Revisiting the size of nonspherical particles recorded by optical array probes with a new method based on the convex hull

Ron Zhn , , , Xu Zhou , , , Honyu Li , , , Hnho Li , Li Wi , Yn Go , , , Qin Xi ,Xinyu Wn ,

a Key Laboratory for Cloud Physics of China Meteorological Administration, Beijing, China

b State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing, China

c Weather Modification Centre, China Meteorological Administration, Beijing, China

d Inner Mongolia Institute of Meteorological Sciences & Inner Mongolia Key Laboratory of Manual Weather Modification, Hohhot, China

e Beijing Weather Modification Center, Beijing, China

f China Huayun Meteorological Technology Group Corporation, Beijing, China

g Weather Modification Center in Eastern Inner Mongolia, Tongliao, China

Keywords:Cloud and precipitation particles Particle image Particle size Particle size distribution

ABSTRACT In recent years, the Cloud Imaging Probe (CIP) and Precipitation Imaging Probe (PIP) produced by Droplet Measurement Technologies (DMT) have been introduced by a number of meteorological research and operation centers in China.The supporting software provided by DMT, i.e., PADS (Particle Analysis and Display System),cannot output detailed information on each individual particle, which definitely limits the in-depth utilization of cloud and precipitation particle image data in China.In this paper, particle-by-particle information was extracted by decompressing the CIP and PIP original particle image data, based on which a new definition of the dimension for nonspherical particles is proposed by using the area of the convex hull enclosing a particle to obtain the equivalent diameter of a circle with equal area.Based on the data detected during one flight in Inner Mongolia, the particle size distribution obtained using the new particle size definition and that used by the other four existing definitions are compared.The results show that the particle number concentration calculated using different particle size definitions can vary by up to an order of magnitude.The result obtained based on the new particle size definition is closest to that calculated with the area-equivalent diameter definition.

1.Introduction

In-situ observation with airborne detection instruments in cloud is undoubtedly the most direct and effective approach to obtain cloud and precipitation particle size.Knollenberg (1970) first developed twodimensional optical array probes to obtain two-dimensional images of cloud and precipitation particles.Thereafter, other similar detection devices have been developed, such as two-dimensional cloud (2D-C) and precipitation (2D-P) particle imaging probes from PMS (Particle Measuring Systems), the Cloud Imaging Probe (CIP) and Precipitation Imaging Probe (PIP) from DMT (Droplet Measurement Technologies), and the 2D-S (two-Dimensional Stereo) and HVPS (High Volume Precipitation Spectrometer) from SPEC (Stratton Park Engineering Co.Inc.).These probes are widely used in cloud physics research, playing an important role in promoting an understanding of cloud microphysical structure and the mechanisms of cloud precipitation processes ( Heymsfield et al.,2006 ; Lawson et al., 2010 ; McFarquhar and Black, 2004 ).

Since the introduction of PMS detection instruments in China in the early 1980s, significant progress has been made in the airborne detection of cloud microphysical structure and weather modification experiments ( Guo et al., 2015 ).At present, CIP and PIP are the two most commonly used cloud and precipitation particle imaging detection instruments in China.Although many studies have been conducted using CIP and PIP detection data, most of them were based on statistical information with 1-s resolution outputs by the supporting software, i.e.,PADS (Particle Analysis and Display System), which does not output detailed particle-by-particle information.One important reason is that these probes are bought from abroad and understanding of the raw data structure is challenging, which makes it difficult to read and parse the original particle image data.Hence, there are few studies focused specifically on obtaining the cloud and precipitation particle sizes from the images detected by CIP and PIP.

Fig.1.Illustration showing different definitions of particle size using an ice crystal particle captured by the PIP (Precipitation Imaging Probe) in an aircraft observation experiment on 21 June 2019 in Inner Mongolia, China.

The sizes of cloud and precipitation particles as well as their distribution (PSD) are one of the fundamental parameters in cloud physics.Currently, there are several different definitions for the sizes of cloud and precipitation particles ( Brenguier et al., 2013 ; Wu and McFarquhar, 2016 ), such as the maximum dimension in the flight direction( Lawson et al., 2015 ), the maximum dimension in the photodiode array direction ( DMT, 2009 ), the area-equivalent diameter ( Leroy et al., 2017 ;Yang et al., 2016 ), and the diameter of the smallest circle enclosing the particle ( Wang et al., 2015 ; Wu and McFarquhar, 2016 ).Although these definitions are equivalent for spherical liquid particles, there can be large differences for nonspherical ice crystal particles, and the scientific community has not yet reached a consensus on which definition should be used.The choice of different particle size definitions has a great impact on PSDs, and thus also affects the particle mass, extinction, ice water content, effective radius, falling velocity, and some other cloud physics parameters derived from PSDs ( McFarquhar and Black, 2004 ;Wu and McFarquhar, 2016 ).

