snow through aggregation, there can be a significant discontinuity and increased uncertainty in the dimensional characteristics of the cloud particle population. The growth process is further complicated in mixed phase clouds where riming can occur. Ono  showed that the occurrence of riming is much more common in particles larger than 150 microns. A better understanding of the transition between cloud ice and snow is important for accurate application of dimensional characteristics in models.
For modeling purposes, the dimensional characteristics of atmospheric ice cloud particles are often described using power law relationships. Power law relationships are commonly used to describe particle mass and projected area relationships with size [Heymsfield et al., 2010; Mitchell, 1996] as well as particle terminal velocity [Mitchell, 1996]. Power law relationships have been shown to predict particle mass and projected area well in size ranges where particles are fractal in nature [Schmitt and Heymsfield, 2010], yet single crystals and aggregates of just a few crystals are not fractal. An inherent problem with power law relationships is that the smallest particles are often assigned the dimensional characteristics of ice spheres leading to large errors, especially in particle mass. As an example, if the frequently used Brown and Francis  is applied to particles smaller than 80 microns, it predicts masses higher than that of ice spheres. Using an appropriate particle size cutoff between particle populations reduces the likelihood of this affecting results.
In this paper a recently developed technique to separate ice particles by complexity using high-resolution aircraft microphysical instrumentation is described. The complexity of particles is related to their formation mechanism, either vapor growth or aggregational growth, and while the separation of particles by complexity does suggest that the two different categories be treated differently with respect to mass and area dimensional relationships, this separation may not always be ideal for modeling purposes. In section 2, we show how ice particles can be separated by complexity using high-resolution ice particle imagery. Section 3 will show the results of the separation scheme for two example data sets. In section 4, uses of the separation scheme are discussed.
2 Data Analysis
The visual appearance of cloud ice particles, typically single crystals often recognizable pristine shapes, and snow, often aggregates of smaller particles, makes it straightforward to visually differentiate the two categories of atmospheric ice particles. To investigate the image characteristics that would be useful in separating particle types, a data set of theoretical pristine ice crystals and aggregates of ice crystals was created. The theoretical crystal aggregation program developed for the Schmitt and Heymsfield  study was used to create two-dimensional images of theoretical single crystals as well as aggregates of up to 15 component hexagonal crystals at random orientations. The program simulates aggregation by first creating a seed crystal, then randomly introducing additional crystals into the nearby space. Differential terminal velocities are assumed leading to the particles contacting, at which point their position with respect to each other is frozen. For each aggregate created, the component crystals are modeled as perfect hexagons with aspect ratios ranging from 5:1 (columns) to 1:5 (thin plates). Small modifications in particle orientation based on computational fluid dynamics calculations are made to account for preferential fall orientations. While this program may not accurately duplicate the in-cloud particle aggregation process, it serves to create representative images of multiple particles aggregated together. Processes not considered include the aggregation of aggregates as well as a rigorous treatment of the aerodynamic effects of a very large particle with a substantially different terminal velocity than the particles being swept up. Both these effects involve large snow particles which are unlikely to be classified as cloud ice. Two-dimensional images of the theoretical particles in random orientations were processed using a suite of routines used on aircraft probe imagery data to calculate various characteristics (maximum dimension, projected area, perimeter, etc.). From these data, a unitless parameter representing the complexity (C') of the particle was derived (equation (1)).
where A is the particle projected area, ar is particle area ratio (defined as the ratio of the particle projected area to the area of the smallest circle that will cover a two-dimensional image of the particle), and P is the perimeter of the image of the particle. The components of the compactness parameter are chosen so that the result is unitless. The area and perimeter values lead to a measure of how convoluted the perimeter of the particle is with respect to area, and the square root of the area ratio was found empirically to remove any dependence on area ratio. In order to be more intuitive, we hereafter define complexity (C) as shown in equation (2).
