Abstract

This paper describes a Multiangle Snowflake Imager (MSI) designed to capture the pseudo-three-dimensional (3D) shape and the fall velocity of individual snowflakes larger than 1.5 mm in size. Four height-offset line-image scanners estimate fall velocities and the four-angle silhouettes are used to reconstruct the 3D snowflake shapes. The 3D shape reconstruction is tested using reference objects (spheres, spheroids, cubes, and plates). The four-silhouette method of the MSI improves the representation of the particle shape and volume compared to two-silhouette methods, such as the two-dimensional video disdrometer (2DVD). The volume (equivolumetric diameters) of snowflakes estimated by the four-silhouette method is approximately 44% (13%) smaller than that estimated by the two-silhouette method. The ability of the imager to measure the fall velocity and particle size distributions based on the silhouette width and the equivolumetric diameter of 3D-shaped particles is verified via a comparison with the 2DVD in three snowfall events.

1. Introduction

Several empirical power-law approximations between the radar reflectivity factor Z and the liquid equivalent snow rate , , have been reported; however, the relationship is scattered on a case-by-case basis (e.g., Fujiyoshi et al. 1990; Rasmussen et al. 2003). Recent Z–SR evaluations incorporate the particle size distributions (PSD) captured by video disdrometers and include snow microphysical properties. The disdrometer estimates the and Z values by summing the volume and the microwave backscattering cross section of the snowflakes over the PSD given an optimal snow density . If the disdrometer retrieves accurate Z and values, then the variation in the Z–SR relationship can be investigated to improve the algorithm for accurate radar estimates. However, there remain uncertainties in the size and volume descriptions of complex-shaped snowflakes with various orientations and in their assignments (e.g., Wood et al. 2013; Huang et al. 2015). Precise shape descriptions of snowflakes will provide information not only for accurate radar estimates but also for investigating the scattering patterns of recent polarimetric radars (e.g., Matrosov 1992; Ryzhkov et al. 2005; Notaroš et al. 2016).

Currently, multiple instruments have been developed to measure the size, shape, and fall velocity of individual solid hydrometeors. Schönhuber et al. (2008) used a two-dimensional video disdrometer (2DVD) to capture hydrometeor silhouettes and fall velocities, and Barthazy et al. (2004) developed a hydrometeor velocity and shape detector (HVSD) containing two height-offset line-scan cameras. The 2DVD records orthogonal views of snowflakes, which estimate the fall velocities by detecting the time difference between the cameras; however, multiparticle silhouettes frequently make it difficult to match identical snowflakes due to the complexity of snowflake shapes. The cameras of HVSD scan snowflakes at the same view angle and measure the exact fall velocities. Contrary to line-scan-type imaging, Muramoto et al. (1990) developed a system that automatically and simultaneously measures the size and falling velocity of snowflakes using two charge-coupled device (CCD) cameras and an image processor. A snowflake video imager (SVI) can capture the 2D grayscale images of snowflakes using a halogen lamp and a CCD camera (Newman et al. 2009). The particle imaging package (PIP), which is the next-generation version of the SVI, enables fall velocity measurements via the speeding up of the frame rate of the video camera (Kneifel et al. 2015). Garrett et al. (2012) developed a Multiangle Snowflake Camera (MASC) to capture high-resolution grayscale hydrometeor photographs that allow the 3D shape to be roughly reproduced. More realistic 3D shapes have been obtained via a modified MASC equipping five cameras, and the data have been analyzed using the visual hull method (Notaroš et al. 2016; Kleinkort et al. 2017).

Here, we report the development of a Multiangle Snowflake Imager (MSI) to acquire pseudo-3D shapes, fall velocities, and PSD by assembling four laser line-image scanners with height offsets. The performance of a single scanner for 2D snowflake imaging and PSD measurement has been demonstrated (Minda et al. 2016). The four-angle silhouettes are used to reproduce the pseudo-3D shapes of the hydrometeors. The MSI is assembled with low-cost parts and is designed to retrieve the 3D shapes of snowflakes larger than 1.5 mm in size, which primarily contribute to the values of and Z. To demonstrate the MSI performance, we simultaneously observed snowfall with a 2DVD and an electrical-balance-type snow gauge at Hokkaido University, Sapporo, Japan (434′99″N, 14120′19″E) from the end of January to mid-March 2015.

The MSI is described in detail in section 2. After introducing the data-processing methods in sections 3 and 4, the data acquired by the MSI are compared with those acquired via 2DVD and the mean is preliminarily estimated by the snow gauge in section 5, which is followed by the summary in section 6.

2. Description of the instrument

The four height-offset line-image scanners oriented 45 apart record the silhouettes of the falling snowflakes through octagonal apertures (side length: 60 mm). Figure 1 shows a planar view of the MSI and an outline of the sensing area. Figure 2 shows the system block diagram, and Table 1 shows the major specifications. A laser diode (LD) and a spherical 60-mm-diameter glass lens form parallel light sheets with sensing widths of 40 mm. A linear photodiode array composed of 384-pixel photodiodes receives the light sheet and captures the hydrometeor silhouettes with a horizontal resolution of 0.105 mm.

