Introduction
Deep convective systems, such as thunderstorms and mesoscale convective
systems (MCSs), play an important role in Earth's climate system, for
example, by conveying ice crystals to the upper troposphere and lower
stratosphere, redistributing latent heat, controlling precipitation, and
regulating the Earth's radiation budget (Jensen et al., 1996; Stephens, 2005;
de Reus et al., 2009; Frey et al., 2011; Feng et al., 2011, 2012; Gayet et
al., 2012; Taylor et al., 2016). Clouds formed by deep convection show
several distinct features. Vigorous turrets associated with deep convection
generate intense precipitation that influences the hydrological cycle and
large anvil shields that modulate radiation due to their extensive spatial
and temporal coverage (Feng et al., 2011, 2012; Wang et al., 2015).
Overshooting tops associated with strong updrafts are responsible for
stratosphere–troposphere exchange (Homeyer et al., 2014; Frey et al., 2015)
and can be an indicator of the severity of a thunderstorm (Proud, 2015).
Clouds formed by deep convection have three thermodynamic phases: liquid,
mixed, and ice. The cloud particles also have different shapes, sizes, and
concentrations that vary in the horizontal and vertical causing horizontal
and vertical variability in radiative properties. For example, precipitating
cores of tropical convective clouds reveal a negative impact on radiation
balance, whereas non-precipitating anvils have a positive impact (Hartmann
and Berry, 2017). A numerical simulation (Fu et al., 1995) showed that the
spatial extent of an anvil cloud is influenced by moisture advection from
the convective turret, radiative effects, and small-scale convection
occurring within the anvil (Lilly, 1988). The relationships between the
spatial and temporal coverage of convectively generated clouds and their
radiative impact are still not well understood and affect the representation
of cloud feedbacks in numerical models (Bony et al., 2015, 2016; Hartmann,
2016; Hartmann and Berry, 2017).
Despite the high height of the tropopause and the remote regions where some
of these cloud systems occur, there have been in situ measurements of the
microphysical and scattering properties of ice crystals in anvil tops (e.g.,
Heymsfield, 1986; McFarquhar and Heymsfield, 1996; Stith et al., 2002, 2004,
2014, 2016; Connolly et al., 2005; Gallagher et al., 2005; Heymsfield et
al., 2005; May et al., 2008; Jensen et al., 2009; Lawson et al., 2010; Frey
et al., 2011; Gayet et al., 2012; Barth et al., 2015; Jensen et al., 2016).
Although in situ aircraft measurements have some limitations as crystals
are not observed where they form (Um et al., 2015), they along with
laboratory experiments (e.g., Bailey and Hallett, 2004, 2009) provide
information on how crystal habit varies with temperature and humidity.
One distinct characteristic of anvil clouds is the frequent occurrence of
plate type crystals and their aggregates, which is different from ice
crystals found in non-convective cirrus, where bullet rosettes and their
aggregates are most common (McFarquhar and Heymsfield, 1996; Stith et
al., 2002; Lawson et al., 2003; Connolly et al., 2005; Um and McFarquhar,
2009; Järvinen et al., 2016). As plate type crystals form at warmer
temperatures (Bailey and Hallett, 2004, 2009) than the typical temperatures at
anvil tops, these plate crystals must form at lower altitudes and be
transported to upper altitudes by convection. It has been hypothesized that
the “chain-like” shaped aggregates frequently observed in convective
clouds may be produced by high electric fields within clouds (Saunders and
Wahab, 1975; Stith et al., 2002, 2004; Lawson et al., 2003; Connolly et al.,
2005; Um and McFarquhar, 2009). These shapes differ from aggregates observed
in non-convective cirrus where aggregates of bullet rosettes are more common
(Um and McFarquhar, 2007) and chain-like structures are not commonly seen.
Another unique feature of ice crystals in deep convective clouds is the high
concentration of small frozen droplets (Gayet et al., 2012; Baran et al.,
2012; Stith et al., 2014). These are no doubt generated from the freezing of
supercooled droplets that have been observed at temperatures as low as
-37.5 ∘C in deep continental convective clouds (Rosenfeld and Woodley,
2000). Below this temperature homogeneous freezing occurs in the strong
updrafts which produces high concentrations of quasi-spherical frozen droplets
with maximum dimensions Dmax<∼50 µm
(Heymsfield and Sabin, 1989; Phillips et al., 2007; Heymsfield et al.,
2009). However, instrumental uncertainties associated with the generation of
artificially high concentrations of small ice crystals from the shattering of
large ice crystals on the tips of in situ probes (Field et al., 2003, 2006;
McFarquhar et al., 2007; Korolev et al., 2011; Lawson, 2011; Jackson and
McFarquhar, 2014; Jackson et al., 2014; Korolev and Field, 2015) cast some
doubt on the exact concentration of these small crystals. Knowledge about
the concentrations, shapes, and scattering properties of these small
crystals at cloud top is crucial for satellite retrievals that rely on
visible and near-infrared wavelengths due to their strong influence on
cloud reflectance (e.g., Stephens et al., 1990; McFarquhar et al., 1999;
Yang et al., 2001).
