The cloud particle concentration, size, and shape data from optical array
probes (OAPs) are routinely used to parameterise cloud properties and
constrain remote sensing retrievals. This paper characterises the optical
response of OAPs using a combination of modelling, laboratory, and field
experiments. Significant uncertainties are found to exist with such probes
for ice crystal measurements. We describe and test two independent methods
to constrain a probe's sample volume that remove the most severely
mis-sized particles: (1) greyscale image analysis and (2) co-location using
stereoscopic imaging. These methods are tested using field measurements from
three research flights in cirrus. For these cases, the new methodologies
significantly improve agreement with a holographic imaging probe compared to
conventional data-processing protocols, either removing or significantly
reducing the concentration of small ice crystals (< 200 µm)
in certain conditions. This work suggests that the observational evidence
for a ubiquitous mode of small ice particles in ice clouds is likely due to
a systematic instrument bias. Size distribution parameterisations based on
OAP measurements need to be revisited using these improved methodologies.
Introduction
A significant amount of our current understanding of cloud microphysics is
based on in situ measurements made using optical array probes (OAPs). This
includes how cloud properties are parameterised in numerical climate and weather
models and how they are retrieved from remote sensing datasets, including
global cloud and precipitation monitoring satellites such as NASA's GPM
(Global Precipitation Mission), CloudSat, and CALIPSO (Cloud-Aerosol Lidar
and Infrared Pathfinder Satellite Observation) (Mitchell et al., 2018;
Sourdeval et al., 2018; Ekelund et al., 2020; Eriksson et al., 2020;
Fontaine et al., 2020).
Optical array probes are a family of instruments that have been widely used
by the cloud physics community for more than the last 40 years. Primarily OAPs have
been operated on research aircraft (Wendisch and Brenguier, 2013). They
collect images of cloud particles and are used to derive cloud particle
concentration, size, and crystal habit (shape). Optical array probes operate
by recording a shadow image as a particle crosses a laser beam that is
illuminating a 1D linear array of photodiode detectors. If the light
intensity at any of the detectors drops below a threshold value, the probe
records an image of the particle and the corresponding timestamp. A
two-dimensional image of the particle is constructed by appending
consecutive one dimensional “slices” from the array of detectors as the
particle moves perpendicular to the laser beam due to the motion of air
through the probe.
The rate at which data need to be acquired from the detectors depends on
the air speed through the probe and the required image resolution. For
example, when operated on research aircraft at a typical airspeed of 100 m s-1, image slices from the detectors are acquired every 0.1 µs to
achieve an image resolution of 10 µm. Modern OAPs have 64- to 128-element detector arrays with pixel resolutions ranging from 10 to 200 µm. Monoscale probes use a 50 % drop in intensity as a threshold
for detection, which results in 1-bit binary images (Knollenberg, 1970;
Lawson et al., 2006), while most greyscale OAPs have three intensity
thresholds, which result in 2-bit greyscale images (Baumgardner et al.,
2001).
When particles pass through the object plane of a probe, they are in focus
and accurate digitised images are recorded. When particles are offset from
this plane, the diffraction of light by the particle alters the size and
shape of the recorded image from its original form. When the distance from
the object plane (Z) is sufficiently large, the reduction in light intensity
at the detector will no longer exceed the detection threshold. This distance
is known as the probe's depth of field (DoF). For large particle sizes, the
DoF is constrained by the physical separation between the laser transmit and
receive optics, which are in protruding structures referred to as “arms”.
The following equation is generally used to define the DoF of monoscale
probes using a 50 % intensity threshold for detection (Knollenberg, 1970):
DoF=±cD024λ,
where D0 is the particle diameter, and λ is the laser
wavelength. c is a dimensionless constant, typically between 3 and 8 (Lawson
et al., 2006; Gurganus and Lawson, 2018). The DoF is used to determine
particle concentration, and as a result uncertainty in c propagates into
uncertainty in the derived concentration. Particle concentration can be
calculated by dividing the number of counts by the sample volume (SVol),
which is given by
SVol=TAS∫-DoF+DoFR(E-1)-D||ZdZ,
where TAS is the true air speed, E is the number of detector array elements,
R is the pixel size of the probe, and D|| is the image
diameter in the axis parallel to the optical array. The integration of the
effective array width (R(E-1)-D||(Z)) is performed over
whichever is smaller out of the DoF and the arm width of the probe.
For spherical particles, corrections exist for the diffraction effects of
sampling offset from the object plane, which allows for the calculation of the
true particle size from the measured image size. Korolev et al. (1991) show
that the diffraction from spherical liquid drops can be approximated by the
Fresnel diffraction from an opaque disc. The ratio of the measured image
diameter to the true particle diameter is a function of the dimensionless
distance from the object plane Zd:
Zd=4λZD02.
Korolev (2007, hereafter K07) describe how the size of the bright
spot at the centre of a diffraction image can be used to determine a
sphere's distance from the object plane and therefore true size. O'Shea et
al. (2019, hereafter O19) show that this correction is effective for modern
OAPs up to approximately Zd= 6, after which the images are too
fragmented to reliably correct. O19 show that greyscale information can be
used to remove these fragments by identifying the distance from the object
plane of spherical particles in the range Zd= 3.5 to 8.5. This
allows a new DoF to be defined that excludes the fragmented images.
There has been significant discussion in the literature about the presence
of high concentrations of small ice particles (< 200 µm)
observed by OAPs in cirrus and other types of ice clouds (Jensen et al.,
2009; Korolev et al., 2011). O19 show that fragmented images near the edge
of the DoF have the potential to significantly bias OAP particle size
distributions (PSDs) and result in an artificially high concentration of
small particles.
This paper quantifies the uncertainties in OAP size and shape measurements
of non-spherical ice crystals and presents corrections that remove large
biases from OAP datasets. In Sect. 3.1, 3D ice crystal analogues are
repetitively passed through the sample volume of an OAP at different
distances from the object plane. These results are used to examine the
ability of a diffraction model based on angular spectrum theory to
characterise the response of OAPs. In Sect. 3.2 to 3.5 a variety of ice
crystals from commonly occurring habits are tested with the diffraction
model to quantify how OAP image quality degrades throughout a probe's sample
volume. Section 4 suggests and tests methods to improve OAP data quality.
The impact these results have on ice crystal PSDs is examined using field
measurements collected during three research flights in frontal cirrus. The
impacts that OAP measurement bias has on our understanding of ice cloud
microphysics are discussed in Sect. 5.
MethodsOptical array probes
This paper uses data from two types of commercially available OAP: a CIP-15
(cloud imaging probe, DMT Inc., USA; Baumgardner et al., 2001) and a 2D-S
(2D stereo, SPEC Inc., USA; Lawson et al., 2006). The CIP-15 has a 64-element photodiode array and effective pixel size of 15 µm. The
laboratory experiments were conducted with a CIP-15 with an arm separation
of 70 mm (Sect. 3.1) and the field measurements with a second CIP-15 with an
arm separation of 40 mm (Sect. 4.1). Images are recorded at three greyscale
intensity thresholds. For this work, they were set to the manufacturer
default settings of 25 %, 50 %, and 75 %. The 2D-S consists of two
optical arrays and lasers orientated at right angles to each other and the
direction of motion of the particles and aircraft. The laser beams overlap at
the centre of the probe's arms, and each pair of transmit and receive arms are
separated by 63 mm. Each optical array has 128 elements and 10 µm pixel
resolution. The 2D-S is a monoscale probe with a single 50 % intensity
detection threshold. Both probes are fitted with anti-shatter tips to
minimise ice shattering on the leading edge of the probe during field
measurements. This was further minimised by removing particles with
inter-arrival times less than 1 × 10-5 s when calculating PSDs from field
measurements (Field et al., 2006).
Baumgardner and Korolev (1997) show that the electronic time response of
older probes can significantly reduce the DoF of small particles. This
effect has been minimised in more modern probes such as the 2D-S and CIP-15,
which have an order of magnitude faster time response.
A range of definitions have been used to define the diameter of ice crystals
from OAP images. Here we test three metrics that have been widely used by
the community. First, the mean of the particle extent along the axes
parallel and perpendicular to the optical array (mean X–Y diameter). Second,
the diameter calculated using D=(4A/π)1/2, where A is the
particle area calculated as the sum of the pixels (circle equivalent
diameter). Third, the major axis length of the ellipse that has the same
normalised second central moments as the region (maximum diameter).