Fig. 1.

Outlines of MSI and hydrometeor intake aperture.

Fig. 1.

Outlines of MSI and hydrometeor intake aperture.

Fig. 2.

System block diagram of MSI. LD is the laser diode. APC is automatic laser power control. CMP denotes a voltage comparator. CLK and TRG denote the pixel switching clock of the photodiode array and the start trigger of line scan. The terms , , and are the dc supply voltages of 5 and 3.3 V, and the reference voltage of the comparator.

Fig. 2.

System block diagram of MSI. LD is the laser diode. APC is automatic laser power control. CMP denotes a voltage comparator. CLK and TRG denote the pixel switching clock of the photodiode array and the start trigger of line scan. The terms , , and are the dc supply voltages of 5 and 3.3 V, and the reference voltage of the comparator.

Table 1.

Major specifications of MSI.

Major specifications of MSI.
Major specifications of MSI.

To reconstruct the 3D shape of the hydrometeors, they need to fall within the central area (13.2 cm2), where the four light sheets overlap and capture the snowflake silhouettes from the four different angles. The laser light sheet is slightly diffused, and a silhouette width for a 3D-shaped measurement differs by at most 2% along the light path in the central area. To estimate the fall velocity, four light sheets are placed at different heights: scanner channel 1 (CH1) is the highest and scanner channel 4 (CH4) is the lowest. The height difference between CH1 and CH4 is 2.6 mm (Fig. 3a). At least two scanners must detect the same particle to estimate its fall velocity, and the sensing area size is 45.2 cm2.

Fig. 3.

(a) Vertical light-sheet layout. (b) Snowflake silhouettes of each scanner, which are upside down. (c) The 3D hydrometeor image, where the images are from the same view angle of the scanners, and the grid resolution is 0.105 mm.

Fig. 3.

(a) Vertical light-sheet layout. (b) Snowflake silhouettes of each scanner, which are upside down. (c) The 3D hydrometeor image, where the images are from the same view angle of the scanners, and the grid resolution is 0.105 mm.

The MSI begins datalogging when one of the upper orthogonal scanners (CH1 or CH2) detects a particle shadow and terminates datalogging when none of the four scanners detect shadows. Datalogging also terminates if the particles are thinner than the gaps between the light sheets because in this case none of the scanners can detect the particles. Particles with heights greater than 1.3 mm, which corresponds to the largest light-sheet gap between CH2 and CH3 (Fig. 3a), are stably captured by the four scanners. The MSI ignores silhouettes detected by only CH3 and/or CH4. The image capture slice rate is set to 17.5 kHz, and the MSI acquires a maximum of 624 lines per silhouette and transfers these data to a network datalogger via a User Datagram Protocol (UDP).

3. Measurement of the fall velocity

The height-offset light sheets are used to measure the fall velocity of the hydrometeors. As shown in Fig. 3a, the differences in height between CH1 and CH2, CH1 and CH3, and CH1 and CH4 are 0.8, 2.1, and 2.6 mm, respectively. Figure 3b shows examples of scan images of a snowflake. The gray horizontal shades indicate areas where no shadow slices are available due to the time differences between CH1 and CHi (i = 2–4). The fall velocity is determined by

 
formula

where is the height difference between CH1 and CHi, is the number of no shadow slices that occurred before the first shadow slice, and is the slice rate. A larger leads to a better velocity estimate because many slices are involved in the acquisition. The definitive fall velocity is obtained from the -weighted average for with a criterion of 5 as follows:

 
formula

This paper estimates the of four-silhouette particles; the slice rate of 17.5 kHz can resolve the with a resolution of 0.03 m s−1 (0.4 m s−1) at = 1 m s−1 ( = 4 m s−1); however, the resolution exceeds 1 m s−1 at = 6.5 m s−1.

4. Reconstruction of pseudo-three-dimensional shapes

Multiangle silhouettes enable the pseudo-3D shape of individual snowflakes to be reconstructed. Figure 3 shows snowflake silhouettes captured by the four scanners (Fig. 3b) and the corresponding 3D image viewed from the same angles as the scanners (Fig. 3c). The 3D shape reconstruction involves the following four steps.

  1. Preprocessing

    • Silhouette images are derived via outline detection. The outline detection allows a two-pixel expansion of the silhouette to identify adjacent split images as a single particle, and it records the location and size of the box surrounding the first outline. When parts of the following outlines appear in the box, the images are identified as parts of the single particle, otherwise the images are discarded. We filter out small particles with maximum widths of less than 10 pixels (size 1.05 mm) due to the difficulty in reconstructing their 3D shapes. For a multiparticle silhouette, the MSI derives only a silhouette on the first shadow slice that triggered the measurement. However, multiple particles can be overlaid to form a single silhouette, which causes different silhouette heights between the multiangle silhouettes, resulting in 3D shape reconstruction failures.