In this study, the raw image data of CIP and PIP were decompressed and parsed, and a new definition of particle size is proposed based on the convex hull enclosing the particles.The PSDs obtained using the new definition were compared with those obtained using the other existing particle size definitions.In addition, some matters needing attention in the use of two-dimensional particle image data are highlighted to ensure the two-dimensional particle image data be used scientifically and reasonably.

2.Definitions of particle size

As mentioned in the introduction, there are at least four different definitions of cloud and precipitation particle size commonly used in previous publications.Fig.1 illustrates the different definitions using an ice crystal particle captured by PIP in an aircraft observation experiment on 21 June 2019 in Inner Mongolia, China.Dx represents the maximum dimension in the flight direction; Dy represents the maximum dimension in the photodiode array direction; Dcircle represents the diameter of the smallest circle enclosing the particle.The area-equivalent diameter (Da)is not shown in this figure since it is the diameter of a circle that has the same area as the particle.The area of the particle is obtained by multiplying the number of obscured pixels contained within the image by the area of each pixel (CIP: 625μm2, PIP: 10000μm2), and the Da is then derived from this area.

The supporting software provided by DMT, i.e., PADS, uses Dy as the particle dimension ( DMT, 2009 ).As can be seen from Fig.1 , PADS will inevitably underestimate (or overestimate) the particle size when Dy is smaller (or greater) than Dx.The definition of Dcircle tends to always overestimate the particle size for nonspherical particles, especially when the dimensions in the two orthogonal directions are very different (such as in needle-shaped or column-shaped ice crystals).Moreover,King (1986) verified that the air disturbances caused by the fuselage could lead to a preferential crystal orientation of the recorded images;hence, Dx and Dy dimensions could be biased, especially when the eccentricity of the particles is high (such as in needle-shaped or columnshaped ice crystals).Compared with Dx and Dy, the Da definition is less influenced by the fuselage-induced preferential crystal orientation.

A new definition of particle size is proposed in this paper by using the area of the convex hull enclosing the particle.In simple terms, the convex hull of a particle can be thought of as the convex polygon produced by stretching an elastic band around the outline of the particle image,as in the blue convex polygon shown in Fig.1 .In this paper, the Quickhull algorithm ( Barber et al., 1996 ) was used to obtain the convex hull.Note that the coordinates of each pixel represents its central position.However, the actual position of each pixel should be represented by the outermost four corners of each pixel.The convex hull obtained using the central point of each pixel cannot totally cover the outermost part of the particle, and hence the area of the convex hull is underestimated.To make the convex hull more accurate, we first obtain the coordinates of the four corners of each pixel, and then obtain the minimum convex polygon surrounding the particle and its area based on the corner points(see Fig.S3 in the supplementary material).The diameter of the circle(the blue dotted circle in Fig.1 ), which has the same area as the convex hull, is regarded as the dimension of the particle, i.e., Dconvex in Fig.1 .Let Sconvex be the area of the convex hull.Then, the equivalent convex area diameter, Dconvex, is:

The particle dimension obtained with this definition can to some extent avoid the underestimation or overestimation of the dimension for high-eccentricity particles, such as needles or columns.Like Da, it is also less influenced by the fuselage-induced preferential crystal orientation.Furthermore, this definition has the potential to be used to determine the shape of particles.For example, the solidity value (the ratio of the area of the particle to the area of the convex hull) can be used to determine how close the particle shape is to a circle.The definition of Dconvex is conceptually similar to that of Da; both are equivalent diameters calculated from the equivalent areas.With improving computer power, Dconvex can be easily extracted from particle images.

3.Effects of particle size definitions

3.1. Dataset

To examine the differences in the particle size definitions among Dconvex and other existing definitions (Dx, Dy, Dcircle, and Da), in-situ measurements of a stratiform cloud on 21 June 2019 in Inner Mongolia was used.The sampling was conducted by the Chinese Academy of Meteorological Sciences’ MA60 (Modern Ark 60) aircraft, which is a twin-turboprop aircraft equipped with many airborne in-situ probes, including CIP, PIP, CDP (Cloud Droplet Probe), and AIMMS-20 (Aventech Aircraft Integrated Meteorological Measurement System), amongst others.Both CIP and PIP are equipped with anti-shattering tips so that they can deflect shattering particles away from the probe sample volume, and thus mitigate the shattering effect in the final dataset.The typical true air speed of the aircraft during the sampling period is 100 m s?1.