An image frame from the OAP may contain more than one object, where
individual objects are defined as collections of pixels with eight-neighbour
connectivity. This can be due to diffraction, with a single particle
appearing as more than one object as the structure and intensity of the
transmitted light degrades due to poor focus. However, it may also be due to
shattering causing multiple particles to have sufficiently small separations
that they are captured in the same image frame or occasionally when there
are very high concentrations of ambient particles. A particle sizing metric
can either relate to the largest object in an image frame or use the
bounding box encompassing all objects. Some previous studies have filled any
internal voids within objects in an image frame. For this work, unless
otherwise stated, the mean X–Y, maximum, and circle equivalent diameters
are calculated using the bounding box encompassing all objects in an image
frame, and any internal voids are not filled.
Ice crystal analogues
Three-dimensional ice crystal analogues were grown from a sodium
fluorosilicate solution (Ulanowski et al., 2003). These analogues have similar
crystal habits to ice and a refractive index of 1.31, virtually identical to
that for ice at visible wavelengths. Three rosette shapes were used in these
experiments with approximate diameters 118 µm (ROS118), 250 µm
(ROS250), and 300 µm (ROS300) (Fig. 1). The CIP-15 was mounted as
shown in Fig. 2 so that the laser beam was vertically aligned. Each analogue
was in turn placed on an anti-reflective optical window that was attached to
a three-axis translation system that allowed the analogue's 3D position to be
controlled. The stages that moved along the axes parallel (x axis) to the
diode array and laser beam (z axis) each had a unidirectional position
accuracy of 15 µm and travel ranges of 100 and 150 mm,
respectively (X-LRM050A and Z-LRM150A, Zaber Technologies Inc., Canada).
Movements along the axis that air flows through the probe under normal
operation (y axis) were made using a belt-driven stage with a maximum speed
of 1.1 m s-1, positional accuracy of 200 µm, and maximum travel
range of 70 mm (X-BLQ0070-EO1, Zaber Technologies Inc., Canada).
Microscope images of sodium fluorosilicate crystals that were used as analogues for ice crystals. These are referred to as ROS118 (a), ROS250 (b), and ROS300 (c).
(a) Image of the experimental set-up for the ice crystal analogue tests of the CIP-15. Panel (b) shows a schematic of the experimental set-up. The CIP-15 is horizontally mounted on the left of the image. The translation stages used to move ice crystal analogues through the CIP-15 sample volume are shown on the right of the image. The x axis is perpendicular to the plane of drawing.
CIP-15 images of the ice crystal analogues were collected by moving them
through the laser beam along the axis of airflow. For each analogue, this was
repeated five times before its position was stepped in 0.5 mm increments
between the probe's vertical arms (along the z axis). This allows images of
the analogues to be compared at different distances from the object plane.
Images were post-processed to take account of any difference in velocity
between the stage and the CIP-15 data acquisition rate by resampling the
images along the axis perpendicular to the optical array. This was performed
to match the aspect ratio at Z= 0 of the CIP-15 image and a microscope
image of each analogue. This typically corresponded to a particle stage
velocity of ∼ 0.1 m s-1.
Synthetic data (angular spectrum theory)
Theoretical shadow images of 2D non-spherical shapes were calculated using a
diffraction model based on angular spectrum theory (referred to as the AST
model). Several previous studies describe this model in detail (Vaillant de
Guélis et al., 2019a, b). We initialised the model using a 2D
binary image of an opaque shape at the object plane (Z= 0) and calculated
the wave field for different positions between the probe arms in the z axis.
This model has been shown to give good agreement with OAP images of several
types of 2D rectangular columns using images printed on a rotating disc
(Vaillant de Guélis et al., 2019a).
In this study, we use a variety of different shapes to initialise the model.
In Sect. 3.1, the diffraction model is compared to CIP15 images of 3D ice
crystal analogues. To initialise the model for the comparisons with ROS250 and
ROS300, the CIP-15 image of them at Z= 0 is used. Due to the smaller size of
ROS118 and coarse pixel size of the CIP-15, a microscope image of the analogue
is used to initialise the model. This image was converted to a binary image.
In Sect. 3.2 the quality of OAP images of commonly occurring ice crystal
habits is explored. This is done by initialising the model with a variety of
different ice crystal images. The ice crystal dataset contains 1060 images
that were collected using a cloud particle imager (CPI, SPEC Inc., USA) and
has previously been used to train habit recognition algorithms (Lindqvist et
al., 2012; O'Shea et al., 2016). It includes images of ice crystals from
arctic, mid-latitude, and tropical clouds. These images have been manually
classified into seven habits (rosette, column/bullet, plate, quasi-spherical,
column aggregate, rosette aggregate, and plate aggregate). To initialise the
model, each CPI image was converted to a binary image. Shadow images were
calculated every 2 mm for the range Z= 0 to 100 mm. These images were
averaged to 10 µm pixel resolution, which is typical of modern OAPs.
All simulations were performed using a light wavelength of 0.658 µm.
Diffraction simulations from an image of a rosette crystal collected in cirrus cloud using a CPI (see text for details). Panel (a) shows the image at Z= 0 that is used to initialise the model. The other panels show images at different distances from the object plane (Z= 5, 10, and 20 mm). Green, blue, and black pixels correspond to decreases in detector intensity of 25 % to 50 %, 50 % to 75 %, and greater than 75 %, respectively.
Same as Fig. 3 but for a column.
An example simulation for a rosette crystal is shown in Fig. 3 and a column
in Fig. 4; the top left panels show the images at Z= 0 that are used to
initialise the model. The other panels show images of the crystals at
different distances from the object plane. Green, blue, and black pixels
correspond to decreases in detector intensity of 25 % to 50 %, 50 % to 75 %,
and > 75 %, respectively. Figures 3 and 4 show the rapid
deterioration in image quality within a few millimetres of the object plane, which
will impact derived properties such as particle size, number, and habit. This
compares to many tens of millimetres for the typical arm separation of modern OAPs.
Aircraft measurements
This paper uses measurements from three flights by the Facility for Airborne Atmospheric Measurements (FAAM) BAe-146 research
aircraft sampling frontal cirrus in the UK on the 11 March 2015 (nominal
flight number B895), 7 February 2018 (C078), and 23 April 2018 (C097). The
first two flights have previously been described in detail by O'Shea et
al. (2016) and O19. For all three flights, the aircraft performed straight and
level runs of approximately 10 min at different temperatures within the
cloud. Ice crystals were dominated by rosettes, columns, and aggregates. Data
from a 2D-S is available for the 11 March 2015 and CIP-15 for 7 February
and 23 April 2018. On all flights the FAAM BAe-146 was fitted with a
holographic imaging probe (HALOHolo). HALOHolo has a 6576 × 4384
pixel CCD (charged-coupled device) detector with an effective pixel size of 2.95 µm and arm
separation of 155 mm. The probe acquires six frames per second, which equates
to a volume sample rate of ∼ 230 cm3 s-1. The
detection of small particles is limited by noise in the background image.
Therefore, a minimum size threshold of 35 µm is applied, above which it
is estimated that the probe's detection rate is greater than 90 %
(Schlenczek, 2017). Shattered particles were minimised by removing all
particles with interparticle distances less than 10 mm (Fugal and Shaw,
2009; O'Shea et al., 2016).
Section 4.2 shows a comparison between the 2D-S and a cloud droplet probe
(CDP, DMT Inc.) during a flight in liquid stratus on 17 August 2018 (C031).
The CDP sizes particles (3 to 50 µm) using the scattered light
intensity assuming Mie scattering theory and spherical particles (Lance et
al., 2010). The probe was calibrated during the campaign using glass
spheres.
Results and discussionOAP and AST model comparison using ice crystal analogues
This section compares CIP-15 images of ice crystal analogues with diffraction
simulations using the AST model. Figures 5–7 show the image size of the ice
crystal analogues ROS118, ROS250, and ROS300 at different distances (Z) from
the object plane measured by the CIP-15 (black markers) and modelled using
angular spectrum theory (red lines). Top left panels show the image diameter
(mean X–Y), while the particle area is shown in the top right; both use a
50 % drop in light intensity for the detection threshold. The other panels
show different combinations of simple greyscale ratios. The abbreviations
A25–50, A50–75, and A75–100 are used to denote the number of
pixels associated with a decrease in detector signal of 25 %–50 %, 50 %–75 %, and 75 %–100 %, respectively. Example CIP-15 images of the ice
crystal analogue ROS300 at three distance from the object plane are shown in Fig. 8.
A comparison between CIP-15 images and diffraction simulations (red lines) of the ice crystal analogue ROS118. Grey dots show data from individual CIP-15 images, and black dots show the median for each 1 mm Z bin. Panel (a) shows the mean X–Y image diameter. Panel (b) shows the number of pixels using 50 % detection thresholds. Other panels show the ratio of the number of pixels (area) at different greyscale thresholds.