  2. Three-dimensional shadow grid map

    • The reconstruction uses silhouettes captured by four—or at least three—scanners. Valid silhouettes should have an identical number of slices, that is, the same height. Invalid silhouettes are discarded when the difference in the number of slices between each silhouette exceeds 5% of the maximum number of slices and when the difference between the maximum and minimum number of slices exceeds 10%. The 3D shadow mapping is composed of two 3D grid volumes from orthogonal silhouette images of CH1 + CH2 and CH3 + CH4. The 3D grid volume of CH3 + CH4 is horizontally rotated 45 and is combined with the volume of CH1 + CH2 via horizontal offset iterations to maximize the number of matched shadow grids.

  3. Remove false grids

    • As shown in Fig. 4a (top view), the silhouette images cannot represent dent shapes or the depth in shadow areas. Because the ambiguity in the shadow depth may cause artificial shadow grids behind the true shadow grids, nonexistent and artificial grids should be eliminated. First, we select reliable grids that are illuminated by three or four light sheets, as shown in Fig. 4b. Next, continuity of the images to adjacent grids is checked upward and downward, and any grid that does not connect to an adjacent grid is removed. Figure 4c shows the result of the removal of the false grids in shadow areas.

  4. Real vertical scaling

    • Because the vertical resolution of the line scanner depends on the particle fall speed, the vertical size of the reconstructed 3D shape is adjusted based on the measured . The grid resolution is both vertically and horizontally uniform at 0.105 mm.

Fig. 4.

Methodology of artificial shadow grid removal. (a) Raw 3D image. (b) Reliable grids lighted by three or four light sheets. (c) Upward and downward continuity (UDC) scanned image.

Fig. 4.

Methodology of artificial shadow grid removal. (a) Raw 3D image. (b) Reliable grids lighted by three or four light sheets. (c) Upward and downward continuity (UDC) scanned image.

We evaluated this method of 3D shape reconstruction using several reference objects. Figure 5 illustrates the 3D shape examples of the sphere, cube, and square, and star-shaped plate. Table 2 shows the differences in the volume between the reference objects and the reconstructed 3D shapes for a sphere, spheroids, and a cube, and ring, circular, and square plates. Figure 6 shows the volume ratios between the reference object and the reconstructed 3D shapes in Table 2. The mean and standard deviations are obtained from 30 samples, where the plates are dropped in a horizontally parallel orientation. The 3D shape volumes are calculated for the four-silhouette and two-silhouette compositions using the orthogonal scanners of CH1 and CH2. As expected, the four-silhouette apparatus reproduces the 3D shape better than the two-silhouette apparatus. The reconstructed 3D shape provides a reasonable volume with small deviations for the spherical, spheroid, and cubical objects. The four-silhouette (two silhouette) method provides approximately 15% (40%) larger volumes than that of the reference objects; however, it overestimates the volumes of thin plates with larger deviations. The four-silhouette (two silhouette) reconstruction overestimates the mean thin plate volumes by 35%–120% (80%–290%), and the errors decrease as the plate thickness increases.

Fig. 5.

Examples of the 3D shape reconstruction for sphere, cube, and square, and star-shaped plates.

Fig. 5.

Examples of the 3D shape reconstruction for sphere, cube, and square, and star-shaped plates.

Table 2.

Size and volume of reference objects and reproduced 3D shapes.

Size and volume of reference objects and reproduced 3D shapes.
Size and volume of reference objects and reproduced 3D shapes.
Fig. 6.

Volume ratios between the reference object and the reconstructed 3D shapes by the four- and two-silhouette methods. Gray (black) box indicates the mean volume (std dev). Size information of the reference objects is listed in Table 2.

Fig. 6.

Volume ratios between the reference object and the reconstructed 3D shapes by the four- and two-silhouette methods. Gray (black) box indicates the mean volume (std dev). Size information of the reference objects is listed in Table 2.

The 3D shape reproducibility of a plate depends on whether an exact lateral shot (the narrow side) exists. The four-silhouette apparatus more easily captures a lateral shot compared to the orthogonal two-silhouette apparatus. Plates inclined to the scanner view angle cause a silhouette expansion in the projection view, resulting in volume overestimations, especially for thin objects. Figure 7 shows an example of a 3D shape reconstruction of a ring plate via the four-silhouette and two-silhouette reconstructions of CH1 and CH2. This orientation is worse for the two-silhouette reconstruction and better for the four-silhouette reconstruction. The orthogonal views of CH3 and CH4 approximately face the plate, and as a result the four-silhouette reconstruction produces a ring shape with 27% volume error. Conversely, the two-silhouette reconstruction of CH1 and CH2 produces a spherelike shape with holes with 314% volume error.

Fig. 7.

The 3D shape reconstruction of ring plate by (a) the four-silhouette method and (b) the orthogonal two-silhouette method of scanner CH1 and CH2, where the MSI captures the projection views as silhouette images. Ring plate is 10 mm in diameter and 1 mm thick with a 5-mm-diameter hole, whose volume is 58.9 mm3.

