Abstract

A reliable understanding of the microphysical properties of ice particles in atmospheric clouds is critical for assessing cloud radiative forcing effects in climate studies. Ice particle microphysical properties such as size, shape, and surface roughness all have substantial effects on the single-scattering characteristics of the particles. A recently developed ice particle probe, the Small Ice Detector-3 (SID-3), measures the two-dimensional near-forward light-scattering patterns of sampled ice particles. These scattering patterns provide a wealth of information for understanding the microphysical and radiative characteristics of ice particles. The SID-3 was operated successfully on 12 aircraft flights during the NASA Midlatitude Airborne Cirrus Properties Experiment (MACPEX) field campaign in April 2011. In this study, SID-3 measurements are used to investigate the frequency of occurrence of a number of ice particle properties observed during MACPEX. Individual scattering patterns (7.5°–23°) are used to infer properties of the observed particles as well as to calculate partial scattering functions (PSFs) for ensembles of particles in the measured size range (~5–100 μm). PSFs are compared to ray-tracing-based phase functions to infer additional properties of the particles. Two quantitative values—halo ratio and steepness ratio—are used to characterize PSFs. The MACPEX dataset suggests that most atmospheric ice particles have rough surfaces or are complex in nature. PSFs calculated for particles that were characterized as having smooth surfaces also appeared to more closely resemble rough crystal PSFs. PSFs measured with SID-3 compare well with those calculated for droxtals with rough surfaces.

1. Introduction

The optical characteristics of atmospheric ice particles are considered to be one of the largest sources of uncertainties in climate models (Liou 1986; Lynch et al. 2002). Wylie and Menzel (1999) showed that midlatitude regions are typically covered by high-altitude (defined as higher than 6 km) clouds approximately 30% of the time. Without considering the ability of climate models to predict the abundance and location of cirrus, the single-scattering characteristics of ice particles are also extremely uncertain. Recently, strong evidence has been advanced in the literature suggesting that ice particle surface roughness can significantly affect ice particle-scattering characteristics (Ulanowski et al. 2012; Neshyba et al. 2013; Schnaiter et al. 2016). The impact of ice particle surface roughness has been substantiated by many means. Using ice crystal analogs, Ulanowski et al. (2006) showed that similarly shaped particles could have substantially different asymmetry parameter values solely based on particle surface roughness (0.80 for smooth vs 0.63 for rough). This result suggests that nearly twice as much energy is reflected in the backward hemisphere by particles with rough surfaces when compared to similarly shaped smooth surfaced particles. A previous study (Yang et al. 2008) illustrates that the phase function is quite sensitive to the degree of particle surface roughness. Baum et al. (2011, 2014) and Cole et al. (2014) showed that polarimetric satellite retrievals across multiple wavelengths were best matched if particles were considered to have severely roughened surfaces.

The SID-3 particle measurements are useful for understanding ice particle single-scattering characteristics. The SID-3 is similar in design and operation to Small Ice Detector version 2 (SID-2), which is described in Cotton et al. (2010) and Johnson et al. (2014). Technical details on the SID-3 can be found in Vochezer et al. (2016). Both SID-2 and SID-3 have open paths to reduce the number of probe surfaces available for particle breakup—a common problem for instruments with inlets (Korolev et al. 2011).

SID-3 measurements appear as a broad annulus that is a measure of the scattered light from 7.5° to 23°. Forward-scattered light (less than 7.5°) is blocked by a dump spot in the optics. Scattering patterns of some pristine ice crystal shapes are easily identified as well as the 22° halo feature when present. The ice particle surface roughness can be estimated by analysis of the intensity speckles in the scattering patterns (Ulanowski et al. 2014; Schnaiter et al. 2016). This is done objectively using the gray-level co-occurrence matrix method (GLCM; Haralick et al. 1973) to infer a qualitative measure of the surface roughness or crystal complexity from the spatial variation of the scattering intensity across the speckled patterns (Lu et al. 2006; Ulanowski et al. 2014). Note that crystal complexity can include inclusions of nonice subparticles or air bubbles within an ice particle. We refer to the combined effects on a single crystal as roughness or rough to conform to previous literature where the combined effects are in question. Pristine hexagonal (plate or column) shaped crystals display scattering patterns that have four- or sixfold symmetry, making it possible to identify these simple shapes when oriented (Vochezer et al. 2016).

The SID-3 was flown on board the NASA WB-57 aircraft during the Midlatitude Airborne Cirrus Properties Experiment (MACPEX) field campaign, which was held in March and April 2011. During MACPEX, the NASA WB-57 aircraft flew 14 missions from Houston, Texas, sampling midlatitude clouds mainly over the continental United States and the Gulf of Mexico. A more detailed description of the MACPEX field program can be found in Jensen et al. (2013). The instrumentation on the WB-57 included multiple instruments for measuring the microphysical properties of ice particles as well as several water vapor instruments. This study reports on measurements by SID-3 during seven research flights, when SID-3 was operating well and with similar probe settings. Most of the flights during MACPEX were through either anvil cirrus or jet stream cirrus associated with intense spring storm systems which passed through the region during the project.

In this study, SID-3 data from MACPEX is used to better understand the microphysical and light-scattering characteristics of sub-100-μm atmospheric ice particles. Section 2 presents an overview of the MACPEX SID-3 measurements as well as results of microphysical properties determined from individual scattering patterns. In section 3 partial scattering functions (PSFs) are estimated for ensembles of particles with different scattering characteristics. In section 4, the PSFs are compared to ray-tracing calculations and a few special cases are explored. In the final section, the work is summarized.

2. SID-3 measurements during MACPEX

Figure 1 shows a diagram of SID-3 head as well as several example scattering patterns. The sampling volume is defined by the intersection of a 532-nm, 100-mW neodymium-doped yttrium–aluminum–garnet (Nd:YAG) laser beam perpendicular to the airflow, and the field of view of two photomultiplier detectors. When a particle passes through the sampling volume, coincident pulses from the two PMT detectors are used to trigger the main detector, an intensified CCD camera that captures an image of forward-scattered light. The sample volume rate is approximately 70 cm3 s−1 at an airspeed of 150 m s−1 (Vochezer et al. 2016). The SID-3 detector collects images of light scattered by particles in the sample volume, which are stored as 780 × 582 pixel images in either jpeg or tiff format. SID-3 can record scattering pattern images at rates of up to 30 s−1, which means that not all scattering patterns are imaged. During the MACPEX field campaign, typically 20 000–40 000 scattering patterns were saved per flight. The sample volume triggers provide a count of particles while the system is busy capturing and recording the scattering pattern. The characteristics of the probe enable the measurement of the scattering characteristics of particles from roughly 5 to 100 μm in size although the size range can vary significantly depending on the probe settings. Also shown in Fig. 1 are a number of example SID-3 scattering patterns. Note that the grayscale for the scattering patterns are inverted in this figure and all future figures to facilitate easier observation of details.