Although not plentiful, there are some observations of the shapes of these
small ice crystals at the tops of anvils and convective towers. Gayet et
al. (2012) reported up to 70 cm-3 of frozen droplets and their
aggregates with chain-like shapes in the overshooting tops of a continental
deep convective cloud at T∼-58 ∘C. A mean effective diameter
of 43 µm, maximum particle size of ∼300 µm, and an
asymmetry parameter of ∼0.776 were observed in the very dense cloud
tops. Single frozen droplets and frozen droplet aggregates (FDAs) were also
observed in midlatitude continental convective clouds during the 2012 Deep
Convective Clouds and Chemistry (DC3) experiment (Barth et al.,
2015; Stith et al., 2014).
Based on these observations, the occurrence of single frozen droplets and FDAs
as a function of position within the anvil cloud and of updraft velocity was
determined (Stith et al., 2014). A positive correlation between the frequency
of occurrence of FDAs and the level of nitrogen oxide (NOx)
produced by lightning suggested that a strong electric force in the updrafts
was playing a role in the formation of the FDAs (Stith et al., 2016). Conversely,
these FDAs have not been observed in tropical or maritime
convective clouds where updrafts are not as strong. Aggregates of faceted
crystals (e.g., plate) are more common in these systems (Stith et al., 2002,
2004; Lawson et al., 2003; Connolly et al., 2005; Um and McFarquhar, 2009;
Gallagher et al., 2012) because droplets originating at cloud base are less
likely to reach the homogeneous freezing level of -38 ∘C
(Heymsfield et al., 2009).
The radiative properties (e.g., albedo) of convective cloud systems depend
strongly on both the concentrations and shapes of crystals in the anvil-cloud
layer. In order to better understand the role of continental convective
clouds in Earth's radiation budget, the fractional contributions of different
habits must be quantified, and the scattering properties of the habits
determined. This is complicated by a couple of issues. First, several
idealized crystal models representing shapes of small crystals have been
proposed (McFarquhar et al., 2002; Yang et al., 2003; Nousiainen and McFarquhar, 2004; Nousiainen et al.,
2011; Um and McFarquhar, 2011, 2013; Järvinen et al., 2016), but it is
not known which best characterizes the shapes. Second, few in situ aircraft
observations of continental convective clouds have been made due to their
high altitudes and the difficulty of flying through or near strong updrafts.
In this study, 22 393 crystals imaged by a cloud particle imager (CPI) on
6 June 2012 in anvil clouds over eastern Colorado during DC3 are analyzed to
determine the morphological properties of single frozen droplets and FDAs
(e.g., size and number of element) and their radiative impacts. Although
previous studies (Gayet et al., 2012; Baran et al., 2012; Stith et al., 2014,
2016) have analyzed FDAs observed in continental deep convective clouds, the
dimensions and three-dimensional (3-D) shapes of FDAs that are important for
radiative implication were not determined as is done in this study.
The remainder of this paper is organized as follows. Section 2 summarizes the
in situ aircraft measurements made during DC3. In Sect. 3, a habit
classification scheme that distinguishes FDAs from other crystals is
introduced along with the methodology used to identify the number and size of
element frozen droplets within FDAs. The morphology of FDAs and their
reconstructed 3-D shapes are shown in Sect. 4. Two different parameters that
describe the 3-D shapes of aggregate particles, fractal dimension and
aggregation index, are also introduced. Furthermore, the characteristics of the
shapes of FDAs are compared against those of black carbon aggregates in
Sect. 4. The significance of this study and concluding remarks are made in
Sect. 5.
Methodology
Ice crystal habit classification
Based on CPI crystal images obtained in tropical ice clouds, Um and
McFarquhar (2009) developed a classification scheme to sort crystals into
eleven habits: small, medium, and large quasi-spheres, columns, plates,
bullet rosettes, aggregates of columns, aggregates of plates, aggregates of
bullet rosettes, capped columns, and unclassified. To represent other crystal
habits commonly found in midlatitude and Arctic clouds, the capability of
sorting into more habits (i.e., dendrite, needle, aggregates of needles, and
FDAs) has been added to the scheme (McFarquhar et al., 2017). Thus, this
habit classification scheme now sorts crystals into 15 different categories
in a quasi-automatic manner that requires some manual intervention.
