Classification of Precipitation Types Using Fall Velocity-Diameter Relationships from 2D-Video Distrometer Measurements

Received 26 October 2014; revised 1 March 2015; accepted 26 March 2015

Snowfall can cause damage to life and property during winter. However, the accurate measurement and prediction of ground snowfall is difficult due to wind-driven horizontal movement of snowflakes, and to the large variability in particle density as a function of the vertical structure of humidity (degree of supersaturation) and air temperature (Roebber et al., 2003; Baker et al., 2012; Nitu, 2013). To accurately estimate the amount of snowfall on the ground, previous studies have been carried out using radar measurements with high spatial and temporal resolutions (e.g. Fujiyoshi et al., 1990; Matrosov, 1992, 1998; Huang et al., 2010). However, it is evident that the accuracy of radar-based snowfall estimations is mainly affected by the radar measurement height, wind shear, and radar reflectivity-snowfall rate relationships (Z-S relationships), which depend on the size, shape, fall velocity and density of the snowflakes (Fujiyoshi et al., 1990; Matrosov, 1992, 1998; Rasmussen et al., 2003). The fall velocity of snowflakes plays a particularly significant role in governing the trail of snowfall, and in representing the density of snow and microphysical processes. Therefore, research on the relationship between the size and fall velocity of snowflakes is essential for the accurate estimation of snowfall amount.

(Langleben, 1954) suggested that melting or riming processes were the main causes of an increase in snowflake fall velocity, and derived fall velocity-diameter relationships (V-D relationship) according to snowflake types. (Hansch, 1999) investigated variables governing fall velocity (e.g., vertical size, area of perpendicular circumscribed circle, and the area ratio between the cross-sectional area and the circumscribed ellipse area) based on a theoretical approach, and conducted experiments using 2D Video Disdrometer (2DVD) measurements; the study suggested various V-D relationships according to snowflake type and degree of riming. It is of note that the variability of coefficients in V-D relationships is greater for the degree of riming than for snowflake types.

(Barthazy and Schefold, 2006) (BS hereafter) presented power-law and exponential V-D relationships for various snowflake types according to the degree of riming (classes 0-5), which is proportional to the coverage ratio of a droplet on a snowflake's surface, using a Hydrometeor Velocity and Shape Detector (HVSD). In their study, the V-D relationships were relatively independent of the degree of riming in weak riming stages (classes 1-3), whereas the relationships varied significantly with the degree of riming in heavy riming stages (classes 3-5). (Zawadzki et al., 2010) investigated the variability and uncertainties in snowfall velocity measurements that occurred when using an HVSD, such as instrument uncertainty in the fall velocity measurement, the effect of wobbling snowflakes on the accuracy of velocity measurements, and natural variability in the homogeneous snow terminal fall velocity. They also analyzed the correlations of the coefficients of V-D relationships with surface temperature, the temperature at echo top, and vertical depth of the precipitation system, all of which were derived using aircraft soundings and a vertically pointing X-band radar.

(Yuter et al., 2006) used the Particle Size and Velocity (PARSIVEL) to present various two-dimensional distributions between the size and fall velocity of rain, mixed-phase precipitation (rain and wet snow), and dry snow, and suggested a classification technique for mixed precipitation. (Sheppard and Joe, 2000) compared automatic measurements from various sensors [Vaisala FD12P, HSS Model 402B, Weather Identifier and Visibility Sensor (WIVis), and the Precipitation Occurrence Sensor System (POSS)] with manned observations, and then presented the limitations of each sensor. (Grazioli et al., 2014) developed the hydrometeor classification method using 2DVD measurements based on the support vector machine method. In addition, dual-polarization weather radar has been recently used to classify hydrometeor types (e.g. Vivekanandan et al., 1999; Liu and Chandrasekar, 2000; Lim et al., 2005; Park et al., 2009). The hydrometeor classification algorithm utilizes a fuzzy logic approach to combine feature parameters by employing polarimetric radar measurements (horizontal reflectivity, differential reflectivity, differential propagation phase shift, correlation coefficient, and linear depolarization ratio), and then classifies various hydrometeor types (such as drizzle, rain, dry snow, wet snow, hailstone, graupel). Furthermore, (Moisseev et al., 2009) showed that dual-polarization radar is a useful tool for identifying the growth processes of snowflakes, such as aggregation, riming, and deposition.