Same as Fig. 5 but for the ice crystal analogue ROS250.
Same as Fig. 5 but for the ice crystal analogue ROS300.
CIP-15 images of the ice crystal analogue ROS300 at three distances from the object plane.
All three analogues have a general trend of diameter initially increasing with
Z. The full DoF was sampled for ROS118 and shows the images fragmenting and
diameter decreasing near the edge of the DoF. In addition to these general
trends, there is a significant amount of fine-scale structure that is
specific to each sample. There is a general trend of the greyscale ratio
A75–100 decreasing with Z, while both A25–50 and A50–75
initially increase for all three analogues. Like the diameter vs. Z plots, there is
a significant amount of fine-scale structure overlaying these general
trends.
In general, the AST model can capture the large-scale structure in these
measured parameters, although some discrepancies are present in the finer
detail. For ROS118, the DoF from the experiments and the model agree to
within ±1 mm (Fig. 5). The size and greyscale parameters calculated
from CIP-15 images are not completely symmetrical about Z= 0. The reason
for this is unclear; potential causes are if the CIP-15 laser beam is not
perfectly collimated, additional refraction caused by the optical window
used to mount the sample, or changes to the CIP-15 background or dark current
calculation due to attenuation by the optical window.
OAP ice crystal sizing
Having investigated the performance of the AST model using 3D analogues of
complex ice, we will now use the AST model to examine the ability of OAPs to
correctly determine the size of commonly occurring ice crystals. Figure 9
left panels show the ratio of the measured diameter (D) to the true diameter
(D0) vs. Zd for diffraction simulations of 1060 ice crystals. The
data for each individual ice crystal are shown as grey lines, while the
coloured lines are the median for each habit. Top panels show plots using
the circle equivalent diameter, while the middle panels use the mean X–Y
diameter and maximum diameter. Right panels show histograms of D/D0 for
each habit calculated for the Zd range from 0 to 10.
Left panels show the ratio of the measured diameter (D) to the true diameter (D0) vs. Zd for diffraction simulations of 1060 ice crystals. The data for each individual ice crystal are shown as grey lines, while the coloured lines are the median for each habit. Right panels show histograms of D/D0 for each habit calculated for the Zd range 0 to 10. Top panels show plots using the circle equivalent diameter, while the middle panels use the mean X–Y and maximum diameters. Bottom panels show the diameter corrected using K07.
Figure 9 shows large differences in these relationships depending on whether
the mean X–Y, maximum, or circle equivalent diameters are used to define the
particle size. For the 1060 ice crystal images used in this study, the median
D/D0 over the Zd range from 0 to 8 is 1.1 using circle equivalent
diameter, 1.0 using the mean X–Y diameter, and 1.0 using the maximum
diameter. However, there is significantly less variability between crystals
using circle equivalent diameter, which has an interquartile range
D/D0 of 0.2 compared to 1.1 and 1.3 using the mean X–Y and maximum
diameters, respectively. This is also shown in Tables S1–S3 in the Supplement, which gives the
median and interquartile range D/D0 at selected Zd for each habit
using the three different size metrics.
There is a general trend of increasing size with distance from the object
plane. Oversized estimations are up to approximately 100 %, 200 %, and 50 % using
mean X–Y, maximum, and circle equivalent diameters, respectively. However,
the degree of oversizing is dependent on habit, with quasi-spherical and
plate aggregates most significantly oversized using all D definitions. In
agreement with O19, once D reaches a maximum, further increases in Z cause
the images to fragment and their size to decrease until they are no longer
visible.
K07 use the size of the internal voids within images of droplets to
determine their Zd and correct their size. O19 show that this
algorithm is effective using modern OAPs for droplets with Zd<∼ 6. For Zd> 6, the images are too fragmented
for their size to be corrected. The K07 approach was derived by considering
Fresnel diffraction from opaque discs and has only been tested for images
of spherical droplets. However, in the absence of an alternative, previous
studies have applied K07 to images of ice crystals (e.g. Davis et al.,
2010). To examine the efficacy of this approach, Fig. 9 bottom panels show
the mean X–Y diameter of the simulated images of ice crystals once the K07 approach has
been applied. The ratio of their K07 corrected diameter to their true
particle diameter is shown as a function of Zd (left panel), while
probability density functions of D/D0 for each habit are shown in the
right panel. The median D/D0 for the Zd range 0 to 8 is 0.9, and
the interquartile range is 1.1. For a number of habits (rosette, plate,
quasi-spherical, rosette aggregate, and plate aggregate), K07 reduce the
number of oversized particles across most of the DoF. For bullets, columns,
and column aggregates, the K07 approach has minimal impact on the probe sizing. For all
habits, the K07 approach is not able to remove the small image fragments that occur when
a particle is near the edge of the DoF.
Depth of field dependence on particle habit
Uncertainty of derived physical quantities (e.g. number concentration) from
OAPs is dependent on the sample volume and therefore uncertainty in the DoF
(see Eq. 2). The DoF of an OAP is commonly calculated using Eq. (1) with a
single c value. The variable c in this equation is the Zd where a
particle is no longer detected by the OAP. If a single c value is used this
would need to be independent of particle shape. Table 1 shows the median and
interquartile range Zd where particles are no longer visible for each
habit using the maximum, mean X–Y and circle equivalent diameters. Using
mean X–Y, the habit median DoF varies between Zd= 5.0 and 9.9 for
rosettes and quasi-spherical particles, respectively. Using the maximum as
the particle sizing metric, the median DoF varies by a similar amount ranging
between Zd= 3.4 and 7.8 for bullets and quasi-spherical crystals. In
addition, particles have significant intra-habit variability using both
maximum and mean X–Y, with most habits DoF interquartile ranges greater
than 2 Zd. The variability is lower using circle equivalent diameter,
with median DoFs ranging between 8.2 and 10.2 for plates and bullets,
respectively, with habit interquartile ranges near 1 Zd. As a result,
derived physical quantities such as number concentration will have lower
uncertainty if circle equivalent diameter is used to define the particle
size compared to maximum and mean X–Y diameters.
Median and interquartile range (IQR) normalised dimensionless distance from the object plane (Zd) where particles are no longer visible for different habits; this is equivalent to c in Eq. (1).
BulletsColumnColumnsPlatesPlateQuasi-RosettesRosetteaggregatesaggregatessphericalaggregatesMaximumMedian3.44.63.95.65.87.84.64.1IQR1.31.52.02.81.92.01.91.9Mean X–YMedian6.86.67.27.07.09.95.05.4IQR2.01.72.13.02.42.02.02.0Circle equivalentMedian10.29.49.98.29.09.48.69.2diameterIQR1.01.00.91.21.11.41.31.1Greyscale information
Greyscale information in OAP imagery has previously been used to filter
severely mis-sized images and enforce a DoF threshold that improves data
quality (O19). Figure 10 shows combinations of simple greyscale ratios as a
function of Zd for the simulation of 1060 ice crystal images described
in the previous section. Left panels use the size metric mean X–Y diameter
in the Zd calculation, whereas the right panels use circle equivalent
diameter in the Zd calculation. Like the ratio D/D0 (Fig. 9), the
greyscale ratios also show significant variability between habits as a
function of Zd. Figure 10 shows this variability is greater if mean X–Y
diameter is used to calculate Zd, although it is still significant using
circle equivalent diameter. The variability is larger still using maximum
diameter (not shown).
Combinations of number of pixels at different greyscale ratios as a function of Zd for the simulated ice crystal images. Panels (a), (c), and (e) show plots where mean X–Y is used as the sizing metric, while panels (b), (d), and (f) use circle equivalent diameter.
The O19 approach uses simple greyscale ratios to determine Zd for spherical liquid
droplets near the edge of the DoF (3.5 <Zd< 8.5).
This allows a new DoF to be defined that excludes fragmented images,
removing significant biases in the PSD. This is possible since all spherical
droplets independent of size have the same greyscale ratios at a given
Zd. Figure 10 shows that this is not true for ice crystals where the
initial shape of the ice crystal has an impact on the greyscale ratios at a
given Zd. As a result, the O19 approach cannot be used to determine Zd in the
same way.