(a) Temperature and altitude of the NSF/NCAR GV aircraft as
a function of time on the 6 June 2012 flight and (b) the 1 s
average concentration of measured CDP and 2DC>100. Determined habit fraction
(c) by number and (d) by projected area as a function of
time. Habit categories for panels (c) and (d) are shown
using the colored legend under the figure . Habits are sorted into 15
categories: frozen droplet aggregates (FDAs), small quasi-sphere (SQS),
medium quasi-sphere (MQS), large-quasi sphere (LQS), plate, aggregates of
plates, bullet rosette, aggregates of bullet rosettes, column, aggregates of
column, needle, aggregates of needles, dendrite, capped column, and
unclassified as shown in Fig. 2. For simplicity single frozen drops (FD)
denoted in this figure includes SQS, MQS, and LQS, while other habits except
FDAs and UC are indicated as “Else” in this figure. Time periods 1, 2, and
3 are shaded gray in each panel.
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In this study, ice crystals classified as small (SQS), medium (MQS), and
large quasi-spheres (LQS) are regarded as single frozen droplets. The FDAs
that occur near anvil tops are often classified as bullet rosettes,
aggregates of bullet rosettes, or unclassified from the automated part of the
algorithm; therefore, an additional manual check was necessary to confirm
whether or not these crystals were FDAs. To be classified as FDAs, there must
be at least two quasi-circular frozen droplets as elements. Habits that
frequently occurred during the 6 June 2012 flight were single frozen droplets
(i.e., SQS, MSQ, and LQS) and their aggregates (i.e., FDAs), whereas very few
pristine shape crystals, such as plates, columns, and bullet rosettes, were
observed (see Table 1 and Fig. 3).
Contributions of ice crystal habits by number (red) and by
projected area (blue) during (a) all periods, (b) period 1, (c) period 2,
and (d) period 3. The total number of samples is indicated in each panel.
Acronyms for crystal habits are indicated in the caption of Fig. 2.
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Technique to identify element frozen droplets
The circle Hough transform (CHT, Duda and Hart, 1972) detects circular
objects in digital images and is one of many feature-extracting techniques
that use the Hough transform (Hough, 1962). Several variants of the Hough
transform have been developed, such as, the fast Hough transform (Li et al.,
1986), two-stage CHT (Yuen et al., 1990), space saving approach CHT (Albanesi
and Ferretti, 1990), and the phase-coding method (Atherton and Kerbyson,
1999). These techniques have been used to detect natural particles with
circular shapes in digital images, such as circular nanoparticles in
transmission electron microscopy (TEM) images (Bescond et al., 2014; Mirzaei
and Rafsanjani, 2017).
CPI images of frozen droplet aggregates (FDAs, left image of each
column) and those with determined element frozen droplets (red circle, right
image of each column). The 46 µm scale bar is shown in each FDA image.
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Prior studies have used such techniques to identify the elemental or primary
particles within black carbon aggregates (e.g., Bescond et al., 2014; China
et al., 2013), most of which are circular. Similar techniques can be applied
to the FDAs observed near the tops of anvil clouds assuming the element
frozen droplets have spherical shapes. The biggest difference between TEM and
CPI images is that the quality of TEM images is, in general, better than that
of CPI images. A CPI image has an inhomogeneous background and debris or
noise, such as impulse noise (i.e., salt-and-pepper noise), which causes
lower quality images. Thus, additional image-quality control was required
before applying the CHT technique to the images. This was accomplished in a
number of steps. First, a median filter that is a nonlinear digital filtering
technique to remove noise is applied to the CPI images classified as FDAs.
The 256-level gray-scale CPI images are then converted to binary images based
on the average intensity of pixels to further remove background noise and
debris. Figure 4 shows example images of CPI FDAs. Two different CHT
techniques, the two-stage CHT and phase-coding method, are then applied to
the images to detect element circles (i.e., frozen droplets) as shown by the
red circles in Figs. 4 and 5. Two different techniques are used because the
performance of each technique varies depending on the CPI image being
classified. The technique used for the subsequent analysis is chosen as that
for which the projected area of the FDAs determined for the element frozen
droplets identified by CHT technique (i.e., area determined by red lines in
Fig. 5) best matches that for the original CPI image (i.e., area enclosed by
green line in Fig. 5). However, the performance of both techniques is quite
similar. For example, the phase-coding technique shows closer agreement with
the imaged area for the FDAs shown in the top row of Fig. 5, while the
two-stage CHT shows closer agreement for the FDAs shown in the bottom row. Although the
phase-coding method provided marginally better results for ∼54 %
cases, the differences in projected area determined by the two techniques were
within 9.7 % for all FDAs. Thus, since the performance of both methods in
replicating the determined area of the CPI images is similar, there should be
minimal bias in the determined results. The number and size of the element
frozen droplets within the FDAs were then determined automatically. The
relative positions (i.e., x and y coordinates) of the element frozen
droplets were also identified.