This study aims to derive new V-D relationships according to snowflake types in Korea, and to develop a new hydrometeor classification algorithm based on the derived relationships using 2DVD measurements. The paper is presented as follows: 2DVD measurements and snowflake photographs used in this study are described in section 2. The quality control process of the 2DVD measurements, and the procedures used to derive the V-D relationships and to develop the hydrometeor classification algorithm are explained in section 3. In section 4, the new V-D relationships are compared with results from the previous studies of BS and (Locatelli and Hobbs, 1974) (LH hereafter), and the Hydrometeor Classification Algorithm (HCA) is evaluated. Section 5 then summarizes the processes and results of this study.

Figure 1.  Photographs of (a) the Nikon D80 camera in the darkroom, and of snowflakes captured on the collection plate: (b) a mixture of types; (c) dendrite; (d) plate; (e) needle; and (f) graupel.

2DVD data and close-up pictures of snowflakes collected at the Cloud Physical Observation Station [CPOS, (37^°41'N, 128^°45'E), 842 m MSL] from 15 January to 9 April 2010 were analyzed. 2DVD instruments provided various details of precipitation particles (e.g., fall velocity, equivalent volume spherical diameter, major and minor axes, and canting angle) using two light sheets (with widths of 10 cm containing 512 pixels each) that are transmitted from two orthogonal light sources to the line scan cameras (which can capture the shadows of a particle) on a horizontal plane (see Fig. 1). The two light sheets were placed at a vertical distance of 6.2 mm from each other, creating a virtual measuring area of 10 cm × 10 cm. The captured images then entered the image processing procedure of the 2DVD, which integrates information received from each line-scan camera in relation to the particles. The fall velocity and equivalent volume spherical diameter were then estimated for particles that fell into the virtual measuring area only (Kruger and Krajewski, 2002; Schonhuber et al., 2008).

Snowflakes were photographed using a high-resolution digital camera system every 10 min after collection, by means of a rectangular-shaped collection plate with a size of 21.0\; cm× 29.7\;cm (623.7 cm²) that was covered with black velvet to alleviate particle breaking (Fig. 2). This plate was exposed to snowfall for approximately 2-5 s, depending on the snowfall intensity. The snowflakes that collected on the plate were then moved into a dark room, where the intensity of illumination was steadily maintained, and the temperature was maintained close to that of the temperature outdoors, to avoid melting the snowflakes. Snowflake photographs were taken using a Nikon D80 Digital Single Lens Reflector camera with a high resolution of 3872× 2592 pixels, a fixed focal length of 60 mm, an exposure time of 1/30 s, and a focal-length-aperture ratio of F3.8 (Fig. 2).

Figure 2.  Schematic of the measuring planes of the 2DVD [reproduced from Kruger and Krajewski (2002) with the kind permission from American Meteorological Society].

To derive the V-D relationships for the various types of snow particles, the 2DVD measurements were classified into four different snowflake types (dendrite, plate, needle, and graupel), based on the dominant snowflakes present after photo-interpretation (Figs. 2c-f), as determined by experts analyzing the silhouettes of snowflakes on the x-z or y-z plane of the 2DVD. Any ambiguous and/or mixed-phased events were excluded (Fig. 2b) from the dataset. If one of the snowflake types accounted for more than at least 70% of all snowflake types in the photograph, it was determined to be the dominant snowflake type. Therefore, even if it is possible to roughly identify the snowflake type using photographs taken of large collections of snowflakes, habit identification is effective. However, such a means of identification has limitations because each size of snowflake and its velocity cannot be determined.

The periods during which the 2DVD measurements were obtained to derive the V-D relationship for each type of snowflake is listed in Table 1. The number of each snowflake type counted was 2754 for dendrite, 824 for plate, 23 584 for needle, and 6698 for graupel. In addition, to evaluate the HCA, a rain-snow transition event (9 February 2010) and three snow events (12 February, 15 February, and 4 March 2010) were used (Table 2).