Habit recognition
The shape of ice crystals is a key microphysical parameter impacting cloud
radiative properties in several ways. A variety of automatic image
recognition algorithms have been applied to OAP datasets to classify
particles into different habits (Korolev and Sussman, 2000; Crosier et al.,
2011; Praz et al., 2018). These algorithms typically rely on geometrical
features extracted from OAP images that have characteristic values for
specific habits. These characteristic values are usually determined by
manually classifying images into habits. These images are then used to set
thresholds or train machine learning algorithms to automatically classify
new images. For example, Crosier et al. (2011) used the following ratio to
discriminate between ice crystals and liquid droplets:
Circularity=P24πA,
where P is the particle perimeter, and A is the particle area including any
internal void. Crosier et al. (2011) used a threshold of 1.25 to
discriminate between these two categories. When images are manually selected
to train habit recognition algorithms, only images that can be identified
“by eye” as a specific habit will be included. For OAPs this is likely to be
images that are “in focus”. However, the shape of an OAP image and therefore
the geometrical features that are used in habit recognition algorithms
depend on where in the probe's sample volume a particle is detected. For
example, Fig. 3 shows a simulated 190 µm rosette at different
distances from the object plane. It is only in the top left panel (Z= 0)
that it can be identified as a rosette from its image alone. Figure 11 shows
how this particle's circularity changes with Z and Zd. At Z= 0 its
circularity is near 4, while at Z= 20 mm it is near 1 and may be confused
with a spherical droplet. Figure 11 demonstrates that the measured particle
shape is highly dependent on the position in the sample volume Zd (and
Z) with the circularity decreasing by a factor 2 by Zd= 1; in
comparison the particle size has only changed by 15 %.
The circularity (Eq. 4) of the rosette shown in Fig. 3 as a function of distance from the object plane Z and Zd.
The variance in geometrical features for each habit will not only be due to
natural variability in the shape of ice crystals but also due to their
position in the sample volume when measured. To date, this second effect has
not been accounted for by habit recognition algorithms. Therefore, currently
the results of habit classification algorithms on OAP datasets cannot be
considered quantitative.
Methods to improve OAP size distributions
Depending on where in the sample volume a particle is observed, the OAP image
size can range between being as small as a single pixel and up to twice the
true particle diameter (see Fig. 9). Algorithms such as those in K07 and O19 have
been derived using spherical shapes and are therefore not directly
applicable to OAP PSDs of non-spherical shapes. However, there are several
possible approaches that could be used to correct OAP ice crystal size
distributions.
Greyscale filtering
Unlike for liquid droplets, the O19 approach does not accurately determine Zd for
non-spherical ice crystals. We now describe a new technique to use greyscale
information to remove the most severely mis-sized ice crystals and constrain
the sample volume with a reasonable uncertainty using circle equivalent
diameter as the particle sizing metric. For example, if the diffraction
simulations are filtered to only include images that have at least one pixel
with a greater than a 75 % drop in light intensity (Fig. 7), then the
median position where particles are no longer visible (using a 50 %
intensity threshold) is Zd= 4.6 (interquartile range 1.1 in
Zd). This removes the fragmented images that begin to occur at
approximately |Zd|> 6. The median ratio
D/D0 for Zd< 4.6 is 1.2 (interquartile range = 0.1);
however, particles may still be oversized by approximately 40 % even with
this filter applied (Fig. 7). Other greyscale thresholds may be used to
provide a more or less restrictive DoF constraint. Table 2 shows the median
(interquartile range) c values for various greyscale thresholds between 65 %
and 85 %. Using a 65 % threshold the median c value is 6.2
(interquartile range = 1.3), while for 85 % it is 3.2 (interquartile
range = 0.9). It should be noted that the lower the greyscale threshold,
the higher the probability of a fragmented image being observed and the
small particle concentration being biased.
Median (interquartile range) depth of field c value (Eq. 1) for 1060 ice crystal images using various greyscale intensity thresholds and circle equivalent diameter. The median (interquartile range) ratio D/D0 for Zd<c is also given.
When determining the effective array width (Eq. 2), the image size along the
direction of the photodiode array should be used. However, this size is a
function of the particle's Z position, which is the reason why the effective
array width needs to be integrated over the depth of field to determine the
sample volume (Eq. 2). This can be calculated using the AST model if the
true particle shape can be assumed (e.g. spherical particles in liquid
cloud). However, if the true particle shape is not known, as is often the
case for ice clouds, then it remains a source of uncertainty in the
calculated sample volume.
Figures 12 and 13 apply this new methodology to ambient measurements
collected during research flights in cirrus on 7 February and 23 April
2018. Figure 12 shows PSDs from the CIP-15 and HALOHolo for a run at
-42 ∘C on 7 February 2018 (16:02:00 to 16:10:00 GMT). This flight
has previously been discussed by O19. Figure 13 shows equivalent PSDs for
temperatures between -47 and -40 ∘C collected on 23 April 2018.
For both probes, the particle diameter given is the circle equivalent
diameter, and particles in contact with the edge of the CIP-15 optical array
have not been included in the PSD calculation. The black lines show the
CIP-15 size distribution when images are filtered to only include those with
at least one pixel at the 75 % intensity threshold. This threshold
significantly reduces the concentration of small particles (< 200 µm) compared to when this filtering is not applied (grey lines) and
generally is in much better agreement with HALOHolo (a holographic imaging
probe) (blue markers). This suggests that for these cases using current data-processing techniques, a significant fraction of the ice crystal number
concentration at sizes < 200 µm is an artefact due to optical
effects.
Size distributions from the CIP-15 and HALOHolo for a run at -42 ∘C on 7 February 2018. The black line shows the CIP-15 size distribution when images are filtered to only include those with at least one pixel at the 75 % intensity threshold.
Size distributions from the CIP-15 and HALOHolo for runs between -47 and -40 ∘C on 23 April 2018. The black line shows the CIP-15 size distribution when images are filtered to only include those with at least one pixel at the 75 % intensity threshold.
HALOHolo's sample volume is not as strongly dependent on particle size as it
is for OAPs. However, as described earlier, measurements of small particles
from HALOHolo are limited by noise in the background image. For a complete
description of the HALOHolo data-processing and quality-control procedures,
see Schlenczek (2017). HALOHolo uses supervised machine learning to
discriminate real particles from artefacts due to noise in the background
image. However, it is possible that small particles could be misclassified
as artefacts or vice versa, and as a result HALOHolo could either
underestimate or overestimate the small ice concentration. For particles
> 35 µm, it is estimated that the probe's detection rate is
> 90 %, and previous work has shown excellent agreement with a
CDP in liquid clouds (Schlenczek, 2017). However, HALOHolo PSDs should not
be considered the true PSD but rather another piece of evidence that
suggests for these cases OAPs overestimate small ice concentrations using
current data-processing techniques.
Stereoscopic imaging
A second method that could be used to constrain the DoF of an OAP is to use
the stereoscopic imaging that is possible with the 2D-S. The 2D-S in effect
consists of two OAPs (known as channels) orientated perpendicular to each
other and the direction of motion of the particle and instrument. Under normal
operation the probe is oriented so that one laser beam is horizontal and the
other is vertical. The two lasers overlap at the centre of each channel's
arms. As well as increasing sampling statistics by having two channels which
can be merged or averaged, this design also allows some ice crystals to be
viewed from two orientations to study their aspect ratios. In this study we
use this feature to constrain the probe's DoF, which greatly limits the
magnitude of diffraction artefacts and represents the first implementation
of stereoscopic analysis on an ambient OAP dataset. The 2D-S was designed so
that Z= 0 on both channels is in the region where the two lasers overlap.
We refer to particles observed by both channels as co-located particles.
Co-located particles have tightly constrained Z position and should not be
subject to significant mis-sizing due to diffraction. For the 2D-S, this is
likely to be true for D0> 20 µm. For a
hypothetical stereoscopic probe with larger optical arrays, it may be
necessary to restrict the distance a particle can be from the centre of the
optical array.
For the case where channel 0 is used for particle sizing and channel 1 is
used to constrain the particle Z position, the sample volume of co-located
particles is given by
SVol=TASminimumcD2/2λ,ERRE-1-DCH0,
where TAS is the true air speed, E is the number of array elements, R is the resolution of the probe, D is the measured particle diameter, and
DCH0 is the particle diameter measured along the axes of the channel 0
optical array. This requires that particles in contact with the edge of the
channel 0 optical array have been removed. If channel 1 is used for particle
sizing instead of channel 0, then particles in contact with the edge of the
channel 1 optical array are removed instead of channel 0, and DCH0 is
replaced by DCH1 in Eq. (5).
For this method to be applicable, it is important to validate that Z= 0 on
both channels is in the laser overlap region. If it is significantly offset
this would prevent small co-located particles from being observed, since the
DoF from one channel would not overlap with the optical array of the other
channel. Increasingly large offsets between the channels prevent
increasingly large co-located particles from being observed. It is therefore
important to check that this offset is not significant by regularly sampling
in environments where small particles are present (i.e. in liquid cloud or
using a droplet generator in a laboratory as in O19).