Fig. 1.

Schematic diagram of the front of the SID-3 probe indicating the principle of operation. The two PMTs detect a particle in the sampling volume, which then trigger the imager. Scattered light from the green laser is measured by the CCD camera detector. Several example scattering patterns are also shown.

Fig. 1.

Schematic diagram of the front of the SID-3 probe indicating the principle of operation. The two PMTs detect a particle in the sampling volume, which then trigger the imager. Scattered light from the green laser is measured by the CCD camera detector. Several example scattering patterns are also shown.

SID-3 operated successfully on 12 of 14 research flights during MACPEX. Here we present data from seven flights: 13, 14, 16, 18, 20, 21, and 26 April 2011. All of these days, except for 13 and 16 April, were associated with intense spring convective systems. The cases on 13 and 16 April were higher-altitude jet stream cirrus. The dates selected included the highest-quality data as well as data from days when the probe was operated with similar settings. SID-3 scattering patterns needed to pass two tests in order to be used as part of this study. Some SID-3 scattering patterns, particularly of larger particles, contain pixels that are saturated. No scattering patterns are included in the calculation if more than 2% of the pixels within the annulus were saturated. Spots created by halos, while likely saturated, normally did not account for 2% of the area of the scattering pattern. The second test was to eliminate the likelihood of scattering patterns of shattered crystals being included in the analysis. SID-3 records a “time of flight” (TOF) value, which is a measurement of how long the particle detector detected a particle in the sample volume. While SID-3 is an open-path instrument, there was evidence that some of the surfaces ahead of the sample volume could be sources of shattered particles (Korolev et al. 2011). Given the airspeed of the WB-57, it is easy to estimate how long a particle should stay in the trigger volume. TOF is measured in terms of clock counts, and given that the clock runs at approximately 48 MHz, one count is approximately 21 ns. With an aircraft speed of around 160 m s−1, the expected time of flight would be approximately 100 counts depending on the particle size. TOF counts exceeded 1000 approximately 10% of the time suggesting that shattering was occurring on a limited basis. Shattered particles were moving either much more slowly through the sample volume or the multiple particles in the detection volume were causing the particle to trigger for longer periods of time. SID3 does not record interarrival times (Field et al. 2003). Scattering function analysis (discussed later) strongly suggested that scattering patterns associated with high TOF values were significantly different from scattering patterns with expected TOF values. For all analysis presented in this article, scattering patterns with TOF values higher than 150 were eliminated. Time of flight errors led to the elimination of between 10% and 20% of all scattering patterns with a mean of 15.5% for the reported flights.

For each forward-scattering pattern measured by SID-3, numerous qualities can be discerned. Particle size, shape (pristine particles), and surface roughness (or small-scale complexity) can be identified. Some particles that produce halos as well as particles that are sublimating can also be identified. For this study, the particle size was estimated by using the forward-scattered light intensity. This technique is similar to that used during the analysis of data from other common light-scattering probes except that other scattering probes have only one detector rather than a charge coupled device (CCD) array detector. As this technique is known to have substantial uncertainty, the sizes reported herein should not be considered to be highly accurate.

Several simple particle shapes have distinctive scattering patterns when observed by SID-3 (Vochezer et al. 2016). Much of the shape information comes from information gathered with SID-3 in the Aerosol Interactions and Dynamics in the Atmosphere (AIDA) cloud chamber (Vochezer et al. 2016; Schnaiter et al. 2016). Surface roughness or particle complexity is determined from SID-3 measurements by the GLCM analysis of the speckled patterns visible in the SID-3 scattering patterns. Details on the implementation of the GLCM method in the SID-3 analysis, including a relation of the deduced complexity parameter to the physical crystal distortion or roughness, are given in Ulanowski et al. (2014) and Schnaiter et al. (2016). Briefly, the GLCM represents the statistical result of gray-level comparisons across the image for pairs of neighboring pixels with a fixed distance and direction (Lu et al. 2006). From the resulting GLCM, different features can be calculated, including the contrast, correlation, energy, and homogeneity (Haralick et al. 1973). Lu et al. (2006) investigated the correlation of the GLCM features to the physical roughness for laser scattering patterns from ground surfaces with defined roughness. They found that the energy feature gives the best correlation to the surface roughness. Moreover, they investigated the robustness of the energy measure for variances in the configuration of the measurement (e.g., laser power stability) and suggested an exponential fit to the energy feature for different pixel distances in the GLCM. The coefficient ke of this exponential fit was found to be the most robust measure of surface roughness. The same method (i.e., the calculation of the “complexity parameter” ke) was then applied to the SID-3 scattering patterns from small ice particles by Schnaiter et al. (2016). In that work, a threshold value of ke = 4.6 was defined that separates smooth from rough particles based on laboratory grown ice particles.

Visually, the scattering patterns of the rough particles appear to be highly speckled. Figure 2 shows several scattering patterns in order from low to high ke values. Also shown in Fig. 2 is a histogram of observed ke values for each flight overlain with the average, demonstrating the consistency of the observations. Complex particles, those that are aggregates of smaller particles, are also likely to have speckled scattering patterns. As SID-3 measures particles from 5 to approximately 100 μm, it is reasonable to assume that fewer than 20%–30% of the particles observed by SID-3 will be aggregates of smaller particles (Schmitt and Heymsfield 2014). For consistency, roughness and pristine particle results presented in this section are for scattering pattern images when the overall average image intensity was within a range (10–25) known to give good results (Schnaiter et al. 2016). This corresponds to a size range of approximately 5–41 μm, depending on the instrument settings. Note that this size range does not include many sizes that are likely to be oriented. For reference, a particle size distribution from SID3 for the 16 April flight is also shown in Fig. 2. Note that not all particles in the 5–41-μm range are included in the roughness and pristine particle analysis as the instrument settings automatically changed every 15 s, which changed the focus size range. For the two different settings, the size ranges are 5–15 and 15–41 μm.

Fig. 2.

Several scattering patterns and ke values showing a range. A cutoff of 4.6 is used to identify rough particles (ke > 4.6) vs smooth particles. Histograms for observed ke values and an example particle size distribution are also shown.

Fig. 2.

Several scattering patterns and ke values showing a range. A cutoff of 4.6 is used to identify rough particles (ke > 4.6) vs smooth particles. Histograms for observed ke values and an example particle size distribution are also shown.

Measurements in the AIDA cloud chamber have shown that pristine particles often have symmetric scattering patterns. Symmetry is determined by doing a fast Fourier transform on the radially summed values of the scattering pattern (Vochezer et al. 2016). To estimate the frequency of occurrence of pristine particles from SID-3, we have chosen to define pristine particles as those whose particle-scattering patterns have two- or fourfold symmetry that are generally columnar shapes or scattering patterns with sixfold symmetry that are likely plate shaped crystals imaged face on. Figure 3 shows a few scattering patterns from particles that appear to be the result of symmetrically scattering by ice crystals. Significant uncertainties can occur with this definition, as pristine particles may not be imaged in an orientation that produces a symmetric scattering pattern. Also shown in Fig. 3 is an image from the Department of Energy (DOE) Southern Great Plains site (SGP) all-sky camera showing a distinct halo from 20 April 2011. This halo was observed at approximately the same time that the WB-57 was in the area sampling. The strong halo was also noted by the WB-57 pilots and would normally suggest an abundance of pristine hexagonal-column-shaped particles.