The quality control procedure used in relation to 2DVD data consisted of two steps. The first step employed 2DVD software to remove mismatched particles caused by contamination, such as the overlap of snow particles in the line of sight and particles crossing the virtual measuring area, in addition to the aerodynamics effects related to the 2DVD, tumbling snowflakes, and side views of snowflakes that were significantly different (particularly needle-type). This used individual information related to particles captured by the upper and lower line-scan cameras (Hansch, 1999; Kruger and Krajewski, 2002; Huang et al., 2010). The following particles were eliminated by quality control: fall velocity >4 m s^-1 or diameter <0.2 mm. In addition, particles that were shown to have significantly different areas in the images taken between one camera and another were eliminated. This quality control may eliminate particles that have very different areas from two cameras, although real snow particles can exhibit different shapes from different view angles. However, these particles may lead to significant errors in the velocity measurements.

In BS, the V-D relationships for four snowflake types (dendrite, plate, needle, and irregular crystals including graupel) were derived based on the degree of riming obtained by using the HVSD at different altitudes. In the present study (PS), the diameter of the precipitation particles was defined as the equivalent diameter of particles as captured by the two line cameras in the 2DVD instruments, whereas the maximum diameter of precipitation particles captured by two parallel beams from HVSD was used in BS. Therefore, the difference in the diameter definitions gives rise to some differences between PS and BS.

Figure 3.  Example of the stepwise quality control procedure used in 2DVD measurements for the snowfall event of 1618-1622 UTC 15 February 2010: scatter plot of (a) raw data, (b) after removal of mismatched particles, and (c) after filtering out particles beyond one standard deviation (σ) from the most probable velocities. Red dots and red vertical bars indicate the most probable velocities and standard deviations of fall velocities in each diameter class, respectively.

Figure 4.  Flow chart of hydrometeor classification. The j indicates six precipitation particle types (rain, wet snow, and snowflake types dendrite, plate, needle, and graupel).

Figure 5.  Two-dimensional frequency distribution between fall velocity and diameter for the snowflake types of (a) dendrite, (b) plate, (c) needle, and (d) graupel. The black solid line indicates the fall velocity-diameter relationship using WTLS regression.

To derive accurate V-D relationships, minor types of snowflakes were removed from the raw 2DVD data. The most probable velocity and its standard deviation (σ) were calculated with a diameter interval of 0.2 mm, and any particles that crossed σ from the most probable velocity were then removed. Figure 3 shows an example of the quality control used for the 2DVD measurements obtained from 1618 UTC to 1623 UTC 15 February 2010. The scatter plot between the fall velocity and diameter of raw 2DVD measurements is described in Fig. 3a, and Fig. 3b shows the distribution after removing mismatched and ambiguous particles. In this example, mismatched particles were mostly distributed at diameters of less than 1.0 mm, and minor types of snowflakes were then removed using a threshold of one standard deviation from the most probable velocity (Fig. 3c).

For a rainfall event, particles that were beyond the following range were identified as mismatched particles (Kruger and Krajewski, 2002) and thus removed: \begin{eqnarray*} |V_{\rm measured}-V_A|<0.4,\\[-4.5mm]\nonumber \end{eqnarray*} where V _measured (units: m s^-1) is the velocity measured by the 2DVD, and V_A indicates the calculated velocity from the V-D relationship (V=9.65-10.3e^-0.6D) for raindrops (Atlas et al., 1973, hereafter AT73).

The V-D relationships for various snowflake types were derived by the power-law regression as follows: \begin{equation} V(D)=aD^b ,(1) \end{equation} where a and b are coefficients, and D and V(D) represent the diameter (mm) and the fall velocity (m s^-1), respectively. Since power-law relationships are simple and useful in determining the analytic solution of a model (e.g. for Doppler spectra calculations), they are mostly used to derive the V-D relationship for snow particles (Langleben, 1954; Hansch, 1999; Zawadzki et al., 2010). In this study, the V-D relationships were derived using the weighted total least squares (WTLS) fitting method (Amemoya, 1997) rather than the ordinary least squares fitting method, as the WTLS method is able to minimize both uncertainties in the diameter, as well as in the fall velocity of 2DVD measurements, unlike the ordinary least squares fit.