Co-located particles could be confused with shattered particles since they
are also associated with short inter-arrival times. Figure 14 (top panel)
shows a histogram of inter-arrival time for particles on the same channel
for measurements in cirrus on 7 February 2018. To minimise shattering
events, each channel was independently filtered for particles using an
inter-arrival threshold of 1 × 10-5 s. It may still be possible to
mistakenly detect shattered particles as co-located particles if one
shattering fragment splits into two particles, triggering each channel
simultaneously but in spatially independent parts of the sample volume.
However, examination of co-located images suggest that this is rare.
(a) Histograms of inter-arrival times for particles on the same 2D-S channel for measurements in cirrus on 7 February 2018. (b) A histogram of the difference in arrival time between a particle on one channel and their closest neighbour on the other channel.
To identify co-located particles, we use the difference in arrival time
between a particle on one channel and their closest neighbour on the other
channel. Figure 14 shows a histogram of co-location times for measurements
in cirrus on 7 February 2018. This distribution is bimodal with a larger
mode centred at approximately 1 × 10-3 s and a smaller mode at
1 × 10-7 s. The larger mode is associated with the typical spatial
separation between ambient particles, with its position dependent on the
particle concentration. Examining pairs of images from the smaller mode
suggests that these images are the same ice crystal viewed from different
orientations. Figure 15 shows example pairs of co-located images, with
channel 0 images shown in yellow and channel 1 images shown in blue. In
addition to overall consistency in the geometrical shapes between channel 0
and channel 1 images, there is also excellent consistency in the particle
size along the airspeed direction (x axis in Fig. 15) between these two
channels.
Example ice crystals observed by both channels of the 2D-S. Images from channel 0 are shown in yellow and images from channel 1 are shown in blue.
Figure 14 shows that most co-located particles do not trigger both channels
simultaneously within the time resolution of the data acquisition system but
are offset by a few hundred nanoseconds. At 100 m s-1 data slices from
the detectors are acquired every 1 × 10-7 s, which corresponds to a
spatial separation of 10 µm. Using the laboratory droplet generator
system described in O19, we were able to generate a continuous stream of
droplets of known size, velocity, rate, and with precise control over the
position within the sample volume. These experiments with particle
velocities of 1 m s-1 resulted in a 1 × 10-5 s mode time delay in
detection events between the two channels of the 2D-S. This also corresponds
to an offset of 10 µm in the sample volume in the axis of airflow through
the probe (y axis). These two sets of analysis provide a robust independent
verification of the spatial offset between the two channels of the 2D-S.
Therefore, when considering ambient data, we classify co-located particles
as those with time separations less than 5 × 10-7 s.
Figure 16 shows a comparison between PSDs collected in liquid stratus cloud
at 13 ∘C on 17 August 2018. The grey lines show the 2D-S data for
each channel using conventional data-processing protocols without
constraining the DoF, while the green and red lines show PSDs for just the
co-located particles. The CDP is shown in blue. For this case, no particles
larger than approximately 200 µm are present. All data-processing
methods are in good agreement up to 100 µm. For larger sizes, the
measurements using the co-located particles are limited by counting
statistics due to the low concentration of these particles. This illustrates
the ability of the 2D-S to detect small co-located particles.
Size distributions from the 2D-S and CDP for different temperatures during a research flight in liquid stratus on 17 August 2018 at 13 ∘C. The grey lines show the 2D-S data using conventional data-processing protocols without constraining the DoF, while the green and red lines show size distributions for just the co-located particles. CDP size distributions are shown in blue.
Size distributions from the 2D-S and HALOHolo for different temperatures during a research flight in cirrus on 11 March 2015. The grey lines show the 2D-S data using conventional data-processing protocols without constraining the DoF, while the green and red lines show size distributions for just the co-located particles. The dashed black line shows a 2D-S processed using a hybrid of conventional and co-location data processing (see text for details). HALOHolo size distributions are shown in blue.
Figure 17 shows size distributions from the 2D-S and HALOHolo for different
temperatures (averaged over ∼ 10 min) during a research
flight in cirrus on 11 March 2015 (see O'Shea et al., 2016). The grey lines
show the 2D-S data for each channel using conventional data-processing
protocols without constraining the DoF, while the red lines show size
distributions for just the co-located particles. HALOHolo size distributions
are shown in blue. For all temperatures, the conventional 2D-S data
processing shows an ice crystal mode at small sizes (< 200 µm). At warmer temperatures (>-39 ∘C) there is also a
clear second mode at larger sizes. However, these high concentrations of
small ice particles are not present in the co-located and the HALOHolo size
distributions. This suggests that using only co-located particles on the dual
channel 2D-S probe is effective at removing significant biases at small
particle sizes. At larger sizes (> 300 µm) the 2D-S data
processing using conventional and stereoscopic methods are in good
agreement; however, the latter method is limited by sampling statistics.
Stereoscopic data processing has the advantage of removing out-of-focus
artefacts that bias the PSD at small sizes, while at larger sizes
traditional processing methods offer significantly improved sampling
statistics. Therefore, a hybrid approach using stereoscopic processing for
small sizes and traditional processing methods for larger sizes is
advantageous. The choice of size threshold to switch between the two methods
is dependent on the arm width of the probe and the level of mis-sizing that
is deemed acceptable. To give an idea of a suitable threshold, we will
choose a size limit that prevents all particles with Zd> 2
from being included in the PSD. The maximum Z that the 2D-S can observe a
particle is Z= 31.5 mm (2D-S arm_width/2). This corresponds to a 222 µm particle at Zd= 2. However, since particles can be mis-sized by a
factor 1.4, a size threshold of 300 µm is needed to ensure that
no particle with Zd> 2 is included. Figure 17 (dashed lines)
shows 2D-S PSDs processed using this hybrid approach.
Other potential methods
There are several other potential methods that could be used to improve OAP
PSD measurements. First, reducing a probe's arm width to physically limit a
distance a particle can be from the object plane would reduce out-of-focus
particles. The amount the arm width would need to be decreased depends on
the level of mis-sizing that is deemed acceptable for a given particle size,
with more accurate sizing and smaller particles requiring smaller arm
widths. However, as well as decreasing the sample volume, reducing the
probe's arm width is likely to increase the proportion of shattered
artefact particles compared to ambient particles that the probe measures,
since shattered artefacts are thought to cluster near the probe's arms.
Second, statistical retrievals have been applied to particle size
distribution measurements where the instrument response is a distorted
version of the true ambient distribution. These methods are reliant on
knowing or empirically approximating the instrument function that distorts
the ambient distribution. These methods have been applied to OAP
measurements of spherical droplets (Korolev et al., 1998; Jensen and
Granek, 2002). For non-spherical particles, the distortion function is
dependent on the ice crystal habits present; therefore, the derived size
distributions would have greater uncertainty, unless the particle shape is
known a priori. However, this methodology may still result in an acceptable
level of uncertainty if circle equivalent diameter is used, since its intra-
and inter-habit D/D0(Zd) variance is smaller than for the mean X–Y
and maximum diameters.
Implications for small-ice-crystal observations
In situ measurements of ice clouds have consistently observed a mode in
particle size distributions at small sizes (< 200 µm). This
would imply that ice nucleation occurs at all cloud levels, since small ice
particles would rapidly grow in regions of ice supersaturation or sublime
in sub-saturated regions. Particle shattering on the leading edge of a probe
has previously been identified as a possible explanation (Korolev and Isaac,
2005; Korolev et al., 2011). However, the impacts of shattering are thought
to have been minimised by modifying the leading edges of probes (Korolev et
al., 2013) and using particle inter-arrival time algorithms (Field et al.,
2006; Korolev and Field, 2015). Yet even with these improved measurements a small ice mode has been
found to be ubiquitous in ice cloud observations (McFarquhar et al., 2007;
Jensen et al., 2009; Cotton et al., 2013; Jackson et al., 2015; O'Shea et
al., 2016).
This work has shown that depending on where in the OAP sample volume a
particle is observed its image size can be as small as a single pixel or up
to a 200 % overestimate of the true particle diameter (see Fig. 9). Only a
relatively small proportion of undersized larger particles are required to
generate a significant bias in number concentration at small sizes
(< 200 µm) due to the size dependence of the DoF (Eq. 1)
(O19). We have tested two methods that could be used to remove out-of-focus
artefacts: greyscale filtering (Sect. 4.1) and stereoscopic imaging (Sect. 4.2). Both methods either remove or significantly reduce the concentration
of small ice crystals observed in specific cirrus cloud cases (Figs. 12,
13 and 17).