Fig. 7.

The 3D shape reconstruction of ring plate by (a) the four-silhouette method and (b) the orthogonal two-silhouette method of scanner CH1 and CH2, where the MSI captures the projection views as silhouette images. Ring plate is 10 mm in diameter and 1 mm thick with a 5-mm-diameter hole, whose volume is 58.9 mm3.

Kleinkort et al. (2017) reconstructed the precise 3D shapes of branched plates in addition to spherical and cubical objects using the modified MASC incorporating two top-view cameras. The top-view images drastically changed the reconstructed shapes, and the volumes became smaller than half the volumes estimated by three side-view cameras for five snowflakes. The MSI 3D shape reconstruction is similar to the modified MASC for the sphere and cube; however, the MSI reconstructs a branched plate falling with a horizontally parallel orientation as an octagonal plate without dents due to the lack of top-view images (Fig. 5). If the plate falls with a vertically parallel orientation, the MSI can reproduce the dents as the hole of a ring plate in Fig. 7 (not shown). Figure 8 shows the simulations of the 3D shape reconstruction for a branched object rotating around a horizontal branch θ. The object is also rotated 22.5 around the z axis, which is half the angle interval of four scanners, to maximize the effect of silhouette expansion in the four-silhouette reconstruction. Both the four- and two-silhouette reconstructions produce a plate on the xy plane with a vertical branch at θ = 0. The four-silhouette reconstruction shows the best 3D shape reproducibility with 66% volume error at an orientation of θ = 45; all the branches are reconstructed, with a horizontal branch expansion causing the volume error. On the other hand, the two-silhouette reconstruction produces a plate with fake branches, and the worst volume error of 338% occurred at θ = 45.

Fig. 8.

Simulations of the 3D shape reconstruction for a branched object rotating around a horizontal branch by the four- and two-silhouette methods. The object consists of three bars of 10 mm 1 mm 1 mm volume and has an offset rotation of 22.5° around the z axis. The arrows denoted with CH1–4 indicate the scanner view angles.

Fig. 8.

Simulations of the 3D shape reconstruction for a branched object rotating around a horizontal branch by the four- and two-silhouette methods. The object consists of three bars of 10 mm 1 mm 1 mm volume and has an offset rotation of 22.5° around the z axis. The arrows denoted with CH1–4 indicate the scanner view angles.

5. Field observations of snowfall

Figure 9 displays the instrument location of the MSI, 2DVD, and an electrical-balance-type snow gauge in the courtyard of the Institute of Low Temperature Science, Hokkaido University, from the end of January to mid-March 2015. The third-floor building acts as a wind breaker. This paper demonstrates the MSI performance compared to the 2DVD data using the following three case studies: a wet snowflake case on 27 February, a dry snowfall in a calm wind on 4 March, and huge snowflakes in humid air on 13 March 2015. Figure 10 shows the time series of the wind speed, surface air temperature, and relative humidity for the three cases (cf. in Fig. 16), where the weather sensor was operated on the rooftop of the building.

Fig. 9.

Instrument layout of MSI, 2DVD, and electrical-balance-type snow gauge.

Fig. 9.

Instrument layout of MSI, 2DVD, and electrical-balance-type snow gauge.

Fig. 10.

Time series of wind speed U, surface air temperature T, and relative humidity RH on (a) 26–27 Feb, (b) 4 Mar, and (c) 13 Mar 2015.

Fig. 10.

Time series of wind speed U, surface air temperature T, and relative humidity RH on (a) 26–27 Feb, (b) 4 Mar, and (c) 13 Mar 2015.

a. Instruments and data

We operated a first-generation 2DVD with a nominal horizontal resolution of 0.2 mm and a slice rate of 33 kHz (Kruger and Krajewski 2002). The 2DVD provides accurate particle volumes and fall velocities for raindrops; however, uncertainties remain for snowflakes, as noted by several researchers. The 2DVD often produces unreasonably large ( m s−1) at small sizes ( mm) due to the particle mismatch when multiple snowflakes fall together. Huang et al. (2010) proposed a particle size determination and rematching algorithm to mitigate the effect of unreasonably fast particles. This paper uses 2DVD data made by the manufacturer-developed algorithm for snow (make_sno), and we focus on the reproducibility of the 3D shape of relatively large snowflakes, measuring the sizes, fall velocities, and the sampling efficiency of the MSI.

The MSI initially filters out noiselike silhouettes, which are dot and line shapes having a maximum width narrower than four pixels (size 0.42 mm) or having fewer than four slices. To normalize particle screening between the MSI and 2DVD, the latter removed particles with fewer than eight slices. The eight-slice threshold comes from the four-slice threshold in the noise filter of the MSI and the nearly twofold speed difference in the slice rate between the MSI and 2DVD (17.5 vs 33 kHz). The four-horizontal-pixel criterion corresponds to the two-pixel width in 2DVD.