Element frozen droplets (red circles) determined using the
phase-coding (left column) and two-stage CHT (middle column) techniques.
Examples of two different FDAs are shown in the top and bottom rows,
respectively. Original CPI images of FDAs are shown in the right column along
with the 46 µm scale bar. The detected boundary (green lines) of the FDAs are shown on
panels in the left and middle columns.
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Results
Frequency of occurrence of ice crystal habits
Figure 3 shows the normalized contribution of each habit to the total number
(red) and to the total projected area (blue) of measured ice crystals during
the three different time periods and integrated over the entire time period.
For all time periods, single frozen droplets represented the dominant habit
by number, whereas FDAs were dominant by projected area (see also Table 1).
The fraction (by number) of single frozen droplets was 73.0 %
(84.1 %; 70.6 %; 71.2 %) for all periods (period 1; period 2;
period 3), whereas the area fraction of FDAs was 46.3 % (27.8 %;
49.6 %; 47.5 %). The fraction of well-defined pristine ice crystals,
such as plates and columns, was less than 0.04 % by number and 0.12 %
by area for all time periods, whereas unclassified crystals represented
6.1 % (3.9 %; 5.3 %; 7.5 %) by number for all periods
(period 1; period 2; period 3) and 13.5 % (6.5 %; 10.9 %;
16.9 %) by area. These fractions of unclassified crystals were lower than
those obtained from anvil cloud in the tropics (Um and McFarquhar, 2009) that
showed more than 22 % and 37 % contributions by number and area,
respectively. The presence of small crystals with relatively simple habit
distributions shown in this study indicates that the anvil clouds were
sampled in an early stage of development, which was verified using radar
observations (Stith et al., 2014, 2016).
The average Dmax for all crystal habits was 80.7±45.4 µm
for all periods, with the average Dmax of 68.4±37.1 µm
during period 1 at T=-60.0±1.2 ∘C smaller than those of
72.4±42.9 and 84.4±48.8 µm during periods 2 and 3 at T=-57.5±0.3 ∘C and T=-56.6±0.5 ∘C, respectively
(Table 1). Table 1 also shows that the contributions of single frozen
droplets and FDAs sampled in the south and north anvil in periods 2 and 3 are
similar, whereas a much higher fraction of small frozen droplets was revealed
in the south anvil during period 1 at a slightly lower temperature. For
example, the fraction (by number) of single frozen droplets was 84.1 % in
period 1, and 70.6 % and 71.2 % in periods 2 and 3, respectively. The
fraction of FDAs in period 1 was 12.1 % and 27.8 % by number and
projected area, respectively, which was substantially lower than those sampled in
periods 2 and 3 (Table 1). Figure 2 shows that the fraction of single frozen
droplets, in general, decreased as the GV penetrated into the center of anvil
cloud (i.e., center of each gray shaded area shown on panels in Fig. 2), and
then increased as it approached the cloud edge (i.e., both sides of each
gray shaded area shown on panels in Fig. 2) for all periods. This variation
in the relative occurrence of small and large crystals is more distinctly seen by
comparing the NCDP and N2CD>100 shown in Fig. 2.
In summary, single frozen droplets and their aggregates dominated the upper
anvil clouds sampled in situ, with the relative frequency of occurrence of
single frozen droplets and FDAs dependent on temperature and position within
the anvil, consistent with the conceptual model proposed by Stith et
al. (2014, Fig. 12) and further detailed in Stith et al. (2016, Fig. 9).