To further explore the impact OAP mis-sizing has on the measured PSD shape,
we use the results from the AST model. Consider the ambient ice crystal PSD
N(D0) with units L-1µm-1. N(D0) is a 1-D array with E elements (the number of array elements). If this distribution is
observed by an OAP with size-dependent sample volume SVol(D0) (units:
L-1 s-1, Eq. 2), then the number of ice crystals observed by the
probe as a function of true particle diameter C(D0) (units: µm-1 s-1) is given by
CD0=ND0⊙SVol(D0).SVol(D0) and C(D0) are both 1-D arrays with E elements. The symbol ⊙ denotes Hadamard (element-wise) multiplication. The number of ice crystals observed as a function of the measured diameter
C(D) is given by
CD=MD,D0⋅CD0,
where M(D,D0) is an E×E array. Each column of M(D,D0) is the probability distribution that a particle of true size D0 has measured size D. These probabilities are
dependent on the particle shape, the particle sizing metric, probe
characteristics (e.g. arm width, laser wavelength), and the data-processing
protocols used (e.g. greyscale filtering, co-location). The PSD observed by
the probe N(D) (1-D array with E elements) can then calculated by
ND=CD⊘SVol(D).
The symbol ⊘ denotes Hadamard (element-wise) division. The probe arm width limits the maximum Zd that a particle of given
D0 can be observed. By choosing an arm width, it is possible to calculate
a probability distribution function of possible D for each D0 from one
of the D/D0(Zd) relationships shown in Fig. 9. For our example, we use an arm width of 70 mm and the median D/D0(Zd) relationship for
rosettes. We calculate M(D,D0) for two cases: when mean X–Y and circle
equivalent diameters are used as the particle sizing metric. To represent the
true ambient distribution, we use three different gamma distributions that
all have the form
ND=N0Dμe-λD,
where N is the number concentration. Figure 18 shows three combinations of the coefficients μ, λ
(cm-1), and N0 (L-1 cm-1). Left panels show plots using
mean X–Y diameter and the right panels show plots using circle equivalent diameter. The
ambient PSDs (blue lines) are compared to simulated OAP observations using
different data-processing methodologies. The grey lines represent an OAP
with arm width of 70 mm using conventional data-processing methods. The red
markers represent a 2D-S using only co-located particles, which has the
effect of limiting the maximum Z a particle can be observed at to 0.64 mm. The
blue markers show simulated OAP measurements from a greyscale probe with 70
mm arm width when the data have been filtered to only include particles that
have at least one pixel with a greater than 75 % decrease in light
intensity.
Simulations of OAP measurements of different gamma PSDs (blue lines). The coefficients μ, λ (cm-1), and N0 (L-1 cm-1) for each gamma PSD are shown in text boxes. Panels (a), (c), and (e) show plots using mean X–Y diameter and panels (b), (d), and (f) show circle equivalent diameter. The grey lines show simulated OAP PSDs with arm width of 70 mm if all the particles are rosettes. The red markers show simulated 2D-S measurements using only co-located particles, which has the effect of limiting the maximum Z a particle can be observed at to 0.64 mm. The blue markers show simulated OAP measurements from a greyscale probe with 70 mm arm width when the data have been filtered to only include particles that have at least one pixel with a greater than 75 % decrease in light intensity.
It should be noted that these simulated distributions only include
mis-sizing due to diffraction and do not include other sources of OAP
measurement uncertainty (e.g. counting statistics). Counting statistics will
be responsible for a larger uncertainty for the co-located PSDs compared to
conventional data-processing methods.
Figure 18 top panels show an ambient distribution (blue lines) dominated by
small particles (μ=-1, λ= 1000 cm-1, and N0= 10 L-1 cm-1), with concentrations increasing with decreasing
size over the displayed size range 10 to 1280 µm, which is
representative of modern OAPs. The grey lines show the simulated OAP
observations of this PSD, which have a similar characteristic shape. The
total particle concentration observed by the simulated OAP over the size
range 10 to 1280 µm is 3 % and 13 % higher than the true PSD
using mean X–Y and circle equivalent diameters, respectively. Figure 18 top
left panel shows the PSD that a 2D-S would observe when only co-located
particles are included (red markers). The total particle concentration from
the co-located PSD differs from the ambient distribution by less than 1 %. The total particle concentration when greyscale filtering is
applied is 2 % lower that the true distribution.
Figure 18 middle panels show an ambient distribution with mode near 100 µm particles (μ= 2, λ= 200 cm-1, and N0= 1 × 104 L-1 cm-1). The simulated OAP PSDs have
significantly different shapes with much higher concentrations of particles
< 100 µm. Here the OAP overestimates the total particle
concentration over the size range 10 to 1280 µm by 74 % and 80 %
using mean X–Y and circle equivalent diameters, respectively. When
stereoscopic imaging is used to constrain the OAP sample volume (red lines),
the small particle mode is removed. The true and simulated OAP total
particle concentration differ by < 1 %. Greyscale filtering again
removes the small particle mode but underestimates the total particle
concentration by 11 %.
Figure 18 bottom panels show an ambient PSD with mode near 400 µm
particles (μ= 4, λ= 100 cm-1, and N0= 1 × 106 L-1 cm-1); like the previous case the simulated OAP PSD
significantly overestimates the small particle concentration. The simulated
OAP PSD is bi-modal, while the true PSD is mono-modal. However, in this case
the artificial small particles contribute a relatively small proportion to
the total number concentration in the 10 to 1280 µm size range; as a
result the simulated OAP only overestimates this by 4 % using both
particle size metrics.
A significant amount of our understanding of cloud microphysics is based on
OAP measurements, with the small particle artefact being present and
manifesting in some manner. This includes how PSDs are parameterised in
numerical models and remote sensing retrievals. Generally in the literature
some formulation of exponential or gamma function has been used to represent
ice crystal PSDs for observation or modelling studies (e.g. Cazenave et al.,
2019; Delanoë et al., 2005, 2014; Field et al., 2007; Heymsfield et al.,
2013; McFarquhar and Heymsfield, 1997). These functions and the
coefficients that are used in the literature all result in the highest ice
crystal concentrations at the smallest sizes. For example, Field et al. (2007) describe a parameterisation based on OAP measurements that is widely
used by the passive and active remote sensing communities (e.g. Mitchell et
al., 2018; Sourdeval et al., 2018; Ekelund et al., 2020; Eriksson et al.,
2020; Fontaine et al., 2020). It describes a characteristic ice crystal PSD
that can be used to calculate moments of a PSD when the ice water content is
known. The functional form of the parameterisation consists of the summation
of a gamma and exponential distribution.
Figure 19 shows a comparison between the 2D-S PSD for 11 March 2015 and the
Field et al. (2007) parameterisations for tropical (Eq. 10) and mid-latitude
(Eq. 11) ice clouds.
10NDM33M42=152e-12.4x+3.28x-0.78e-1.94x,11NDM33M42=141e-16.8x+102x2.07e-4.82x,
where the number concentration (N(D)) and diameter are normalised using the
second (M2) and third (M3) moments of the PSD, and x is equal to
DM2/M3. The 2D-S PSD in Fig. 19 has been calculated using only
co-located particles for D< 300 µm and all particles for D> 300 µm. Both the tropical and mid-latitude
parameterisations show rapidly increasing concentrations with decreasing
size. At larger sizes the 2D-S and these parameterisations are in good
agreement, while they diverge at smaller sizes. The green line in Fig. 19
shows the gamma component of the mid-latitude F07 parameterisation (Eq. 12),
which is in much better agreement with the observations at small sizes.
NDM33M42=102x2.07e-4.82x
This work suggests that the data used for derived PSDs parameterisations are
subject to significant artefacts. As a result, the parameterisations are
likely to have incorrect fundamental shape for ice cloud PSDs. The impacts
of these artefacts can be expected to propagate to inaccuracies in remote
sensing retrievals, which will be assimilated into weather forecast models,
and to incorrect radiative properties due to a bias towards small particle
sizes. Future work is needed to quantify the impact on retrievals and our
understanding of ice microphysics and cloud radiative properties using the
improved measurement methodologies presented in this paper.
Comparison between 2D-S size distributions of co-located particles from a research flight in cirrus on 11 March 2015 and Field et al. (2007) parameterisations for tropical and mid-latitude ice clouds.