The electrical-balance-type snow gauge surrounded by a 2-m width and a 3-m-tall enclosure continuously measures the mass of the deposited snow. The (mm h−1) of the electrical-balance snow gauge is determined as follows:

 
formula

where is the mass increment with time (g s−1), is the water density (1 g cm−3), and S is the sampling area size (cm2). An electrical balance with a resolution of 0.1 g and a sampling area of 1960 cm2 was used. It can measure the every minute with a resolution of 0.03 mm h−1 (Fujiyoshi et al. 1990).

b. Evaluation of the fall velocities

Figure 11 shows the relationship between the maximum image width of the snowflake silhouettes and the of the MSI and 2DVD, which are the 3-h accumulations for 0100–0359 Japan standard time (JST) 27 February (Fig. 11a), 0900–1159 JST 4 March (Fig. 11b), and 1100–1359 JST 13 March 2015 (Fig. 11c). The of 2DVD is the larger of the silhouette widths measured by the two cameras, and the of the MSI is the largest width derived from the four silhouettes. On February 27, the mean of the MSI agreed with that of 2DVD; moreover, the deviations agreed at 3 mm. Large deviations in 2DVD at 3 mm are emphasized by the contamination of erroneously fast particles (6 m s−1). In other words, the MSI measures adequate with few erroneously fast . The MSI- and 2DVD-measured near 3 m s−1 appeared between the relationships of raindrops and graupels, which suggests small-sized raindrops and a wet snowflakes mixture. On March 4 and 13, the DwVf relationship indicated a 1 m s−1 with small deviations in the MSI; however, 2DVD showed remarkable deviations at 3 mm. The contamination of the erroneously fast values biased the mean and the deviations. Neglecting the fast particles (6 m s−1) gives a mean 1 m s−1 over the entire size range, and the mean of the MSI and 2DVD match for the rimed aggregates relationship.

Fig. 11.

Relationship between and captured by the MSI and 2DVD at (a) 0100–0359 JST 27 Feb, (b) 0900–1159 JST 4 Mar, and (c) 1100–1359 JST 13 Mar 2015. Closed circles and error bar indicate the mean and standard deviation of , respectively; note that the 2DVD has the under limit at 0.5 m s−1. The open circle indicates the mean of the 2DVD without the erroneously fast particles (6 m s−1). Relationship between and for raindrops, lump graupels, and rimed aggregates, where (Atlas and Ulbrich 1977), (Locatelli and Hobbs 1974), and (Ishizaka et al. 2013), respectively.

Fig. 11.

Relationship between and captured by the MSI and 2DVD at (a) 0100–0359 JST 27 Feb, (b) 0900–1159 JST 4 Mar, and (c) 1100–1359 JST 13 Mar 2015. Closed circles and error bar indicate the mean and standard deviation of , respectively; note that the 2DVD has the under limit at 0.5 m s−1. The open circle indicates the mean of the 2DVD without the erroneously fast particles (6 m s−1). Relationship between and for raindrops, lump graupels, and rimed aggregates, where (Atlas and Ulbrich 1977), (Locatelli and Hobbs 1974), and (Ishizaka et al. 2013), respectively.

Figure 12 shows the probability density function (PDF) and the cumulative distribution function (CDF) of estimated from the particles captured by MSI and 2DVD during the periods of 0100–0359 JST 27 February (Fig. 12a), 0900–1159 JST 4 March (Fig. 12b), and 1100–1359 JST 13 March 2015 (Fig. 12c). The speed of is classified into 31 bins as indicated in Table 3. The PDFs and CDFs measured by the MSI and 2DVD indicate similar shapes; the PDFs indicate a narrow concentration range of approximately 2 m s−1, and the CDFs indicate that nearly all particles appeared at 6 m s−1. On 27 February, the PDF and CDF show good agreement between the MSI and 2DVD; they indicate a concentration at 1.6–4 m s−1 and that 99% of the particles appeared at 5.6 m s−1. On 4 and 13 March, the PDFs indicate concentrations at 0.5–2 m s−1; however, the PDF and CDF show a slight slow offset of 0.2 m s−1 in the MSI on 4 March. The CDFs measured by the MSI (2DVD) indicate that 99% (96%) of the particles appeared at 2.8 m s−1 on 4 March and at 6.4 m s−1 on 13 March. The PDF and CDF on 13 March show slight disagreement for both slow and fast . The PDF suggests that the MSI can measure particles with 0.5 m s−1, while the 2DVD manufacturer algorithm cannot. The difference in the minimum detectable and the occurrences of fast particles (4 m s−1) for 2DVD cause the disagreements on the slow and fast sides. Therefore, both the PDF and CDF of , and the DwVf relationship demonstrate the adequate performance of the measurement by the MSI.

Fig. 12.

PDF and CDF of 3 h of cumulative measured by the MSI and 2DVD at (a) 0100–0359 JST 27 Feb, (b) 0900–1159 JST 4 Mar, and (c) 1100–1359 JST 13 Mar 2015.

Fig. 12.