Morphology of single frozen droplets and FDAs
Among the 4667 CPI images of FDAs, the CHT technique succeeded in identifying
element frozen droplets for 4356 FDAs, whereas it failed for 311 FDAs
(6.66 %). The number, size, and 2-D position of the element frozen
droplets within the FDAs were thus determined automatically. Figure 6a
shows the frequency distribution of the number of element frozen
droplets within FDAs. The average number of frozen droplets within FDAs is
4.7±5.0 and the FDAs with two element frozen droplets are dominant with
a frequency of occurrence of 42.0 %. This occurrence frequency gradually
decreases with the number of element frozen droplets. The average and
standard deviation of the diameter of the determined element frozen droplets
(blue) are shown as a function of the number of element frozen droplets
(Fig. 6b). The average and standard deviation of Dmax of
the single frozen droplets (red) are also shown for comparison. Considering
plausible errors (∼±4.6 µm) in the identifying algorithm
and the 2.3 µm CPI resolution, the average and standard deviation
of the diameter of the element frozen droplets (31.79±7.12 µm) are
comparable with those of the Dmax of single frozen droplets (34.03±6.22 µm). The CPI errors in sizing particles vary with focus
(Connolly et al., 2007) and can be larger than those considered in this
study. The quasi-spherical shapes, non-pristine shapes, and similarity of
single and element droplet sizes indicate that diffusional growth was likely
not effective for the anvils sampled, and the large ice crystals (i.e., FDAs)
grew mainly through aggregation. They also indicate that the sampled anvil
clouds are in an early stage of development as verified by radar observations. The
more complex structure of FDAs with an increase in the number of elements may
cause errors in the estimated size of the element frozen droplets. For
example, the increase in the determined diameter of element frozen droplets
as the number of element frozen droplets increases from two to five in Fig. 6b
may not be a physical effect, but rather caused by uncertainty
in the methodology. The sizes of the element frozen droplets here (31.79±7.12 µm) are larger than those (15–20 µm) noted by
Gayet et al. (2012) and those (∼10 µm) measured during
laboratory experiments (Pedernera and Ávila, 2018). It is hard to
determine the extent to which differences in methodology as opposed to
physical differences in droplet sizes caused these differences because Gayet
et al. (2012) did not specify how they determined frozen droplet size. However,
despite the unavoidable errors in identifying the element frozen droplets due
to the quality of the CPI images, the differences are large enough to suggest
physical differences.
(a) Normalized frequency of occurrence of the number of
component frozen droplets within 4356 FDAs analyzed. (b) The average
and standard deviation of the diameter of frozen droplets as a function of number
of component frozen droplets within FDAs (blue). The average (red solid line)
and standard deviation (red dash line) of the Dmax of single frozen
droplets are also shown.
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Three-dimensional representations of FDAs and comparison with
black carbon aggregates
To determine microphysical (e.g., fall velocity) and scattering (e.g.,
asymmetry parameter) properties of cloud particles required for models,
idealized 3-D models of the crystals are needed. However, cloud particle images
recorded by cloud probes are silhouettes (i.e., 2-D images) of 3-D cloud
particles (Nousiainen and McFarquhar, 2004). Retrieving the 3-D shapes of
cloud particles based on the recorded silhouettes is difficult, especially
for non-spherical ice crystals that have non-pristine shapes. It is easier
to reconstruct 3-D shapes of well-defined pristine crystals, such as columns
and plates. For example, an iterative approach to retrieve the 3-D shapes of
bullet rosette crystals was developed (Um and McFarquhar, 2007). Assuming
that the element crystals all had the same shape (e.g., plates), the 3-D
shapes of more complex crystal aggregates (e.g., aggregates of plates) have
also been reconstructed from crystal silhouettes (Um and McFarquhar, 2009).
FDAs consist of at least two element frozen droplets whose shapes are assumed
to be spheres even though the elements are in fact quasi-spherical, meaning
they have some departures from a spherical shape. The number, size, and 2-D
position of the element frozen droplets within the FDAs were determined from
the CPI images as explained in Sect. 3.2. Using this information, the 3-D
shapes of FDAs are reconstructed for the given 2-D silhouette (i.e., CPI
image) with the following assumptions:
element frozen droplets of FDAs are spheres;
there is no overlap between the elements of the frozen droplets; and
the maximum number of contacting points of an element frozen droplet with
other frozen droplets is two.
Since the relative positions (i.e., x and y coordinates) and sizes of the
element frozen droplets are known, the reconstruction problem becomes one of
stacking spheres with varying combinations of a vertical (z) coordinate.
The abovementioned assumptions reduce the number of possible 3-D realizations of FDAs
for a given 2-D projection so that a maximum number of 2np-2 3-D
realizations is possible, where np is the number of element
frozen droplets. For example, for FDAs with five element frozen droplets
(i.e., np=5), a maximum number of eight different 3-D realizations is
possible, while a maximum number of 256 3-D realizations is possible for FDAs with
10 elements. Figure 7 shows six different example 3-D realizations of the FDA
shown in the top-left panel of Fig. 4. Since this FDA has 12 element frozen
droplets, theoretically a total of 1024 3-D realizations are possible.