Fig. 3.

All-sky camera image from the DOE SGP ARM site on 20 Apr 2011 showing strong halo as NASA WB-57 approached. Examples of SID-3 scattering patterns showing two-, four-, and sixfold symmetry from the same flight.

Fig. 3.

All-sky camera image from the DOE SGP ARM site on 20 Apr 2011 showing strong halo as NASA WB-57 approached. Examples of SID-3 scattering patterns showing two-, four-, and sixfold symmetry from the same flight.

Tables 1 and 2 show the results of the particle properties determined from individual SID-3 scattering patterns. In both tables, the number of particles sampled is in parentheses in the first column. Table 1 shows the percentage of pristine particles based on the symmetry analysis as well as the percentage of rough particles based on the ke values for each of the research flights. Note that pristine particles and rough particles are not mutually exclusive; which is why the percentages do not add up to 100%. Data from 13 and 16 April, the jet stream cirrus days, were not significantly different from the other days, suggesting that jet stream cirrus and anvil cirrus (in these sizes) have similar scattering properties. The halo observations on the 20 April flight coincided with an above average percentage of pristine particles, although the percentage of rough particles observed during the 20 April flight was similar to other days. The other days that had pristine particle percentages similar to 20 April were not over the ARM site and the pilots did not note halos in the postflight briefing. Note that only a few particle-scattering patterns from this flight showed strong halo features. The bottom two SID-3 scattering patterns in Fig. 1 are examples of the halo features observed during this time period. This suggests that it only takes a small percentage of pristine smooth particles to produce observable halos.

Table 1.

For each flight day, the percentage of particles identified as having rough surfaces and the percentage of particles that could be pristine. The number in parentheses indicates the number of particles used in this determination (as described in the text).

For each flight day, the percentage of particles identified as having rough surfaces and the percentage of particles that could be pristine. The number in parentheses indicates the number of particles used in this determination (as described in the text).
For each flight day, the percentage of particles identified as having rough surfaces and the percentage of particles that could be pristine. The number in parentheses indicates the number of particles used in this determination (as described in the text).
Table 2.

For the full dataset, the percentage of particles identified as having rough surfaces and the percentage of particles that could be pristine separated by temperature range. The number in parentheses indicates the number of particles used in this determination (as described in the text).

For the full dataset, the percentage of particles identified as having rough surfaces and the percentage of particles that could be pristine separated by temperature range. The number in parentheses indicates the number of particles used in this determination (as described in the text).
For the full dataset, the percentage of particles identified as having rough surfaces and the percentage of particles that could be pristine separated by temperature range. The number in parentheses indicates the number of particles used in this determination (as described in the text).

As has been suggested by Baum et al. (2011) and Ulanowski et al. (2014) and numerous others, the percentage of particles in the atmosphere that are either complex or have rough surfaces is high. Schmitt and Heymsfield (2014) suggest that around 20% of particles smaller than 100 μm are likely to be aggregates of smaller particles. For single particles, rough surface can also include features such as stepped growth or hollowness (Schmitt et al. 2006), which would lead to similar scattering patterns. Using the Schmitt and Heymsfield (2014) estimate as an upper bound for the possibility of aggregates, it is possible to conclude that at least 60% of the nonaggregate particles in the sub-100-μm size range are rough based on SID-3 analysis.

Several studies have shown that pristine ice particles are rare in natural atmospheric clouds (Korolev et al. 1999; Korolev and Sussman 2000). These studies have generally been conducted with instrumentation that is limited in its ability to detect the shapes of ice crystals smaller than 25 μm [SPEC cloud particle imager (CPI); Lawson et al. (2001)] or 100 μm (two-dimensional optical array probes such as the SPEC 2DS or PMS 2DC or DMT CIP). The results of the scattering pattern symmetry analysis show that the percentage of pristine crystals (smooth or rough) in the atmosphere is likely to be around 20% for particles smaller than 100 μm.

When data were broken down by temperature (Table 2), there were no significant trends observed in the dataset for either rough or pristine particles. Reductions in the percentage of pristine particles at the warmest and coldest temperatures were likely an artifact due to fewer particles being sampled in those temperature ranges.

While most of the MACPEX flights were in cirrus layers associated with convective systems, some of the flights were conducted in in situ generated cirrus. There were not substantial differences in the small particle composition based in the SID-3 roughness and pristine particle determination. This includes the analysis of the time period when the halos were observed; again demonstrating that it does not take a high concentration of halo-producing particles to produce an observable halo.

3. SID-3 partial scattering functions

The scattering phase function of a particle is a measure of the direction that incident light is scattered. In radiative transfer calculations, the phase function is generally integrated into the asymmetry parameter, which is a directionally weighted measure of how much incident light is scattered in the forward versus back (Takano and Liou 1989). Ray-tracing calculations are generally used to estimate the particle-scattering phase function, but calculations are limited to more defined crystal shapes compared to the shapes observed in natural clouds. With advances in computing power and improved techniques, ray-tracing calculations are being carried out with increasingly complex particle shapes from particles with hollows (Schmitt et al. 2006) to aggregates of hexagonal crystals (Um and McFarquhar 2009; Xie et al. 2011), to fractal particles (Mitchell et al. 1996). While ray-tracing calculations for these more complex particles are an improvement, the variety of particle shapes in natural clouds is much greater. Recently, varying degrees of surface roughness have also been considered (Yang et al. 2008). Careful inspection of the figures in Yang et al. (2008) shows that the phase function can be significantly different for particles with different surface roughness properties. This is particularly true in the angular range observed by SID-3. Thus, SID-3 measurements offer a unique opportunity to evaluate the shape of the phase function as compared to ray-tracing calculations.

Figure 4 shows several individual SID-3 scattering patterns, along with the associated PSF. Values from 0° to 7.5° (the optical dump spot) and beyond 23° (the edge of the detector) are shaded in this and all further figures. To calculate the PSF from SID-3 scattering patterns, the intensity values measured along a radius are averaged, as the image is rotated 360°. At each radial distance, 90 values are taken at 90 different angles (every 4°). Fewer than 90 angles led to noise in the resulting PSF and more was computationally excessively time consuming for little gain. Three of the particles shown in Fig. 4 have strong halo spots at the 22° angle, though it is uncertain how strong this peak should be as the CCD detector is generally saturated at these locations. Given that the phase functions for smooth-surfaced hexagonal particles shown in Yang et al. (2008) show that the halo can be more than an order of magnitude stronger for a rotationally averaged phase function, it is likely that the SID-3 detector is highly saturated at these halo spots (while SID-3 can record 12-bit images, 8-bit ones were used in MACPEX, resulting in a dynamic range of only just above two decades). Note that the PSFs in Fig. 4 are not smooth because they are only determined from one orientation of one ice particle and it is not reasonable to compare the variability in a PSF from a single orientation to a ray-tracing rotationally averaged phase function.