Conclusions
This paper quantifies the optical response of OAPs to non-spherical
particles for understanding ice crystal observations, expanding the work of
O19. We make the following comments and recommendations on the use of OAP
data:
The shape and size of an OAP image depends significantly on where in the OAP
sample volume a particle is observed. Particles < 200 µm are
the most significantly mis-sized. The measured size of a particle can range
between being as small as a single pixel up to being as large as a 200 %
overestimate of the true particle.
Particle mis-sizing and the size dependence of the OAP sample volume cause
an artefact which results in systematic overestimate of small ice (< 200 µm) concentrations. The persistent mode of small sizes observed
in many previously studied cases is likely artificial. However, the
importance of this artefact is strongly influenced by the true shape of the
ambient PSD.
Algorithms to correct OAP size distributions such as those in K07 and O19 that have been
derived using spherical particles are not applicable to non-spherical ice
crystal images without significant uncertainty.
New methods that may be used to filter OAP ice crystal size distributions
were tested, including filtering using greyscale and the use of
stereoscopic imaging.
For greyscale instruments (such as the CIP-15), filtering images so that
they must include one pixel with at least a 75 % decrease in detector
intensity removes the most severely fragmented particles near the edge of
the DoF. This approach constrains the DoF to c= 4.6 (interquartile range
1.1) using circle equivalent diameter.
Using the stereoscopic imaging that is possible with the 2D-S can constrain
the sample volume to only in-focus images. A hybrid approach using
stereoscopic processing for small sizes and traditional processing methods
for larger sizes is advantageous, as it limits any negative impacts on
sample volume and therefore counting statistics. The choice of size
threshold to switch between the two methods is dependent on the arm width of
the probe and the level of mis-sizing that is deemed acceptable. For the
2D-S, we suggest that 300 µm is a suitable threshold for particle
sizing using the mean X–Y diameter.
These new methodologies were tested using data from three research flights
sampling cirrus. In these cases, they significantly improved agreement with
a holographic imaging probe compared to conventional data-processing
protocols and either removed or significantly reduced the concentration mode
at small particle sizes (< 200 µm). This raises questions
over the interpretation of many existing datasets such as those used to
parameterise PSDs (e.g. Delanoë et al., 2005, 2014; Field et al., 2007)
and the persistent observation of small particles throughout the entire
vertical extent of ice clouds, which has been difficult to reconcile with
concepts of ice nucleation.
Past datasets from OAPs need to be revisited, and where possible the filtering
and sample volume adjustments described in this paper should be applied. The
impact these corrections have on how PSDs are parameterised in numerical
models, remote sensing retrievals, and radiative calculations of ice clouds
needs to be examined.
Data availability
The data presented here can be provided on request to the contact author.
The supplement related to this article is available online at: https://doi.org/10.5194/amt-14-1917-2021-supplement.
Author contributions
SO'S, JC, JD, LG, and ZU performed laboratory experiments. SO'S, JC, JD, WS, KB, OS, RC, and CW collected and/or processed airborne measurements. SO'S performed model experiments. SB provided and supported the use of the holographic probe. SO'S and JC analysed and interpreted the data. SO'S wrote the paper. All authors commented on and/or edited the paper.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
We would like to thank Thibault Vaillant de Guélis for his help with the
AST model. We are grateful to Jacob Fugal for assistance with HALOHolo. The
authors wish to thank Hannakaisa Lindqvist (CSU) for making her
CPI training dataset available. Airborne data were obtained using the BAe-146-301
Atmospheric Research Aircraft (ARA) flown by Directflight Ltd and managed by
the Facility for Airborne Atmospheric Measurements (FAAM), which is a joint
entity of the Natural Environment Research Council (NERC) and the Met
Office. The CIP-15 instruments were provided by the National Centre for Atmospheric
Science and FAAM. The National Centre for Atmospheric Science provided
support for the ice crystal analogue experiments.
Financial support
This research has been supported by NERC (grant nos. NE/P012426/1 and NE/L013584/1).
Review statement
This paper was edited by Szymon Malinowski and reviewed by two anonymous referees.
ReferencesBaumgardner, D. and Korolev, A.: Airspeed Corrections for Optical Array
Probe Sample Volumes, J. Atmos. Ocean. Tech., 14, 1224–1229,
10.1175/1520-0426(1997)014<1224:ACFOAP>2.0.CO;2, 1997.Baumgardner, D., Jonsson, H., Dawson, W., O'Connor, D., and Newton, R.: The
cloud, aerosol and precipitation spectrometer: a new instrument for cloud
investigations, Atmos. Res., 59–60, 251–264,
10.1016/S0169-8095(01)00119-3, 2001.Cazenave, Q., Ceccaldi, M., Delanoë, J., Pelon, J., Groß, S., and Heymsfield, A.: Evolution of DARDAR-CLOUD ice cloud retrievals: new parameters and impacts on the retrieved microphysical properties, Atmos. Meas. Tech., 12, 2819–2835, 10.5194/amt-12-2819-2019, 2019.
Cotton, R. J., Field, P. R., Ulanowski, Z., Kaye, P. H., Hirst, E.,
Greenaway, R. S., Crawford, I., Crosier, J., and Dorsey, J.: The effective
density of small ice particles obtained from in situ aircraft observations
of mid-latitude cirrus, Q. J. Roy. Meteor. Soc., 139, 1923–1934, 2013.Crosier, J., Bower, K. N., Choularton, T. W., Westbrook, C. D., Connolly, P. J., Cui, Z. Q., Crawford, I. P., Capes, G. L., Coe, H., Dorsey, J. R., Williams, P. I., Illingworth, A. J., Gallagher, M. W., and Blyth, A. M.: Observations of ice multiplication in a weakly convective cell embedded in supercooled mid-level stratus, Atmos. Chem. Phys., 11, 257–273, 10.5194/acp-11-257-2011, 2011.Davis, S., Hlavka, D., Jensen, E., Rosenlof, K., Yang, Q., Schmidt, S.,
Borrmann, S., Frey, W., Lawson, P., Voemel, H., and Voemel, T. P.: In situ
and lidar observations of tropopause subvisible cirrus clouds during TC4, J.
Geophys. Res.-Atmos., 115, D00J17, 10.1029/2009JD013093, 2010.Delanoë, J., Protat, A., Testud, J., Bouniol, D., Heymsfield, A. J., Bansemer, A., Brown, P. R. A., and Forbes, R. M.: Statistical properties of the normalized ice particle size distribution, J. Geophys. Res., 110, D10201,
10.1029/2004JD005405, 2005.Delanoë, J. M. E., Heymsfield, A. J., Protat, A., Bansemer, A., and
Hogan, R. J.: Normalized particle size distribution for remote sensing
application, J. Geophys. Res.-Atmos., 119, 4204–4227,
10.1002/2013JD020700, 2014.Ekelund, R., Eriksson, P., and Pfreundschuh, S.: Using passive and active observations at microwave and sub-millimetre wavelengths to constrain ice particle models, Atmos. Meas. Tech., 13, 501–520, 10.5194/amt-13-501-2020, 2020.Eriksson, P., Rydberg, B., Mattioli, V., Thoss, A., Accadia, C., Klein, U., and Buehler, S. A.: Towards an operational Ice Cloud Imager (ICI) retrieval product, Atmos. Meas. Tech., 13, 53–71, 10.5194/amt-13-53-2020, 2020.