However, FDAs such as this with a large number of element frozen droplets usually have
notably fewer 3-D realizations due to the abovementioned assumptions, in
particular due to the no overlap assumption.
As the number of element frozen droplets increases, the number of possible
3-D realizations also increases. For FDAs with 20 element frozen droplets, a
maximum number of 262 144 different 3-D realizations is possible.
Considering all 262 144 3-D realizations of FDAs is impractical for
calculations of single-scattering properties. Thus, parameters that
characterize the 3-D shapes of particles and link the 3-D shapes to
scattering properties are required. Um and McFarquhar (2009) used several
parameters, such as the aggregation index (AI), the area ratio, and the
normalized projected area, to characterize the 3-D shape and to link to the
scattering properties of aggregates of plate crystals. The motivation for the
use of the AI is that the asymmetry parameter (g) of aggregates of plates
was previously seen to increase with AI (Um and McFarquhar, 2009). In this
study, a similar approach is adapted and the AI is defined as
AI=∑i=1np∑j=1npDijMax∑i=1np∑j=1npDij,
where Dij is the distance between the center of frozen droplet i and
that of frozen droplet j and np≥3. Physically, AI
represents the ratio of the sum of the distances between the centers of all
frozen droplets compared to that when they all lie on a straight line. Thus,
when all frozen droplets lie on a straight line AI=1, whereas
a smaller AI implies a more compact shape. The AI is calculated for every 3-D
realization. Thus, there are 262 144 AIs for FDAs with 20 element frozen
droplets. Since the 3-D shape complexity of a particle (i.e., AI) and its g
was previously shown to have a positive relationship for aggregates of plate
(Um and McFarquhar, 2009), the maximum, minimum, and average AI are
calculated for a given FDA. The calculated maximum, minimum, and average AI
of FDAs as a function of the number of element frozen droplets (for
np>2) are shown in Fig. 8. The AI of FDAs decreases with np, which
indicates that larger FDAs with more element frozen droplets have more
compact shapes. Figure 9 shows that the AI of FDAs decreases slightly with
increasing temperature. Stith et al. (2014) showed that FDAs were frequent in
the lower regions (i.e., higher temperatures) of the upper anvil.
Six different examples of 3-D representations of FDA. Each image has
the same projected area (gray) as the CPI image shown in Fig. 4 (top-left
image).
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The calculated maximum (blue), minimum (green), and average (red)
aggregation index (AI) of FDAs (circles) as a function of the number of
element frozen droplets. Best-fit lines are shown using solid lines.
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A fractal dimension (Df) has been widely used to describe the 3-D
shape or compactness of black carbon (soot) aggregates (e.g., Bescond et al.,
2014; China et al., 2013) and can be represented using the following scaling
law:
np=kfRgrpDf,
where Rg, rp, and kf are the radius of
gyration, average radius of elements frozen droplets, and fractal prefactor
(or structural coefficient) (Mandelbrot, 1982), respectively. The radius of
gyration is represented as
Rg2=∑inpxi2mi∑inpmi,
where mi is the mass of ith element and xi is the distance
between element i and the center of mass of the FDA. The radius of gyration
is an overall cluster radius. The chain-like shapes of FDAs observed near the
tops of anvil clouds (e.g., Fig. 1) show similarity with those of black
carbon (BC) aggregates (see Figs. 6–8 in Lewis et al., 2009). Thus,
identifying fractal dimensions of FDAs and comparing them against those of BC
aggregates is of great interest to calculate the scattering properties as a
function of shape. In this study, possible 3-D realizations of FDAs are
represented using both AI and Df with subsequent comparison to
the shape of BC aggregates.
The average aggregation index (AI, red circles in Fig. 8) as a
function of temperature (blue circles). The mean and standard deviation of
AI for six temperature ranges are indicated by the red circles and vertical
bars, respectively.
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To provide an overview of the shapes of the FDAs, the Df,
kf, Rg, and rp are calculated for three
3-D realizations of a FDA that represent the maximum, minimum, and average
AI. For each 3-D realization Rg/rp is plotted against np in Fig. 10.
Then, the Df and kf are determined by fitting to
Eq. (2). For a given Df, kf represents the degree of
compactness, with a smaller kf indicating less packing density
(Lewis et al., 2009). The FDAs with the maximum, minimum, and average
Rg/rp have a Df (kf) of 1.2083
(2.0998), 1.4329 (2.3864), and 1.4124 (2.0412), respectively. A smaller
Df indicates a more linear shape with 1.0 indicating a perfectly
linear shape; the compactness also increases with Df. Thus, FDAs
with the maximum Rg/rp have more linear (chain-like)
shapes, while FDAs with the minimum Rg/rp have more
compact shapes.