Fig. 4.

Some SID-3 scattering patterns and their associated PSFs calculated by averaging the angular intensity of the image around a full 360°. Note the halo spots that lead to peaks of varying size at the end of the PSF. The left end of the PSFs is the dump spot. Note that the nonuseful range is shaded. HR and SR (defined in the text) are listed for each of the individual PSFs.

Fig. 4.

Some SID-3 scattering patterns and their associated PSFs calculated by averaging the angular intensity of the image around a full 360°. Note the halo spots that lead to peaks of varying size at the end of the PSF. The left end of the PSFs is the dump spot. Note that the nonuseful range is shaded. HR and SR (defined in the text) are listed for each of the individual PSFs.

The “halo ratio” (HR) originally defined by Auriol et al. (2001) and Gayet et al. (2011) has been used by Ulanowski et al. (2014) to quantitatively characterize the scattering properties of ice particles. HR is the ratio of the scattered energy measured at 22° and 18.5°. Halo-producing particles would have higher values than non-halo-producing particles. Per Ulanowski et al.’s (2014) definition, HR for SID-3 particles is the average energy between 21.5° and 22.5° divided by the average value between 18° and 19°. For the purposes of this study we also define a “steepness ratio” (SR). SR is the ratio of the scattered light intensity between 8.5° and 9.5° to the intensity between 18° and 19°. The SR gives a quantitative comparison of how steep the scattering function is between these two angular ranges.

Tables 1 and 2 also include the average HR and SR and the standard deviations observed for each of the categories. These values are very similar across all of the data categories, with the exception being that the standard deviation of SR is increased in categories associated with a special case where quasi-spherical particles were observed (discussed in the results section). Although there is a slight increase in the observed pristine particles during the 20 April case there was no significant difference in HR that day. Note that average HR was 0.94 for the 1-h time period around when the halo was observed. Sensitivity tests were conducted to understand the effects of the different thresholds used to select scattering patterns. Adjusting the 2% pixel saturation level (to 5%) led to changes in HR and SR, as well as the percentages in the tables by less than 1%. Changing the TOF cutoff led to changes in HR and SR of up to 1.3%, but generally much less.

Figure 5 shows HR, SR, and asphericity [same as asymmetry in Cotton et al. (2010)] are plotted as a function of ke or the roughness parameter. Mean values and the 25th and 75th percentiles are also shown on the plots. Contrary to the results shown in Ulanowski et al. (2014), the MACPEX data show a slight decrease in HR with decreasing roughness (decreasing ke). The Ulanowski et al. (2014) measurements were conducted in much more northerly locations and some were in January and February, when convective systems were unlikely. It is not surprising that there could be significant differences in particle-scattering properties considering the vastly different formation mechanisms. Since very few scattering patterns in the MACPEX dataset showed signs of halos, this suggests that smoother non-halo-producing particles have lower HRs. SR shows a distinct increasing trend as ke decreases yet both HR and SR include a lot of variability as we are only capturing one orientation. Examining of the plots in Yang et al. (2008) would suggest that SR should increase for particles with less rough surfaces. Asymmetry factor (or asphericity) is calculated as in Vochezer et al. (2016) and should be equivalent to the asymmetry factor calculated for SID2 or SID2H.

Fig. 5.

HR and SR plotted vs ke for portion of dataset where ke is best suitable for estimating particle roughness. The thick line in each plot represents the mean value per each 0.1 step in ke. The 25th and 75th percentiles are also shown. Asphericity (similar to what is calculated by earlier versions of SID) is also shown as a function of roughness.

Fig. 5.

HR and SR plotted vs ke for portion of dataset where ke is best suitable for estimating particle roughness. The thick line in each plot represents the mean value per each 0.1 step in ke. The 25th and 75th percentiles are also shown. Asphericity (similar to what is calculated by earlier versions of SID) is also shown as a function of roughness.

Phase functions determined from ray-tracing calculations use a large number of particle orientations (Um and McFarquhar 2009). While this is not possible for individual particles observed by SID-3, it is possible to average the individual PSFs from a number of particles to achieve a similar effect. Essentially, this provides an estimate of the phase function for the ensemble of particles detected by SID-3. Figure 6 shows several PSFs calculated by averaging 5, 15, and 100 SID-3 PSFs. Note that average PSFs are calculated from unnormalized individual PSFs. The y axis for the plots in Fig. 6 and all further PSF plots is in units of average pixel value, which is arbitrary and therefore values are not shown. For the PSFs calculated from fewer individual measurements, there is a lot of variation, while for higher numbers the PSFs become smoother. With appropriate particle selection it is possible to calculate reasonable PSFs to represent different particle types as well as to determine the PSF for particles under specified atmospheric conditions. Per Fig. 6, it was best to average at least 100 individual PSFs in order to consistently get smooth ensemble PSFs.

Fig. 6.

PSFs calculated from different numbers of SID-3 particle-scattering patterns. The PSFs calculated from 5 and 15 images are noticeably noisy while those calculated from 100 images are substantially smoother.

Fig. 6.

PSFs calculated from different numbers of SID-3 particle-scattering patterns. The PSFs calculated from 5 and 15 images are noticeably noisy while those calculated from 100 images are substantially smoother.

A critical assumption in this calculation is the assumption of random orientation. The random orientation assumption is reasonable for particles in the atmosphere that are smaller than 20 μm that would have typical tilt angle during fall of greater than 10° according to Bréon and Dubrulle (2004), while Cho et al. (1981) showed that particles larger than 30 μm could be oriented by airflow in convective systems. As atmospheric particles are typically more compact than pristine plates and the turbulence is likely much higher in the vicinity of the aircraft than the values assumed in Bréon and Dubrulle, random orientation is probably not a bad assumption for most of the SID-3 size range.

PSFs can be calculated for a number of particle types based on other parameters derived from SID-3 observations during MACPEX. It was found that there was very little difference between calculated PSFs for different days, suggesting that either the cloud particles in the SID-3 size range were all similar in scattering characteristics, or that in general there is not much difference in the scattering characteristics of ice particles. The one exception, which will be explored later, was the 21 April flight during which one cloud was penetrated that contained high concentrations of what appeared to be frozen droplets (Järvinen et al. 2016). Figure 7 shows PSFs calculated for ensembles of particles with different light-scattering characteristics. Also plotted are the standard deviations curves for the profiles. Note that the standard deviations all appear to be similar in shape to the PSFs with the exception of the particles classified as smooth that were affected by the 21 April special case. HR and SR values for each PSF are listed on the figure panels. The data are averaged for particles identified with the listed characteristics for all analyzed flights except the 21 April flight and the 26 April flight. The 21 April flight will be discussed later and the probe settings were different for the 26 April flight.