Fig.2.The average PSDs (particle size distributions) measured by CIP (Cloud Imaging Probe, red) and PIP (Precipitation Imaging Probe, blue) during the period 21:37:13–21:41:13 (BJT, Beijing Time).

Fig.3.The sample volumes of CIP (Cloud Imaging Probe, red) and PIP (Precipitation Imaging Probe, blue) as a function of particle size at an assumed TAS(true air speed) of 100 m s ? 1 , calculated with “all-in ” (solid line) and “center-in ”(dotted line) techniques.

The flight lasted nearly four hours, during which the highest altitude was about 5700 m and the temperature was mainly between ? 3 and ? 8°C.The measurements of flight altitude and temperature during the sampling period are shown in Fig.S4.The measurements used in this study were the image data from the CIP and PIP probes.The resolutions of the CIP and PIP probes used in this study were 25 and 100μm, respectively.The CIP and PIP data during the period 21:37:13–21:41:13 BJT (Beijing Time), when the aircraft was continuously flying within the cloud and both CIP and PIP had detected effective particles, were selected to form a composite PSD.From Fig.S4 it can be seen that during this period the flight altitude was about 5100 m and the ambient temperature was about ? 6°C.

The composite PSD was generated from the CIP and PIP probes by finding a point at which the size distributions from each overlapped,or where the concentrations were comparable.The PSDs of CIP and PIP(using Dy as the particle size definition) are shown in Fig.2 , from which it can be seen that the two PSDs are in good agreement when the particle size is close to 200μm, but the oscillation amplitude of the CIP size distribution becomes larger when the particle size is greater than 200μm.Therefore, 200μm was selected as the breakpoint to form the composite PSD.Thus, the portion of the composite size distribution smaller than 200μm is from the CIP observations and that larger than 200μm is from the PIP observations.The representative particles imaged by CIP and PIP during this period are shown in Figs.S5 and S6.It can be seen that nonspherical ice particles are dominant during this period.

3.2. Effects of different particle size definitions on PSDs

In order to test the differences among different particle size definitions, the PSDs obtained from these definitions are compared in this section.To calculate the PSDs, an estimation of the probe sample volume must be made.The sample volume is defined as the amount of air that passes through the sensitive area (i.e., the sample area) of the laser beam during the sample period.The sample volume per unit time (1 s)is defined as:

where SA is the sample area, TAS is the true air speed perpendicular to the laser beam, DOF is the depth of field, and WEA is the effective array width.The DOF used here is not exactly the depth of field used in optical design, but rather the length of the beam where a particle will cause attenuation of photodiode illumination by more than 50%.For optical array imaging probes, DOF increases with an increase in particle size,but is limited by the distance between the probe arms.The calculation formula is ( Knollenberg, 1970 ):

whereWarmis the window-to-window distance between the probe arms along which the laser travels (70 mm for CIP and 260 mm for PIP),Dis the particle size, andλis the wavelength of the laser (658 nm both for CIP and PIP).WEA is called the effective array width since it varies with the size of the particle and can commonly be calculated in two ways ( Brenguier et al., 2013 ): “all-in ” or “center-in ”.The “all-in ” technique accepts only entire particles whose images are completely within the limits of the diode array, and particles that cover either or both of the end elements are rejected.The “center-in ” technique considers not only entire particles but also partially imaged particles whose center can be determined to be within the diode array.Fig.3 shows the variation in the sample volume from CIP and PIP with particle size calculated with the two techniques when the true air speed is 100 m s?1.It can be seen that using the “center-in ” technique can obtain a larger sample volume than the “all-in ” technique.When the particle size exceeds a certain value (175μm for CIP and 400μm for PIP), the sample volume from “all-in ” decreases as the particle size increases, whereas the sample volume from “center-in ” remains unchanged.Although the“center-in ” technique provides a larger sample area, it is usually applied only to circular or quasi-circular images as there is greater uncertainty when implementing it for nonspherical ice crystals ( Baumgardner et al.,2017 ).Since the data used in this study were obtained at altitudes above the freezing level and most of the particles were nonspherical (as shown in Figs.S5 and S6), the “all-in ” technique was used to calculate WEA.The “all-in ” definition of WEA is ( Heymsfield and Parrish, 1978 ):

where Res is the probe resolution (25μm for CIP and 100μm for PIP),Nis the number of photodiodes (64 for both CIP and PIP), andXis the number of diodes obscured by a particle.From Eq.(4) , it can be seen that WEA from the “all-in ” technique decreases with an increase in particle size since there is an increased probability that the particle will cover one or both ends of the photodiode array and be rejected.