PDF and CDF of 3 h of cumulative measured by the MSI and 2DVD at (a) 0100–0359 JST 27 Feb, (b) 0900–1159 JST 4 Mar, and (c) 1100–1359 JST 13 Mar 2015.

Table 3.

Classes of and .

Classes of  and .
Classes of  and .

c. Evaluation of particle size distribution

Figure 13 indicates the 3-h cumulative PSDs of the MSI and 2DVD based on on 27 February (Fig. 13a), 4 March (Fig. 13b), and 13 March 2015 (Fig. 13c). The size of is classified into 34 bins as shown in Table 3. The MSI can make three PSDs: a PSD of particles captured by at least two scanners, that of particles captured by four scanners, and that of particles with reconstructed 3D shapes. The sampling area for particles captured by two scanners and four scanners is 45.2 and 13.2 cm2, respectively. The PSD (m−3 mm−1) is expressed as follows:

 
formula

where S is the sampling area size (cm2), is the sampling time (s), is the of the jth particle in the ith size bin, and (mm) is the width of the ith size bin. The four PSDs show similar values in the 2–10-mm size range. The PSD measured via the four-silhouette MSI is larger than that measured via the two-silhouette 2DVD. This result suggests that the four-silhouette apparatus captures wider more easily than the two-silhouette apparatus. The PSDs of the MSI are always lower than those of 2DVD at 2 mm. Less sensitivity in the MSI to particles with a silhouette height shorter than 1.3 mm causes the deviation from 2DVD at 2 mm. The criterion of 1.05 mm in the 3D shape reconstruction also causes a deviation between the MSI and 2DVD at the small size range for the 3D particles. A distinct separation between the PSDs of the 3D-shaped particles and the four-silhouette particles on 13 March indicates 3D shape reconstruction failures.

Fig. 13.

The 3-h averaged PSDs based on captured by the MSI and 2DVD at (a) 0100–0359 JST 27 Feb, (b) 0900–1159 JST 4 Mar, and (c) 1100–1359 JST 13 Mar 2015. PSDs of particles captured by at least two scanners (solid line), particles captured by the four scanners (dashed line), and 3D-shape-reconstructed particles of MSI (chain line). PSD captured by 2DVD (solid line with circle).

Fig. 13.

The 3-h averaged PSDs based on captured by the MSI and 2DVD at (a) 0100–0359 JST 27 Feb, (b) 0900–1159 JST 4 Mar, and (c) 1100–1359 JST 13 Mar 2015. PSDs of particles captured by at least two scanners (solid line), particles captured by the four scanners (dashed line), and 3D-shape-reconstructed particles of MSI (chain line). PSD captured by 2DVD (solid line with circle).

d. Evaluation of the equivolumetric diameter

The four-silhouette apparatus of the MSI improves the representation of the particle volume compared to two-silhouette apparatuses, such as the 2DVD. Table 2 indicates that the volumes of the reference objects reconstructed using four silhouettes are closer to the true volumes than those reconstructed using two silhouettes; however, it also suggests that the pseudo-3D snowflake of the MSI exceeds the real volume. Figure 14 compares the values of the equivolumetric diameter measured by the four silhouettes with those measured by two silhouettes . Values of are 13% larger than those of ; that is, measured via the 2DVD may exceed the real value of by at least 13% (44% in volume).

Fig. 14.

Scatterplot between (two silhouettes) and (four silhouettes) of MSI on 27 Feb and 4 and 13 Mar 2015. Shown is the 13% difference (dashed line).

Fig. 14.

Scatterplot between (two silhouettes) and (four silhouettes) of MSI on 27 Feb and 4 and 13 Mar 2015. Shown is the 13% difference (dashed line).

Figure 15 demonstrates the size correction to provided by the 2DVD manufacturer algorithm incorporating an ellipsoidal particle assumption. It shows the 1-h PSDs of measured by the MSI and measured by the 2DVD on 27 February (Fig. 15a), 4 March (Fig. 15b), and 13 March 2015 (Fig. 15c), which indicates the PSDs before and after the 13% size-corrected (hereinafter ). The PSD shapes of and appear to agree with each other at 1.5 mm on 27 February and 4 March 2015. If the PSD of on 4 March is multiplied by 0.7, then the PSDs match for and . These agreements demonstrate the efficacy of the 13% size correction; however, the PSD of on 13 March indicates a PSD slope similar to the uncorrected . On 13 March, the MSI captured huge snowflakes with 10 mm and suffered from multiple 3D shape reconstruction failures. The silhouettes of huge snowflakes frequently overlay other snowflakes, which causes silhouette height differences resulting in 3D shape reconstruction failures. Huge snowflakes obscure small-sized snowflakes, which makes the sampling efficiency of the 3D-shaped snowflakes worse and may result in shallow-sloped PSDs.

Fig. 15.

The 1-h PSDs based on captured by the MSI and 2DVD at (a) 0200–0259 and 0300–0359 JST 27 Feb, (b) 0900–1059 and 1000–1159 JST 4 Mar, and (c) 1100–1159 and 1200–1359 JST 13 Mar 2015. PSD of MSI (circle). PSD of 2DVD before (dashed line) and after (solid line) the 13% size correction.