Fig. 7.

SID-3 PSFs calculated for a number of different particle-scattering characteristics. Details on the selection criteria for each comparison are given in the text. The thin lines represent the standard deviation at each angle. HR and SR for each plot with standard deviations are listed.

Fig. 7.

SID-3 PSFs calculated for a number of different particle-scattering characteristics. Details on the selection criteria for each comparison are given in the text. The thin lines represent the standard deviation at each angle. HR and SR for each plot with standard deviations are listed.

The following criteria were used for selecting scattering patterns displayed in Fig. 7. For all plots, data were limited to times when the temperature was colder than −30°C, increasing the likelihood of all particles being ice. Only scattering patterns acquired when the probe settings were the same (gain = 195) were used because averaging PSFs from different gain settings would have led to strong biases. For “small” and “large” (Figs. 7a,b), particles whose sizes were between 15 and 20 and between 50 and 70 μm, respectively, were selected. For “smooth” and “rough” (Figs. 7c,d), the selection criteria described in the individual particle analysis section were used and particles were limited to the 15–20-μm range, the range where the roughness calculation is most reliable for the probe gain setting. For “cold” and “warm” (Figs. 7e,f), temperature ranges of −30° to −40° and −50° to −60°C were used and, to assure consistency, only particles between 30 and 40 μm were selected in these temperature ranges. For the “pristine” versus “nonpristine” comparison (Figs. 7g,h), again the size range was limited to 15–20 μm for easy comparison with Figs. 7c,d, and the symmetry criteria described earlier was used to discriminate between pristine and nonpristine scattering patterns. All PSFs are normalized by their peak value for easy shape comparison as scaling unnormalized scattering functions would be beyond the scope of this work.

The most striking observation regarding Fig. 7 is that all of the PSFs look very similar. The comparison of PSFs created for particles in different size ranges shows that the PSF is more concave for smaller particles than for larger particles. This is in agreement with the trends observed with ray-tracing calculations. The PSF for rough particles shows a modest sign of enhancement at the 22° halo region, which is not apparent on the smooth PSF, exactly the opposite of what one would expect. Neither warm versus cold nor pristine versus not pristine show significant differences. Interestingly, the PSF calculated for the 20 April halo time period showed no significant difference from other time periods. Halos are definitely observable in scattering data [see Shcherbakov et al. (2006)], but given that there were very few scattering patterns with halos (the bottom two in Fig. 1 are two examples of three found), it is not surprising that a pronounced halo was not observed in the PSF.

Figure 8 shows the results of a special case observed on 21 April. As shown in Table 1, the 21 April case had the lowest apparent concentration of pristine particles. This corresponds to the day when an active anvil was penetrated, during which numerous quasi-spherical particles were observed. Images of spherical ice particles and aggregates of spherical ice particles from this time period are shown in Järvinen et al. (2016). Note that during this anvil penetration, only 9.2% of scattering patterns suggested that the particles were pristine. Figure 8 shows several scattering patterns from this time period which appear to be distorted Mie theory patterns. Scattering patterns such as these have been observed in the AIDA cloud chamber at temperatures (colder than −40°C) when it was impossible for liquid water to be present (Järvinen et al. 2016) and have been associated with near-spherical ice particles. These measurements were made as the WB57 penetrated a very recently developed anvil and ascended to an altitude of 12 000 m and a cloud-top temperature of approximately −55°C, suggesting that there could not be liquid water in the cloud. The anvil had developed very recently and the WB-57 penetrated the earliest stages of the tropopause spreading of the anvil. As there was likely abundant super cooled liquid water in the developing storm, it is not surprising that quasi-spherical ice particles could exist in the early-developing anvil considering that there had not been much time for aggregation or other particle processing. PSFs are calculated for two different size ranges (15–20 and 30–40 μm) and further separated into particles identified as smooth and rough. While the PSFs for rough-surfaced particles are somewhat similar to those shown in Fig. 7, the PSFs for particles identified as having smooth surfaces are drastically different from the respectively sized rough PSFs as well as very different from all of the PSFs shown in Fig. 7. Note that while the HR values are not too dissimilar to those shown in Fig. 7, the SR values for the smooth particles are substantially different. The mean asphericity of particles observed during this anvil penetration was significantly lower than the averages for the remainder of the dataset suggesting that these particles could be identified by earlier versions of SID. The observed tendency (much less light scattered near 20° than near 10°) is exactly the trend that would be expected based on Yang et al. (2008) calculations for the SID-3 angular range when comparing particles with smooth versus rough surfaces. Note that these are averages of all of the particles present in the cloud and not just the quasi-spherical particles. This would suggest that particles in active anvils could have substantially different scattering characteristics compared to less active clouds. This result agrees with Järvinen et al. (2016), who showed a similar reduction in scattered light intensity at larger angles but for more complete measured phase functions. Approximately 5% of the images were removed by hand as they appeared to be the result of particle coincidence. This did not significantly affect HR but reduced SR by about 10% and reduced the standard deviation of SR by a factor of 2.

Fig. 8.

PSFs calculated from data collected at the top of an active anvil on 21 Apr 2011. (a),(b) 30–40-μm particle scattering patterns as well as (c),(d) 15–20-μm particle scattering patterns are separated into smooth and rough PSFs. SID-3 scattering patterns showed numerous near-spherical scattering patterns likely from frozen droplets. The thin lines represent the standard deviation at each angle. HR and SR for each plot with standard deviations are listed.

Fig. 8.

PSFs calculated from data collected at the top of an active anvil on 21 Apr 2011. (a),(b) 30–40-μm particle scattering patterns as well as (c),(d) 15–20-μm particle scattering patterns are separated into smooth and rough PSFs. SID-3 scattering patterns showed numerous near-spherical scattering patterns likely from frozen droplets. The thin lines represent the standard deviation at each angle. HR and SR for each plot with standard deviations are listed.

We emphasize that this time period constituted approximately 5% of the in-cloud time analyzed for this publication. While this may not have been a substantial portion of the dataset, it is worth noting that observations in AIDA of sublimating ice particles often show that as particles start to sublimate, their scattering patterns tend to change to be closer to the scattering characteristics of spheres. Particles near cloud edges or cloud tops could be sublimating and therefore becoming more quasi spherical and thus their scattering properties could be changing to be more like spheres. The same could be plausible for subvisible cirrus particles [such as those shown in Lawson et al. (2008)]. Though not frequently observed, this type of light scattering by near-spherical particles could be more important than the ~5% observed in MACPEX.