Complexity as defined in equation (2) is more intuitive in that increasing complexity is represented by higher values and the scale is at a more reasonable level. When applied to the data set of theoretical particles, a clear cutoff was apparent between single pristine particles and aggregates with two or more components. Figure 1a shows complexity plotted versus particle size for the theoretical particles and particle aggregates. Stars represent individual particles, while dots represent aggregates of two or more hexagonal crystals. Particle maximum dimension for the theoretical particles is estimated by assuming that the component crystals are roughly 100 microns in maximum dimension, though this value is arbitrary and was chosen to facilitate easy comparisons in the figure. The complexity value for single theoretical crystals never reaches a value of 0.4, while for aggregates, there are few particles with complexity values that are low. Figure 1b shows the same data set with complexity plotted versus particle area ratio. This comparison is made to show that C does not have a strong dependence on area ratio, meaning that a thin column and a thin hexagonal plate would both be classified as pristine independent of viewing orientation.
To demonstrate the utility of the complexity calculation, we use it to identify pristine and complex ice particles imaged by the CPI probe. Data from the CPI probe have an image resolution of 2.3 microns per pixel. This resolution is reasonable for determination of particle dimensional characteristics such as area and aspect ratio for particles larger than 35 µm [Korolev and Isaac, 2003]. For demonstration purposes, the complexity of CPI images from the 16 July 2002 Cirrus Regional Study of Tropical Anvils and Cirrus Layers-Florida Area Cirrus Experiment (CRYSTAL-FACE) flight has been plotted versus particle maximum dimension in Figure 1c. As can be seen, particles smaller than approximately 100 microns generally have values of C < 0.2. Figure 1d shows the complexity plotted versus particle area ratio analogous to Figure 1b for the theoretical data. In general, the complexity values are lower for the CPI particles than they are for the theoretical particles (specifically, note the high area ratio end of plots 1b and 1d). This is likely due to the way the perimeter is calculated in relation to the image resolution. It is important to note that the perimeter measurement is not a universal measurement in that it is image resolution, focus, and measurement technique dependent. When attempting to apply this technique to different data sets, it is important to consider the perimeter calculation and how it affects the C value. Also, note that the theoretical limit of C for a perfect circle is C = 0.204 (determined from C’ = 1/4π). This value is asymptotically approached from above and below for the CPI images as the area ratio approaches 1.0.
Figure 2 shows example particle images from the CPI data sorted by their C values. Particles are shown with C values ranging from 0.15 (very pristine) to 0.45 (complex). Particles with C < 0.2 do not appear to have more than one component. A cutoff value of C < 0.22 (represented by the horizontal line in the figure) was chosen as a reasonable cutoff for separating cloud ice particles from snow particles for CPI observations. Figure 2 also shows some images of theoretical particles and aggregates of varying complexity generated by the aggregation program. Chance orientation might lead to a modestly complex particle being classified as cloud ice due to a component being hidden from view, but truly complex particles will have a complex appearance from any angle. For theoretical particles, this is shown in Figures 1a and 1b where there are some points representing aggregates with similar complexity values as the stars (single crystals). When the cutoff complexity value is optimized for the theoretical crystals, 10% of the single crystals were miss-classified as complex while 10% of the aggregates of two crystals were miss-classified as being single crystals.
3 Example Results
Applying this technique to atmospheric data sets demonstrates its utility in separating cloud ice from more complex particles. Results from two substantially different case studies from different cloud types are shown. The first example is from the Atmospheric Radiation Measurement (ARM) Intensive Operation Program (IOP) near the ARM Southern Great Plains (SGP) site in Oklahoma during March 2000. The goal of the campaign was to conduct aircraft observations of midlatitude ice clouds near the ARM SGP site. On 12 March 2000, a thick lower level ice cloud formed over the SGP site. The University of North Dakota (UND) Citation aircraft sampled ice cloud microphysical properties at temperatures ranging from −31°C to near 0°C [Heymsfield et al., 2002]. Ice particle observations showed that the cloud particles were mostly side planes or dendritic in shape. The second example is from the Cirrus Regional Study of Tropical Anvils and Cirrus Layers-Florida Area Cirrus Experiment (CRYSTAL-FACE) which took place in the summer of 2002. On the 16 July 2002 research flight, the UND Citation aircraft sampled anvil cirrus over Florida. Anvil cirrus was sampled in steps from the −15°C to the −50°C level (8000–12,000 m). CPI probe images showed that the large particles were generally highly complex aggregates with occasional small pristine ice appearing in the measurements as well.