Fig. 15.

The 1-h PSDs based on captured by the MSI and 2DVD at (a) 0200–0259 and 0300–0359 JST 27 Feb, (b) 0900–1059 and 1000–1159 JST 4 Mar, and (c) 1100–1159 and 1200–1359 JST 13 Mar 2015. PSD of MSI (circle). PSD of 2DVD before (dashed line) and after (solid line) the 13% size correction.

e. Evaluation of the sampling efficiency of the MSI

The (mm h−1) values of the MSI and 2DVD ( and , respectively) are obtained by summing the particle masses over the PSD; then, the cumulative mass is divided by the water density (1 g cm−3), the sampling area size S (cm2), and the time interval (s), and the is determined as follows:

 
formula

where the suffix j denotes the jth particle in . This evaluation assigns = 1 g cm−3, and the mass corresponds to the fallen particle volume. To correct the small number concentration due to 3D shape reconstruction failures, the is adjusted by the particle concentration ratio γ between the four-silhouette particles and the 3D-shaped particles as follows:

 
formula

where () is the of the four-silhouette particles (the 3D-shaped particles). The volume-weighted mean (hereinafter ) is an index to express the PSD shape, and is obtained from the following equation for and :

 
formula

Figures 16 and 17 show the time series of the 20-min averaged and (a) from 2100 JST 26 February to 0530 JST 27 February (Figs. 16a and 17a), from 0800 to 1530 JST 4 March (Figs. 16b and 17b), and from 2300 JST 12 March to 0300 JST 13 March and from 1000 to 1430 JST 13 March 2015 (Figs. 16c and 17c). The figures display in addition to and . The and show agreements between the MSI and 2DVD. The agreement demonstrates the adjustment by γ and the agreement suggests PSD shape similarity in the 20-min accumulation; however, it indicates underestimations in at 2200 and 2300 JST 26 February, 0000 and 0220 JST 27 February, and 1240 JST 13 March 2015. Particle undercatch in intermittent light snowfall at 2200 JST 26 February and a clear sky at 1247–1253 JST 13 March (cf. Fig. 10) are responsible for the distinct outliers because the MSI has a weakness when representing accurate PSDs for short snowfalls due to its small sampling area. Cases with suggest undercatches or 3D shape reconstruction failures for large-sized snowflakes and result in outliers at 0000 and 0220 JST 27 February.

Fig. 16.

Time series of on (a) 26–27 Feb, (b) 4 Mar, and (c) 12–13 Mar 2015. Bar graph indicates the measured by the electrical balance snow gauge (EB). Shown are (blue solid line) and (black dashed line), and The red solid indicates the γ (red solid line).

Fig. 16.

Time series of on (a) 26–27 Feb, (b) 4 Mar, and (c) 12–13 Mar 2015. Bar graph indicates the measured by the electrical balance snow gauge (EB). Shown are (blue solid line) and (black dashed line), and The red solid indicates the γ (red solid line).

Fig. 17.

Time series of on (a) 26–27 Feb, (b) 4 Mar, and (c) 12–13 Mar 2015, showing (circle) and (solid line).

Fig. 17.

Time series of on (a) 26–27 Feb, (b) 4 Mar, and (c) 12–13 Mar 2015, showing (circle) and (solid line).

Figure 18 shows the and scatterplots between the MSI and 2DVD on 13 and 27 February and 4 and 13 March 2015. The data are derived from 20-min consecutive snow intervals; that is, 3D-shaped particles are detected every minute, when the number of 3D-shaped particles is greater than 200 (50) in each 20-min (5 min) interval. The error bar indicates the mean and standard deviation over the observation period, and the deviation shows similarities over the 4 days. In the 20-min averaging, the values appear on a 1:1 line with a correlation coefficient of 0.94, and the 5-min averaging shows a linear relationship with a correlation coefficient of 0.90 with dispersion within the 50% difference lines. If the 13% size correction to , which corresponds to a 44% volume correction, is not applied, then the γ-adjusted appears near the line indicating 50% underestimation (not shown). The scatterplot shows a linear relationship with a correlation coefficient of 0.94 (0.87) in the 20-min (5 min) average, and it demonstrates PSD shape similarities between the MSI and 2DVD; however, the MSI indicates a large bias at 2 mm due to the less sensitivity of small-sized snowflakes with 1.5 mm hardly reconstructing the 3D shapes. The 5-min averaged on 13 March tends to indicate large values corresponding to a shallow-sloped PSD with a much larger number of large-sized snowflakes, as seen in Fig. 15c. Consequently, the and agreements suggest that the MSI has the potential to adequately acquire PSDs of 3D-shaped particles with 1.5 mm during several-minute-long accumulations in consecutive snowfalls.

Fig. 18.

Scatterplots of 20- and 5-min averaged and between MSI and 2DVD in 20-min consecutive snows on 13 and 27 Feb, and 4 and 13 Mar 2015. Shown are the mean and standard deviation during the entire the observation period (error bar), and differences of 50% (20%) in ()

Fig. 18.