4. Ray-tracing comparisons

As noted earlier, the shape of the phase function in the angular range of SID-3 does not vary significantly with different particle-scattering characteristics, the one exception being the special case time period shown in Fig. 8. In this section we compare the SID-3 PSF shape to the shape of ray-tracing phase functions. For comparison purposes, the primary ray-tracing phase function is normalized to the value of the SID-3 PSF at 16° in each plot. The second and third PSFs are normalized by the same factor so that the overlain ray-tracing phase functions are comparable. PSF Fig. 9 shows several comparisons between SID-3 PSFs and ray-tracing calculations from Yang et al. (2008). For each of the SID-3 PSFs, all of the accepted SID-3 scattering patterns from the flights between 13 and 21 April were used. (26 April was not used as the detector gain was set differently, which reduced the intensity of the measured values.) Table 3 shows the HR and SR values calculated for each of the SID-3 PSFs and the ray-tracing phase functions as well. Figures 9a,b show the same SID-3 PSF, calculated for particles that had scattered light intensity suggesting that they were between 50 and 70 μm in size. Figure 9a shows the SID-3 PSF compared to severely, moderately, and nonroughened droxtals (thin solid, dotted, and dashed lines, respectively). HR and SR are substantially different from the SID-3 values for the nonseverely roughened particles. Figure 9b shows the same SID-3 PSF compared to severely roughened droxtals, plates, and columns (thin solid, dotted, and dashed, respectively). For these comparisons, the ray-tracing phase functions were determined by averaging the available phase functions in the size range used for the SID-3 average PSF. Clearly the severely roughened particle phase function better matches SID-3 and the severely roughened droxtal phase function is much closer to the SID-3 PSF than other shapes for the larger particle size range. HR and SR for the SID-3 PSF agree much better with the droxtal than the other shapes. Figures 9c,d show the same comparison but for smaller particles (20–25 μm). While the agreement is not as good, the severely roughened droxtal still appears to be in better agreement with the SID-3 measurements. Figures 9e,f show SID-3 PSFs derived from the special case already mentioned and shown in Fig. 8. In this case, the SID-3 PSF determined for only the rough particles is shown in Fig. 9e as compared to rough droxtals, columns, and plates. Figure 9f shows the SID-3 PSF determined from the scattering measurements of smooth particles, compared to smooth droxtals, columns, and plates. Also shown in Fig. 9f is the PSF estimated using Mie theory for ice spheres. Note that SR agrees reasonably well with the SID-3 PSF values. The Mie theory PSF was determined by averaging the Mie theory phase functions calculated for particles between 30 and 40 μm. Varying the size range did not lead to substantial differences in SR and HR. Again, for the special case, it appears that the rough droxtal phase function compared well to the SID-3 measurement for rough particles (Fig. 9e). For smooth particles, none of the ray-tracing phase functions agreed well for the entire SID-3 range, yet the ice sphere PSF agrees reasonably well.

Fig. 9.

Comparisons of SID-3 PSFs and ray-tracing phase functions from Yang et al. (2008). (a)–(e) Note that the thin solid line that represents the ray-tracing phase function for droxtals with severely rough surfaces agrees with the SID-3 PSFs. (f) Comparing smooth-surface ray-tracing calculations with a SID-3 PSF that was likely influenced by the spherical ice scattering. Also shown in (f) is a PSF calculated using Mie theory for spheres for particles in the estimated size range.

Fig. 9.

Comparisons of SID-3 PSFs and ray-tracing phase functions from Yang et al. (2008). (a)–(e) Note that the thin solid line that represents the ray-tracing phase function for droxtals with severely rough surfaces agrees with the SID-3 PSFs. (f) Comparing smooth-surface ray-tracing calculations with a SID-3 PSF that was likely influenced by the spherical ice scattering. Also shown in (f) is a PSF calculated using Mie theory for spheres for particles in the estimated size range.

Table 3.

Table of HR and SR for curves in Fig. 9. (column 1) Corresponding figure panel. (column 2) The data for the SID-3 PSF displayed in each panel with the indicated size range for Figs. 9a–d while Figs. 9e,f are from the 21 Apr special case. (columns 3–5) Descriptors of which ray-tracing phase functions are plotted with the line style indicated at the top of the column. The second line below the descriptors is in the form “HR/SR.” HR and SR for spherical ice particles represented by the long-dashed curve in Fig. 9f are 0.62 and 3.67, respectively.

Table of HR and SR for curves in Fig. 9. (column 1) Corresponding figure panel. (column 2) The data for the SID-3 PSF displayed in each panel with the indicated size range for Figs. 9a–d while Figs. 9e,f are from the 21 Apr special case. (columns 3–5) Descriptors of which ray-tracing phase functions are plotted with the line style indicated at the top of the column. The second line below the descriptors is in the form “HR/SR.” HR and SR for spherical ice particles represented by the long-dashed curve in Fig. 9f are 0.62 and 3.67, respectively.
Table of HR and SR for curves in Fig. 9. (column 1) Corresponding figure panel. (column 2) The data for the SID-3 PSF displayed in each panel with the indicated size range for Figs. 9a–d while Figs. 9e,f are from the 21 Apr special case. (columns 3–5) Descriptors of which ray-tracing phase functions are plotted with the line style indicated at the top of the column. The second line below the descriptors is in the form “HR/SR.” HR and SR for spherical ice particles represented by the long-dashed curve in Fig. 9f are 0.62 and 3.67, respectively.

For radiative transfer modeling purposes, the key parameter derived from the scattering phase function is the asymmetry parameter. Our effort has been focused on using the shape of the SID-3 PSFs to infer particle properties, as calculation of the difference in the asymmetry parameter that could be associated with observed SID-3 differences is beyond the scope of this publication. On average, the SID-3 PSFs suggest that the asymmetry parameter could be slightly higher than that calculated for severely roughened droxtals of the same size. The PSFs determined for the spherical ice case suggest that the full phase function might be more similar to that of water droplets (the values at 22° are much lower than at 7° when compared to nonspherical ice PSFs) similar to the result found in Järvinen et al. (2016).

5. Summary and conclusions

The SID-3 probe is a unique probe for understanding the light-scattering characteristics of atmospheric ice crystals. From individual SID-3 scattering pattern measurements, it is feasible to identify particle roughness, identify particles that could be pristine, and identify quasi-spherical particles. Forward-light-scattering patterns can be used to estimate the scattering phase functions observed by SID-3 at scattering angles between 7.5° and 23° for ensembles of particles. These PSFs can be compared to theoretical phase functions from the ray-tracing simulation, toward a better understanding of the properties of ensembles of particles. Results from this study are based on the MACPEX dataset, which included observations from predominantly convective systems. Common particle types in these conditions are significantly different from other cloud types as noted throughout the manuscript when comparing to other datasets. Key findings from this study include the following:

  • The PSFs as determined by SID-3 for the 7.5°–23° range are very similar across a wide variety of conditions, suggesting that there is little variability in scattering properties of convective ice clouds. Halo ratio and steepness ratio quantitative calculations show a similar lack of variability with the exception of the special case when quasi-spherical ice particles were observed where SR was substantially enhanced.