The CPI probe, like other probes with inlets, is likely plagued by particle shattering problems [Korolev et al., 2011]. For this study, only particles imaged at the rate of one particle per frame are considered as they are less likely to be products of shattering. Since the sample volume of the CPI varies by particle size, results are presented in terms of the ratio of cloud ice versus snow particles for size ranges. Figure 3 shows the ratio of particles in 10 micron size bins which fell into the cloud ice versus snow categories. Figure 3a shows the result for the ARM IOP research flight, and Figure 3b shows the results for the CRYSTAL-FACE research flight. Note that the results do not show a clear step function, as there can be cloud ice particles at sizes in excess of 300 microns and complex particles smaller than 50 microns. The ARM IOP data were collected in a cloud containing higher concentrations of larger vapor grown plate-shaped crystals due to its relative warmth. This is easily seen in Figure 3a where larger cloud ice particles exist at sizes well above 500 microns. The CRYSTAL-FACE data set included fewer large cloud ice particles. The highly chaotic environment of low-latitude convective systems likely led to aggregation being the dominant growth process in that case.
We propose that the size range where the complexity value classifies the majority of particles being cloud ice particles to the majority of particles being snow is a reasonable cutoff between the two categories. Note that the cutoff size is different for the two data sets (~250 microns for ARM IOP and ~150 microns for CRYSTAL-FACE), reflecting their different growth and transport processes. The results from other data sets analyzed generally fell in between the two example cases shown here.
In this short article we have demonstrated a technique to separate single ice crystals from ice crystal aggregates using high-resolution aircraft microphysical data. Given the significant differences in particle properties, it is suggested that this separation is analogous to the “cloud ice” versus “snow” separation commonly used in models. Based on the results for the two example data sets, sub-150 or sub-250 micron particles are more likely to be pristine single crystals, while larger particles are more likely to be aggregates. These results show that there is a significant variation based on cloud type suggesting that further investigation would be advantageous. This separation of particles, based on their “complexity,” is useful in several ways. Power law relationships are typically used to describe the mass and area properties of ice cloud particles, yet they do not recognize the dual nature of natural ice crystals. Typical power law mass dimensional relationships necessitate that particles smaller than a certain size will have the mass and projected area of ice spheres. Generally, the spherical particle cutoff is smaller than the cloud ice cutoff suggested in this study. By treating cloud ice and snow with separate mass and area dimensional relationships, it should be possible to reduce or eliminate the uncertainty caused by the need to assume particles are spheres. Given that single crystals have much lower densities than spheres, improved characterization should lead to more realistic representations in models. Appropriate mass and area dimensional relationships should be used for both cloud ice and snow particle types and should be applied with an understanding of an appropriate size cutoff based on cloud type to reduce uncertainties.
A further use of this technique is the potential simplification of the calculation of electromagnetic scattering properties of ice clouds. Ice cloud radiative properties are calculated using either the scattering properties of a single particle habit or an assortment of particle habits. The fact remains that most of the theoretical particle shapes used in light scattering studies bear little resemblance to atmospheric ice cloud particles. Two exception would be Xie et al.  and Um and McFarquhar  who recently calculated the scattering properties of more complex aggregates of plate-shaped ice crystals. These studies showed that different configurations of plate-shaped crystals in the aggregates did not strongly affect the scattering properties. Iaquinta et al.  similarly showed that the scattering properties of bullet rosette-shaped crystals were not strongly dependent on the number or the orientation of the branches. The results of these studies suggest that the scattering properties of ice clouds could be simplified to a two-particle system with particle size being the separator. The scattering properties of a pristine shape such as plates or column could be used for the “cloud ice” fraction of the population, while a more complex aggregate or mixture of aggregates could be used for estimating the scattering properties of the “snow” portion of the cloud.
This work was partially supported by the NASA MACPEX project through grant (NNX11AC07G) Hal Maring, Program Manager, and NASA grant (NNX08AF81G) subcontract to the National Center for Atmospheric Research through the University of Wisconsin-Madison. Additional support was provided by the National Science Foundation's Center for Multi-Scale Modeling of Atmospheric Processes (CMMAP) managed by the Colorado State University under cooperative agreement ATM-0425247. The authors appreciate the useful discussions with Dr. Ping Yang of Texas A&M University, Dr. Bryan Baum of the University of Wisconsin-Madison, and Dr. Steve Platnick of the NASA Goddard Space Flight Center.
The Editor thanks two anonymous reviewers for their assistance in evaluating this paper.