Field, P. R., Heymsfield, A. J., and Bansemer, A.: Shattering and Particle
Interarrival Times Measured by Optical Array Probes in Ice Clouds,
J. Atmos. Ocean. Tech., 23, 1357–1371, 2006.Field, P. R., Heymsfield, A. J., and Bansemer, A.: Snow Size Distribution
Parameterization for Midlatitude and Tropical Ice Clouds, J. Atmos. Sci.,
64, 4346–4365, 10.1175/2007JAS2344.1, 2007.Fontaine, E., Schwarzenboeck, A., Leroy, D., Delanoë, J., Protat, A., Dezitter, F., Strapp, J. W., and Lilie, L. E.: Statistical analysis of ice microphysical properties in tropical mesoscale convective systems derived from cloud radar and in situ microphysical observations, Atmos. Chem. Phys., 20, 3503–3553, 10.5194/acp-20-3503-2020, 2020.Fugal, J. P. and Shaw, R. A.: Cloud particle size distributions measured with an airborne digital in-line holographic instrument, Atmos. Meas. Tech., 2, 259–271, 10.5194/amt-2-259-2009, 2009.Gurganus, C. and Lawson, P.: Laboratory and flight tests of 2D imaging
probes: Toward a better understanding of instrument performance and the
impact on archived data, J. Atmos. Ocean. Tech., 35, 1533–1553, 10.1175/JTECH-D-17-0202.1, 2018.Heymsfield, A. J., Schmitt, C., and Bansemer, A.: Ice cloud particle size
distributions and pressure dependent terminal velocities from in situ
observations at temperatures from 0 to -86∘C, J. Atmos. Sci., 70, 4123–4154, 2013.Jackson, R. C., McFarquhar, G. M., Fridlind, A. M., and Atlas, R.: The
dependence of cirrus gamma size distributions expressed as volumes in
N0-λ-µ phase space and bulk cloud properties on environmental conditions: Results from the Small Ice Particles in Cirrus Experiment (SPARTICUS), J. Geophys. Res.-Atmos., 120, 10351–10377,
10.1002/2015JD023492, 2015.Jensen, E. J., Lawson, P., Baker, B., Pilson, B., Mo, Q., Heymsfield, A. J., Bansemer, A., Bui, T. P., McGill, M., Hlavka, D., Heymsfield, G., Platnick, S., Arnold, G. T., and Tanelli, S.: On the importance of small ice crystals in tropical anvil cirrus, Atmos. Chem. Phys., 9, 5519–5537, 10.5194/acp-9-5519-2009, 2009.Jensen, J. B. and Granek, H.: Optoelectronic Simulation of the PMS 260X
Optical Array Probe and Application to Drizzle in a Marine Stratocumulus, J. Atmos. Ocean. Tech., 19, 568–585,
10.1175/1520-0426(2002)019<0568:OSOTPO>2.0.CO;2, 2002.Knollenberg, R. G.: The optical array: An alternative to scattering or
extinction for airborne particle size determination, J. Appl. Meteorol., 9,
86–103, 10.1175/1520-0450(1970)009<0086:TOAAAT>2.0.CO;2, 1970.
Korolev, A.: Reconstruction of the sizes of spherical particles from their
shadow images, Part I: Theoretical considerations, J. Atmos. Ocean. Tech.,
24, 376–389, 2007.Korolev, A. and Field, P. R.: Assessment of the performance of the inter-arrival time algorithm to identify ice shattering artifacts in cloud particle probe measurements, Atmos. Meas. Tech., 8, 761–777, 10.5194/amt-8-761-2015, 2015.Korolev, A. and Isaac, G. A.: Shattering during sampling by OAPs and HVPS,
Part 1: Snow particles, J. Atmos. Ocean. Tech., 22, 528–542,
10.1175/JTECH1720.1, 2005.
Korolev, A. and Sussman, B.: A technique for habit classification of cloud
particles, J. Atmos. Ocean. Tech., 17, 1048–1057, 2000.Korolev, A., Emery, E., and Creelman, K.: Modification and Tests of Particle
Probe Tips to Mitigate Effects of Ice Shattering, J. Atmos. Ocean. Tech.,
30, 690–708, 10.1175/JTECH-D-12-00142.1, 2013.
Korolev, A. V., Kuznetsov, S. V., Makarov, Y. E., and Novikov, V. S.:
Evaluation of measurements of particle size and sample area from optical
array probes, J. Atmos. Ocean. Tech., 8, 514–522, 1991.Korolev, A. V., Strapp, J. W., and Isaac, G. A.: Evaluation of the accuracy
of PMS optical array probes, J. Atmos. Ocean. Tech., 15, 708–720,
10.1175/1520-0426(1998)015<0708:EOTAOP>2.0.CO;2, 1998.Korolev, A. V., Emery, E. F., Strapp, J. W., Cober, S. G., Isaac, G. A.,
Wasey, M., and Marcotte, D.: Small ice particles in tropospheric clouds: Fact
or artifact? Airborne icing instrumentation evaluation experiment,
B. Am. Meteorol. Soc., 92, 967–973, 10.1175/2010BAMS3141.1, 2011.Lance, S., Brock, C. A., Rogers, D., and Gordon, J. A.: Water droplet calibration of the Cloud Droplet Probe (CDP) and in-flight performance in liquid, ice and mixed-phase clouds during ARCPAC, Atmos. Meas. Tech., 3, 1683–1706, 10.5194/amt-3-1683-2010, 2010.Lawson, R. P., O'Connor, D., Zmarzly, P., Weaver, K., Baker, B., Mo, Q., and
Jonsson, H.: The 2D-S (stereo) probe: design and preliminary tests of a new
airborne, high-speed, high-resolution particle imaging probe, J. Atmos.
Ocean. Tech., 23, 1462–1477, 10.1175/JTECH1927.1, 2006.Lindqvist, H., Muinonen, K., Nousiainen, T., Um, J., McFarquhar, G. M.,
Haapanala, P., Makkonen, R., and Hakkarainen, H.: Ice cloud particle habit
classification using principal components, J. Geophys. Res., 117, D16206,
10.1029/2012JD017573, 2012.McFarquhar, G. M. and Heymsfield, A. J.: Parameterization of tropical cirrus
ice crystal size distributions and implications for radiative transfer:
Results from CEPEX, J. Atmos. Sci., 54, 2187–2200,
10.1175/1520-0469(1997)054<2187:POTCIC>2.0.CO;2, 1997.McFarquhar, G. M., Um, J., Freer, M., Baumgardner, D., Kok, G. L., and Mace,
G.: The importance of small ice crystals to cirrus properties: Observations
from the Tropical Warm Pool International cloud Experiment (TWP-ICE),
Geophys. Res. Lett., 57, L13803, 10.1029/2007GL029865, 2007.Mitchell, D. L., Garnier, A., Pelon, J., and Erfani, E.: CALIPSO (IIR–CALIOP) retrievals of cirrus cloud ice-particle concentrations, Atmos. Chem. Phys., 18, 17325–17354, 10.5194/acp-18-17325-2018, 2018.O'Shea, S. J., Choularton, T. W., Lloyd, G., Crosier, J., Bower, K. N.,
Gallagher, M., Abel, S. J., Cotton, R. J., Brown, P. R. A., Fugal, J. P.,
Schlenczek, O., Borrmann, S., and Pickering, J. C.: Airborne observations of
the microphysical structure of two contrasting cirrus clouds, J. Geophys.
Res., 121, 13510–13536, 10.1002/2016JD025278, 2016.O'Shea, S. J., Crosier, J., Dorsey, J., Schledewitz, W., Crawford, I., Borrmann, S., Cotton, R., and Bansemer, A.: Revisiting particle sizing using greyscale optical array probes: evaluation using laboratory experiments and synthetic data, Atmos. Meas. Tech., 12, 3067–3079, 10.5194/amt-12-3067-2019, 2019.Praz, C., Ding, S., McFarquhar, G. M., and Berne, A.: A versatile method
for ice particle habit classification using airborne imaging probe data, J.
Geophys. Res., 123, 13472–13495, 10.1029/2018JD029163, 2018.Schlenczek, O.: Airborne and ground-based holographic measurement of
hydrometeors in liquid-phase, mixed-phase and ice clouds, PhD thesis,
University of Mainz, Mainz, Germany, 10.25358/openscience-4124, 2017.Sourdeval, O., Gryspeerdt, E., Krämer, M., Goren, T., Delanoë, J., Afchine, A., Hemmer, F., and Quaas, J.: Ice crystal number concentration estimates from lidar–radar satellite remote sensing – Part 1: Method and evaluation, Atmos. Chem. Phys., 18, 14327–14350, 10.5194/acp-18-14327-2018, 2018.
Ulanowski, Z., Hesse, E., Kaye, P. H., Baran, A. J., and Chandrasekhar, R.:
Scattering of light from atmospheric ice analogues,
J. Quant. Spectrosc. Ra., 79, 1091–1102, 2003.Vaillant de Guélis, T., Schwarzenböck, A., Shcherbakov, V., Gourbeyre, C., Laurent, B., Dupuy, R., Coutris, P., and Duroure, C.: Study of the diffraction pattern of cloud particles and the respective responses of optical array probes, Atmos. Meas. Tech., 12, 2513–2529, 10.5194/amt-12-2513-2019, 2019a.
Vaillant de Guélis, T., Shcherbakov, V., and Schwarzenböck, A.:
Diffraction patterns from opaque planar objects simulated with
Maggi-Rubinowicz method and angular spectrum theory, Opt. Express, 27,
9372–9381, 10.1364/OE.27.009372, 2019b.
Wendisch, M. and Brenguier, J.-L.: Airborne Measurements for
Environmental Research: Methods and Instruments, Wiley-VCH Verlag GmbH and Co. KGaA, Weinheim, Germany, ISBN 978-3-527-40996-9, 2013.