  • Based on the analysis of individual scattering patterns observed by SID3, a high percentage of the particles during MACPEX likely are rough.

  • In addition to the individual scattering pattern analysis, PSFs calculated for ensembles of SID-3 measurements also suggest particle surface roughness when compared to ray-tracing calculations determined for particles with rough surfaces.

  • Particles that could be pristine—those whose scattering patterns displayed two-, four-, or sixfold symmetry—were present in approximately 22% of all observations. PSFs calculated for pristine particles did not agree with ray-tracing calculations for smooth surfaced plates columns or droxtals, suggesting that the scattering patterns of rough particles are likely better even when measurements suggest less roughness.

  • Two unusual cases were observed during the MACPEX mission. The first was an active anvil, which was shown to contain numerous quasi-spherical frozen drops and aggregates of frozen drops. The SID-3 forward-scattering measurements often showed “Mie theory” type scattering patterns that were distorted even though the temperature was too cold for water to be present in the liquid form. The PSF calculations for this time period showed distinctly different phase function shapes in the SID-3 angular range than at most other times, suggesting that active convective systems may have significantly different light-scattering characteristics than more aged cirrus.

  • The second unusual case occurred when halos were observed from both the ground and the aircraft. Although SID-3 did see individual scattering patterns that indicate that halos could be present, substantial increases in concentration of pristine or smooth surfaced particles were not observed. This suggests that it does not require high concentrations of halo-producing particles to produce an observable halo. For this period, the SID-3 PSFs did not show significant difference from most other time periods.

The results of this study suggest that a substantial portion of the noncomplex atmospheric ice particles smaller than 100 μm are likely to be rough either on surfaces or internally as a result of inclusions. The individual scattering patterns suggest this as well as there is much better agreement between scattering phase functions calculated from ray tracing with the PSFs derived from SID-3 measurements. It should be emphasized that the results of this study do not suggest that the scattering characteristics of severely roughened droxtals are the best solution. For the instrument setting used during MACPEX, no particles larger than 100 μm could be observed. As shown in Schmitt and Heymsfield (2014), it is unlikely that high numbers of aggregates were observed. The special case noted on 21 April clearly demonstrates this. The CPI data [see Järvinen et al. (2016)] from the anvil case clearly demonstrates that the switch from simple to complex particles happens at a very small size. The PSFs determined for this time period are significantly different from more general cases. Based on this finding, it is very important to consider the scattering characteristics of both the small mode (observed by SID-3 in most cases) and the larger more complex mode. It should also be emphasized that the results of this study are applicable to convective observations and should not be seen as contradicting results from measurements taken in nonconvective cloud systems.

Acknowledgments

Schmitt, Heymsfield, Hirst, Bansemer, and Schnaiter were supported by the NASA MACPEX research project (Hal Maring, program manager) under Contract NNX11AC07G. Schnaiter was also partially supported by the German Research Foundation (DFG) within the HALO priority program 1294 (Contract SCHN 1140/1-2). Ping Yang’s research is supported by the National Science Foundation under Grant AGS-1338440. The authors wish to thank Joseph Ulanowski for his suggestions.