Relationships between the ratio of the radius of gyration
(Rg) to the average diameter of element frozen droplets
(rp) and the number of element frozen droplets (np).
Maximum (blue), minimum (green), and average (red)
Rg/rp are shown using circles, and corresponding best-fit
lines are plotted using solid lines. The calculated fractal dimension
(Df) and the fractal prefactor (kf) of FDAs with maximum,
minimum, and average Rg/rp are embedded. The
Df and kf of ambient (black) and denuded (yellow)
black carbon aggregates determined in China et al. (2013) are indicated
along with those commonly determined (purple) in several studies.
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Relationship between aggregation index (AI) and the ratio
of radius of gyration to the average radius of elements
(Rg/rp) of FDAs. The number of element frozen droplets
(no. elements) and number of all possible 3-D realizations (no. 3-D
realizations) are indicated. The best fit and correlation coefficient (r)
for the relationship between the AI and Rg/rp are
shown in red. Corresponding CPI images of FDAs are also embedded in
each panel.
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The Df=1.8 and kf=1.35 for BC aggregates determined
in previous studies (Meakin, 1983; Kolb et al., 1983; Sorensen and Robert,
1997; Lattuada et al., 2003; Pierce et al., 2006; Heinson et al., 2012;
Heinson and Chakrabarty, 2016) are shown in the purple dashed line in Fig. 10
for comparison. The Df=1.85 and kf=1.46 determined
for ambient BC aggregates (black dashed line) and Df=1.53 and
kf=2.40 for denuded BC aggregates (yellow dashed line) sampled
from the Las Conchas fire (New Mexico, 2011) (China et al., 2013) are also
shown in Fig. 10. The calculated fractal dimensions (1.20–1.43) of FDAs are
smaller than those of BC aggregates (1.53–1.85), which indicates that FDAs
have more linear branched shapes compared with the compact shapes of BC
aggregates. Previous studies have shown that the Df of fresh BC
aggregates is between 1.6 and 1.8 (e.g., Chakrabarty et al., 2006;
Köylü et al., 1995; Sorensen, 2001; Pierce et al., 2006; Heinson et
al., 2012) and becomes larger than 1.8 in aged BC aggregates (Lewis et al., 2009).
It was also shown that the scattering
properties of BC aggregates depended heavily on their Df (e.g.,
Sorensen, 2001; Liu et al., 2008). Thus, it is required to characterize the
3-D shapes of FDAs for the accurate calculation of radiative properties.
There is a fundamental difference in the nature of the variables AI and
Df that describe the 3-D shapes of aggregates. The former is a
3-D shape indicator of individual aggregates, whereas the latter is an
indicator for a group of aggregates. Each parameter has advantages and
disadvantages. For example, AI is useful to describe the 3-D shape of
individual aggregates and their scattering properties. As the
Df is intended to describe a group of aggregates, a statistically
significant number of samples is required to determine meaningful values and
they should not be used to describe individual aggregates. Though AI and
Df cannot be compared, a comparison between AI and
Rg/rp is possible. Comparisons between AI and
Rg/rp of FDAs with 10 (left) and 20 (right) element
frozen droplets are shown in Fig. 11. The CPI images of FDAs are embedded in
each panel. For the FDA with 10 elements a total 127 3-D realizations are
possible, whereas a total 65 535 3-D realizations are possible for the FDA
with 20 elements (Fig. 11). The best fits illustrated in Fig. 11 show
that AI and Rg/rp of FDAs are positively correlated
with high correlation coefficients. For all FDAs with np
>2, an average r of 0.942±0.094 is revealed. It indicates
that the AI and Rg/rp of aggregates are highly
correlated and both parameters can be used to describe individual and/or a
group of aggregates for the calculations of microphysical and radiative
properties.