Fig.4 compares the PSDs computed using the five different particle size definitions (Dx, Dy, Da, Dcircle, and Dconvex) during the period 21:37:13–21:41:13 BJT, with the upper subplot showing the PSDs in the form of particle number concentrations per size bin normalized by the bin width (denoted by N(D)), and the bottom subplot showing the ratio of concentrations of different size definitions to that of the Dconvex definition.The PSDs were first obtained in 1-s intervals using the specific sample volume for each second and then averaged over the period.It can be seen from Fig.4 that the particle number concentration obtained with different definitions shows a relatively large difference at the two ends of the PSDs, which is particularly pronounced at the large-size end.Since PSD is determined by the number of particles in each bin and the sample volume for particles with the given size, both factors contribute to the difference in the PSDs.The difference in the small-size end (approximately<100μm) is mainly due to the dependence of depth of field on particle size, since it is a function of the square of particle size (see Eq.(3) ).As shown in Fig.3 , the sample volume varies greatly with particle size at the small-size end.The smaller the particle size, the smaller the sample volume, leading to a greater difference in PSDs.Meanwhile,the main reason for the difference at the large-size end is that the effective array width obtained with the “all-in ” technique is getting smaller(and therefore the sample volume is getting smaller) as the particle size becomes larger.In addition, there are usually far fewer particles in the larger size bins, and hence the differences can be exacerbated between different particle size definitions.The ratio of the number concentrations of different size definitions to that of Dconvex can vary by up to an order of magnitude.As can be seen from Fig.1 , Dcircle is always the largest and Da is the smallest among the five size definitions for the same nonspherical particle.Therefore, the number concentration of Dcircle is smallest when the particle size is smaller and is greatest when the particle size is larger, while the opposite is true for Da.Since the sizes of Dx and Dy have no fixed trend relative to Dconvex, the ratio of N(Dx) and N(Dy) to N(Dconvex) varies with particle size –sometimes greater than 1 and sometimes less than 1.Overall, the PSD of Da is the closest to that of Dconvex, with an average ratio of 0.8859.

Fig.4.(a) The composite PSDs (particle size distributions) during the period 21:37:13–21:41:13 BJT (Beijing Time) computed with the five different particle size definitions; both vertical and horizontal axes use logarithmic scales.(b) The ratio of concentrations of the five definitions to that of the Dconvex definition;only the horizontal axis uses logarithmic scales.

4.Summary and discussion

It can be seen from previous publications that there have been several different size definitions for cloud and precipitation particles.Although these definitions are equivalent for spherical particles, they may be quite different for nonspherical ice particles.Also, there still remains an open discussion on which definition should be used for nonspherical particles.In this study, the particle-by-particle information was extracted by decompressing and parsing the original binary image data,and a new definition of particle size based on the area of the smallest convex polygon enclosing a particle was proposed.The new size definition has the advantage that it is independent of the particle shape and is less influenced by fuselage-induced preferential crystal orientation;hence, it can to some extent avoid the underestimation or overestimation of the dimension for high-eccentricity particles, such as needles or columns.Furthermore, it has the potential to be used in determining particle shape in future studies.Considering the powerful performance of computers now, the extra time consumed in computing with this new size definition compared to the other definitions could be negligible.Therefore, this study provides one more option for future studies involving the computation of particle size.

The PSDs computed with the new size definition and that with the other four existing definitions were compared.It was found that the PSDs computed with different size definitions show a large difference at the two size ends.The difference at the small-size end is mainly caused by the dependence of depth of field on particle size, whereas the difference at the large-size end is mainly attributable to the dependence of the effective array width on particle size, and the relative scarcity of large particles further exacerbated the difference at the large-size end.Overall, the PSDs computed with the newly defined convex-based particle size is closest to that computed with the area-equivalent diameter as the size definition.

As can be seen from the results of this study, considerable differences exist in PSDs computed with different particle size definitions.Therefore, it is recommended that all future studies involving cloud and precipitation particle measurements should clearly describe the particle size definition used.In addition, the necessary processing method, such as the calculation of depth of field and effective array width, as well as the handling of partially imaged particles, should also be clarified, so that the results from different studies can be compared quantitatively and eventually promote an understanding of the microphysical properties of clouds in different geographical locations.

Funding

This work was jointly funded by the National Key R&D Program of China [grant numbers 2019YFC1510301 and 2018YFC1505702] and the Basic Research Fund of the Chinese Academy of Meteorological Sciences [grant number 2020Z008].

Acknowledgments

We thank all of the experimental research team, especially the flight crew of the MA-60 aircraft who participated in the data collection effort on 21 June 2019.

Supplementary materials

Supplementary material associated with this article can be found, in the online version, at doi: 10.1016/j.aosl.2021.100136 .