REFERENCES

REFERENCES
Auriol
,
F.
,
J.-F.
Gayet
,
G.
Febvre
,
O.
Jourdan
,
L.
Labonnote
, and
G.
Brogniez
,
2001
:
In situ observations of cirrus cloud scattering phase function with 22 and 46 halos: Cloud field study on 19 February 1998
.
J. Atmos. Sci.
,
58
,
3376
3390
, doi:.
Baum
,
B. A.
,
P.
Yang
,
A. J.
Heymsfield
,
C. G.
Schmitt
,
Y.
Xie
,
A.
Bansemer
,
Y.-X.
Hu
, and
Z.
Zhang
,
2011
:
Improvements in shortwave bulk scattering and absorption models for remote sensing of ice clouds
.
J. Appl. Meteor. Climatol.
,
50
,
1037
1056
, doi:.
Baum
,
B. A.
,
P.
Yang
,
A. J.
Heymsfield
,
A.
Bansemer
,
B. H.
Cole
,
A.
Merrelli
,
C.
Schmitt
, and
C.
Wang
,
2014
:
Ice cloud single-scattering property models with the full phase matrix at wavelengths from 0.2 to 100 µm
.
J. Quant. Spectrosc. Radiat. Transfer
,
146
,
123
139
, doi:.
Bréon
,
F.-M.
, and
B.
Dubrulle
,
2004
:
Horizontally oriented plates in clouds
.
J. Atmos. Sci.
,
61
,
2888
2898
, doi:.
Cho
,
H.-R.
,
J. V.
Iribarne
, and
W. G.
Richards
,
1981
:
On the orientation of ice crystals in a cumulonimbus cloud
.
J. Atmos. Sci.
,
38
,
1111
1114
, doi:.
Cole
,
B. H.
,
P.
Yang
,
B. A.
Baum
,
J.
Riedi
, and
L.
C.-Labonnote
,
2014
:
Ice particle habit and surface roughness derived from PARASOL polarization measurements
.
Atmos. Chem. Phys.
,
14
,
3739
3750
, doi:.
Cotton
,
R.
,
S.
Osborne
,
Z.
Ulanowski
,
E.
Hirst
,
P. H.
Kaye
, and
R. S.
Greenaway
,
2010
:
The ability of the Small Ice Detector (SID-2) to characterize cloud particle and aerosol morphologies obtained during flights of the FAAM BAe-146 research aircraft
.
J. Atmos. Oceanic Technol.
,
27
,
290
303
, doi:.
Field
,
P. R.
,
R.
Wood
,
P. R. A.
Brown
,
P. H.
Kaye
,
E.
Hirst
, and
R.
Greeaway
,
2003
:
Ice particle interarrival times measured with a fast FSSP
.
J. Atmos. Oceanic Technol.
,
20
,
249
261
, doi:.
Gayet
,
J.-F.
,
G.
Mioche
,
V.
Shcherbakov
,
C.
Gourbeyre
,
R.
Busen
, and
A.
Minikin
,
2011
:
Optical properties of pristine ice crystals in mid-latitude cirrus clouds: A case study during CIRCLE-2 experiment
.
Atmos. Chem. Phys.
,
11
,
2537
2544
, doi:.
Haralick
,
R. M.
,
K.
Shanmugam
, and
I.
Dinstein
,
1973
:
Textural features for image classification
.
IEEE Trans. Syst. Man Cybern.
,
3
,
610
621
, doi:.
Järvinen
,
E.
, and Coauthors
,
2016
:
Quasi-spherical ice in convective clouds
.
J. Atmos. Sci.
,
73
,
3885
3910
, doi:.
Jensen
,
E. J.
,
R. P.
Lawson
,
J. W.
Bergman
,
L.
Pfister
,
T. P.
Bui
, and
C. G.
Schmitt
,
2013
:
Physical processes controlling ice concentrations in synoptically forced, midlatitude cirrus
.
J. Geophys. Res. Atmos.
,
118
,
5348
5360
, doi:.
Johnson
,
A.
,
S.
Lasher-Trapp
,
A.
Bansemer
,
Z.
Ulanowski
, and
A. J.
Heymsfield
,
2014
:
Difficulties in early ice detection with the Small Ice Detector-2 HIAPER (SID-2H) in maritime cumuli
.
J. Atmos. Oceanic Technol.
,
31
,
1263
1275
, doi:.
Korolev
,
A.
, and
B.
Sussman
,
2000
:
A technique for habit classification of cloud particles
.
J. Atmos. Oceanic Technol.
,
17
,
1048
1057
, doi:.
Korolev
,
A.
,
G. A.
Isaac
, and
J.
Hallett
,
1999
:
Ice particle habits in Arctic clouds
.
Geophys. Res. Lett.
,
26
,
1299
1302
, doi:.
Korolev
,
A.
,
E. F.
Emery
,
J. W.
Strapp
,
S. G.
Cober
,
G. A.
Isaac
,
M.
Wasey
, and
D.
Marcotte
,
2011
:
Small ice particles in tropospheric clouds: Fact or artifact?
Bull. Amer. Meteor. Soc.
,
92
,
967
973
, doi:.
Lawson
,
R. P.
,
B. A.
Baker
,
C. G.
Schmitt
, and
T. L.
Jensen
,
2001
:
An overview of microphysical properties of Arctic clouds observed in May and July 1998 during FIRE ACE
.
J. Geophys. Res.
,
106
,
14 989
15 014
, doi:.
Lawson
,
R. P.
,
B.
Pilson
,
B.
Baker
,
Q.
Mo
,
E.
Jensen
,
L.
Pfister
, and
P.
Bui
,
2008
:
Aircraft measurements of microphysical properties of subvisible cirrus in the tropical tropopause layer
.
Atmos. Chem. Phys.
,
8
,
1609
1620
, doi:.
Liou
,
K. N.
,
1986
:
Influence of cirrus clouds on weather and climate processes: A global perspective
.
Mon. Wea. Rev.
,
114
,
1167
1199
, doi:.
Lu
,
R. S.
,
G. Y.
Tian
,
D.
Gledhill
, and
S.
Ward
,
2006
:
Grinding surface roughness measurement based on the co-occurrence matrix of speckle pattern texture
.
Appl. Opt.
,
45
,
8839
8847
, doi:.
Lynch
,
D. K.
,
K.
Sassen
,
D. O’C.
Starr
, and
G.
Stephens
, Eds.,
2002
: Cirrus. Oxford University Press, 480 pp.
Mitchell
,
D. L.
,
A.
Macke
, and
Y.
Liu
,
1996
:
Modeling cirrus clouds. Part II: Treatment of radiative properties
.
J. Atmos. Sci.
,
53
,
2967
2988
, doi:.
Neshyba
,
S. P.
,
B.
Lowen
,
M.
Benning
,
A.
Lawson
, and
P. M.
Rowe
,
2013
:
Roughness metrics for prismatic facets of ice
.
J. Geophys. Res. Atmos.
,
118
,
3309
3318
, doi:.
Schmitt
,
C. G.
, and
A. J.
Heymsfield
,
2014
:
Observational justification and quantification of the separation of cloud ice and snow
.
Geophys. Res. Lett.
,
41
,
1301
1307
, doi:.
Schmitt
,
C. G.
,
J.
Iaquinta
, and
A. J.
Heymsfield
,
2006
:
The asymmetry parameter of cirrus clouds composed of hollow bullet rosette–shaped ice crystals from ray-tracing calculations
.
J. Appl. Meteor. Climatol.
,
45
,
973
981
, doi:.
Schnaiter
,
M.
, and Coauthors
,
2016
:
Cloud chamber experiments on the origin of ice crystal complexity in cirrus clouds
.
Atmos. Chem. Phys.
,
16
,
5091
5110
, doi:.
Shcherbakov
,
V.
,
J.-F.
Gayet
,
B. A.
Baker
, and
R. P.
Lawson
,
2006
:
Light scattering by single natural ice crystals
.
J. Atmos. Sci.
,
63
,
1513
1525
, doi:.
Takano
,
Y.
, and
K. N.
Liou
,
1989
:
Solar radiative transfer in cirrus clouds. Part I: Single-scattering and optical properties of hexagonal ice crystals
.
J. Atmos. Sci.
,
46
,
3
19
, doi:.
Ulanowski
,
Z.
,
E.
Hesse
,
P. H.
Kaye
, and
A. J.
Baran
,
2006
:
Light scattering by complex ice analogue crystals
.
J. Quant. Spectrosc. Radiat. Transfer
,
100
,
382
392
, doi:.
Ulanowski
,
Z.
,
E.
Hirst
,
P. H.
Kaye
, and
R.
Greenaway
,
2012
:
Retrieving the size of particle with rough and complex surfaces from two-dimensional scattering patterns
.
J. Quant. Spectrosc. Radiat. Transfer
,
113
,
2457
2464
, doi:.
Ulanowski
,
Z.
,
P. H.
Kaye
,
E.
Hirst
,
R. S.
Greenaway
,
R. J.
Cotton
,
E.
Hesse
, and
C. T.
Collier
,
2014
:
Incidence of rough and irregular atmospheric ice particles from Small Ice Detector 3 measurements
.
Atmos. Chem. Phys.
,
14
,
1649
1662
, doi:.
Um
,
J.
, and
G. M.
McFarquhar
,
2009
:
Single-scattering properties of aggregates of plates
.
Quart. J. Roy. Meteor. Soc.
,
135
,
291
304
, doi:.
Vochezer
,
P.
,
E.
Järvinen
,
R.
Wagner
,
P.
Kupiszewski
,
T.
Leisner
, and
M.
Schnaiter
,
2016
:
In situ characterization of mixed phase clouds using the small ice detector and the particle phase discriminator
.
Atmos. Meas. Tech.
,
9
,
159
177
, doi:.
Wylie
,
D. P.
, and
W. P.
Menzel
,
1999
:
Eight years of high cloud statistics using HIRS
.
J. Climate
,
12
,
170
184
, doi:.
Xie
,
Y.
,
P.
Yang
,
G. W.
Kattawar
,
B. A.
Baum
, and
Y.
Hu
,
2011
:
Simulation of the optical properties of plate aggregates for application to the remote sensing of cirrus clouds
.
Appl. Opt.
,
50
,
1065
1081
, doi:.
Yang
,
P.
,
G. W.
Kattawar
,
G.
Hong
,
P.
Minnis
, and
Y.
Hu
,
2008
:
Uncertainties associated with the surface texture of ice particles in satellite-based retrievals of cirrus clouds: Part II—Effect of particle surface roughness on retrieved cloud optical thickness and effective particle size
.
IEEE Trans. Geosci. Remote Sens.
,
46
,
1948
1957
, doi:.