Scatterplots of 20- and 5-min averaged and between MSI and 2DVD in 20-min consecutive snows on 13 and 27 Feb, and 4 and 13 Mar 2015. Shown are the mean and standard deviation during the entire the observation period (error bar), and differences of 50% (20%) in ()

f. Mean snow density estimation

The value greatly affects the accuracies of the and Z estimates and is approximated by an empirical size–mass relationship (Locatelli and Hobbs 1974; Ishizaka et al. 2013). The mean snow density divides the liquid equivalent snow accumulation of the snow gauge by the cumulative particle volume captured by the disdrometers (e.g., Huang et al. 2015; Kneifel et al. 2015), and minute accumulations characterize the and median volume diameter relationship in consecutive snowfalls (Brandes et al. 2007).

Dividing by or gives the , and Fig. 19 shows the time variations in the . On 27 February 2015, the surface air temperature fluctuated near 1C and the varied within the range of 0.1–0.4 g cm−3 from 0000 to 0420 JST, suggesting the existence of wet snowflakes. The large values account for the relative fast of 2.8 m s−1. On 4 March, the air temperature varied around the freezing point and the was approximately 0.05 g cm−3, suggesting dry snow except at the beginning and end of the snowfall, which indicated moist ( 0.2 g cm−3). Dominations of small snowflake suggested by 2 mm appear in the time intervals with 0.1 g cm−3. The large of the MSI may be caused by underestimations due to the less sensitivity to the small-sized snowflakes of 1.5 mm. The by the 2DVD may suggests that partly melted small snowflakes dominate at the beginning and end of a snowfall because the size– relationship indicates large for small particles, which suggests easy melting (Brandes et al. 2007). On 13 March, a dry of 0.05 g cm−3 occurred. The air temperature varied below the freezing point from 0000 to 0200 JST; however, it fluctuated near 0.5C in humid air from 1100 to 1400 JST. The dry snowflake signature in the humid air may suggest the domination of large-sized snowflakes, which take time to melt. The diameter of 5–10 mm suggests large snowflake domination. In addition, the distinct outlier in the MSI at 1240 JST was caused by a small particle concentration due to an interval of clear sky.

Fig. 19.

Time series of the mean snow density by the MSI and 2DVD on (a) 26–27 Feb, (b) 4 Mar, and (c) 12–13 Mar 2015.

Fig. 19.

Time series of the mean snow density by the MSI and 2DVD on (a) 26–27 Feb, (b) 4 Mar, and (c) 12–13 Mar 2015.

6. Summary

We developed a novel 3D snowflake imager capable of and PSD measurements for snowflakes with 1.5 mm. The apparatus is composed of four laser line-image scanners with different viewing angles and height offsets. This paper described the 3D shape reconstruction using reference objects (spheres, spheroids, cubes, and plates). The , , and PSD measured by the MSI in snow were compared to those obtained using a 2DVD, and the results led to the following conclusions.

  • Estimates of the fall velocity

    • The four sensing light sheets of the MSI are aligned within a 2.6-mm height gap. These narrow gaps simplify particle matching on each light sheet. The DwVf relationship showed similarities between the MSI and 2DVD, where the MSI estimated the with small standard deviations. The PDFs and CDFs of obtained by the MSI and 2DVD were consistent with each other. These results confirmed the velocity estimates of the MSI.

  • Equivolumetric diameter

    • The 3D shapes of snowflakes captured by the MSI provided more precise results for the and were approximately 13% smaller than those obtained using the two-silhouette method. This suggests that a 13% size correction would improve the accuracy of for snowflakes measured by 2DVD.

  • Sampling efficiency of the MSI

    • The adjustment via the particle concentration ratio between and , which is the correction for the 3D shape reconstruction failures, reasonably adjusted , in particular on 13 March. The time series and scatterplots of the and values indicated good correlations between the MSI and 2DVD for 20-/5-min accumulations when consecutive snowfalls occurred. These results demonstrate the equivalent performance of the PSD measurements between the MSI and 2DVD during consecutive snowfall events except for light snowfalls composed of many small-sized snowflakes with De< 1.5 mm.

We performed a preliminary calculation of the by dividing by or to obtain a dataset of the 3D shapes, , and the particle temperatures of the snowflakes to calculate microwave scattering properties in future studies. Development of the MSI is ongoing. The MSI showed a remarkable PSD deviation with respect to the values of 2DVD at 1.5 mm; however, algorithm developments for use with single-scanner particles may mitigate this problem. By incorporating top-view cameras, we hope to obtain more precise 3D shapes, including dents in the horizontal plane.

Acknowledgments

The authors thank the three anonymous reviewers for their valuable comments and suggestions, which helped to improve the quality and clarity of the paper. This study is supported by JSPS KAKENHI Grant JP26400464 and the Joint Research Program of the Institute of Low Temperature Science, Hokkaido University, Japan.

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Footnotes

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