Summary and conclusions
During the 2012 Deep Convective Clouds and Chemistry (DC3) experiment the
National Science Foundation/National Center for Atmospheric Research
Gulfstream V (GV) aircraft sampled the upper anvils of two storms that
developed in eastern Colorado on 6 June 2012. A cloud particle imager (CPI)
mounted on the GV aircraft recorded images of ice crystals at altitudes of
12.0 to 12.4 km and temperatures (T) of -61 to -55 ∘C. The GV flew two constant
altitude runs during this period that were segregated into three periods
according to the anvil and the temperature level sampled. A total of
22 393 CPI crystal images were analyzed, all with a maximum dimension
Dmax<433 µm and with an average Dmax of 80.7±45.4 µm. Dominant crystal habits observed during the 6 June 2012
flight were single frozen droplets and frozen droplet aggregates (FDAs, see
Fig. 1). A new algorithm that uses the circle Hough transform technique was
developed to automatically identify the number, size, and relative position
of element frozen droplets within FDAs and was applied to 4667 FDAs. Using
this information, the 3-D shapes of FDAs were reconstructed for given 2-D
silhouettes (i.e., CPI images) and two different parameters describing the
3-D shapes of aggregate particles, the aggregation index (AI) and fractal
dimension (Df), were determined. The characteristics of the
shapes of FDAs were compared against those of black carbon (BC) aggregates.
The anvil cloud selected for this study was an early-stage anvil associated
with a strong continental storm and appeared to provide conditions most
favorable for the formation of frozen drops and FDAs, as other ice particle
types were mostly absent in the location selected for study. Other anvils
from DC3 exhibited FDA's as common ice particle types, but to a lesser extent
than the cloud regions sampled here (Stith et al., 2014).
The most important findings from this study are summarized as follows:
For all time periods, single frozen droplets represented the dominant
habit by number, whereas FDAs were dominant by projected area. The fraction
(by number) of single frozen droplets was 73.0 % (84.1 %; 70.6 %;
71.2 %) for all time periods (period 1; period 2; period 3), whereas the
area fraction of FDAs was 46.3 % (27.8 %; 49.6 %; 47.5 %).
The fraction of well-defined pristine ice crystals (i.e., plates and
columns) was less than 0.04 % by number and 0.12 % by area for all
time periods, whereas unclassified crystals represented 6.1 % (3.9 %;
5.3 %; 7.5 %) by number for all periods (period 1; period 2; period
3) and 13.5 % (6.5 %; 10.9 %; 16.9 %) by area.
The high concentrations of small crystals (i.e., single frozen
droplets) with relatively simple habit distributions shown in this study
indicates that the anvil clouds were sampled in an early stage of development as
also verified using radar data.
The relative frequency of occurrence of single frozen droplets and
FDAs was dependent on temperature and position within the anvil, consistent
with the conceptual model proposed by Stith et al. (2014, 2016). The fraction
of single frozen droplets, in general, decreased as the GV penetrated into
the center of the anvil cloud, and then increased as it approached the cloud
edge for all three periods.
The average number of element frozen droplets within FDAs is
4.70±5.0. The FDAs with two elements were dominant with a frequency of
occurrence of 42.0 %. This occurrence frequency gradually decreased with
the number of element frozen droplets.
The average diameter of the element frozen droplets (31.79±7.12 µm) was comparable with that of single frozen droplets
(34.03±6.22 µm). The quasi-spherical shapes, non-pristine
shapes, and similarity of single and element droplet sizes indicate that
diffusional growth was likely not effective and that the large ice crystals (i.e.,
FDAs) mainly grew through aggregation.
The AI of FDAs decreases with an increase in the number of
element frozen droplets, which indicates that larger FDAs with more element
frozen droplets have more compact shapes. The AI of FDAs decreases with
increasing temperature, which agrees with the frequent occurrence of FDAs in
the lower regions (i.e., higher temperatures) of the upper anvil (Stith et
al., 2014).
The calculated fractal dimensions of FDAs (1.20–1.43) in this study
are smaller than those of BC aggregates (1.53–1.85), which indicates that
FDAs have more linear branched shapes compared against the compact shapes of
BC aggregates.
A strong positive relationship (r=0.942±0.094) between
AI and the ratio of radius of gyration (Rg) to the average radius
of element frozen droplets (rp) of FDAs is shown. Both parameters
can be used to describe 3-D shapes of aggregates and to link the scattering
properties, especially AI and Df for an individual and a group of
aggregates, respectively.
The results of this study have important implications for the improvement of
the calculations of the microphysical (e.g., fall velocity) and radiative
(e.g., asymmetry parameter) properties of ice crystals in upper anvil clouds,
especially continental convective clouds. To implement the results of this
study for numerical models and satellite-retrieval algorithms, a role of
electric fields within convective clouds should be identified and quantified
systemically. A recent laboratory experiment (Pedernera and Ávila, 2018)
showed that the collision and adhesion process was highly related to
electrical forces that stimulated the aggregation process of frozen droplet
aggregates. A subsequent study will calculate the single-scattering
properties and fall velocities of FDAs using the morphological features and
models of FDAs proposed here, which will have high impacts on clouds formed
over the US Great Plains and east Andes where strongest convection and electric
field exist.