The proposed HCA classifies the hydrometeor into six particle types (rain, wet snow/sleet, and the snowflake types of dendrite, plate, needle, and graupel), based on the AT73 relationship for raindrops and the newly proposed relationships for four different types of snowflakes. To classify the hydrometeor types, the HCA utilizes the difference between the velocity [V_j(D _obs,i)] from empirical relationships and the measured velocity (V _obs,i) from the 2DVD as follows: \begin{equation} f_j=\dfrac{1}{N}\sum_{i=1}^{i=N}|V_j(D_{{\rm obs},i})-V_{{\rm obs},i}| , \end{equation} where D _obs,i and V _obs,i are the diameter and velocity of each particle measured by 2DVD within a given time window (e.g., 5 min); j indicates the hydrometeor type (rain, or the snowflake types of dendrite, plate, needle, and graupel); and N is the total number of particles. Thus, five f_j are calculated for a time window of 5 min. Figure 4 shows a flow chart of the HCA. The theoretical fall velocity [V_j(D _obs,i)] at a given diameter was firstly calculated from the V-D relationships for each hydrometeor type. The averaged absolute value (f_j) of the difference between the theoretical fall velocity from the V-D relationship and the measured velocity from the 2DVD were then calculated using Eq. (3). When the minimum value (\(f_j,\min\)) among the calculated f_j was less than the threshold (f _threshold), the subscript j was finally identified as one of the hydrometeor types (e.g., rain, or the snowflake types of dendrite, plate, needle, or graupel); otherwise, it was classified as wet snow/sleet.

Figure 5 shows the two-dimensional normalized frequency distribution between the fall velocity and diameter in the 2DVD measurements, according to the type of snowflakes based on photo-interpretation by human experts. Class intervals for the diameter and fall velocity were 0.1 mm and 0.1 m s^-1, respectively. The solid line shown in Fig. 5 represents the V-D relationship fitted by the WTLS method. The fall velocities of both dendrite and plate are distributed in the range from 0.6 to 1.3 m s^-1. The diameter of dendrite has a range from 0.0 to 4.0 mm, with a relatively high frequency at diameters <1.5 mm (Fig. 5a), whereas that of plate is confined to less than around 2.0 mm. The exponents and coefficients in the V-D relationship are 0.82 and 0.24 for dendrite, and 0.74 and 0.35 for plate, respectively. However, their fall velocities tend to remain almost constant (between 0.6 and 1.3 m s^-1), with a small exponent (<0.4) and coefficient (<1.0), due to their low densities and flat-snowflake shapes. The exponent of dendrite is particularly small, which indicates that the growth of dendrite was by aggregation and deposition, causing an increase in size but no significant change in density.

The diameters of needle and graupel range from 0.0 to 4.0 mm, and are mostly concentrated at diameters under 1.5 mm; the range of their fall velocities (0.6-2.2 m s^-1) is wider than that of dendrite and plate (0.6-1.3 m s^-1). While the diameter ranges of both needle and graupel are similar to that of dendrite, their fall velocities increase more rapidly than that of dendrite, with increasing diameters. This indicates that the needle-type particles developed under a riming regime, as the riming process usually causes the fall velocity to increase significantly. Furthermore, weak aggregated or rimed needles were frequently observed during the photo-interpretation in the field (Fig. 2e). In addition, the graupel-type particles were a result of significant riming, which caused such a change in the original shape of the snowflake that it was no longer identifiable. Therefore, the coefficients and exponents of both the needle (1.03 and 0.71, respectively) and the graupel (1.30 and 0.94, respectively) in the V-D relationships were larger than those of both the dendrite and plate.

Figure 6.  V-D relationships of four snowflake types in this study and those of previous studies, after applying correction to mean sea level (MSL). The numbers (1)-(9) denote relationships of moderately rimed/densely rimed dendrites, unrimed/moderately rimed/densely rimed plates, unrimed/moderately rimed/densely rimed needles, and graupel in the study of Barthazy and Schefold (2006), respectively. The numbers (10)-(13) indicate the relationships derived for the snowflake types of dendrite, plate, needle and graupel, respectively, in this study. Finally, the numbers (14)-(18) indicate relationships of unrimed/densely rimed dendrites and lump/hexagonal/cone-shaped graupel in the study of Locatelli and Hobbs (1974), respectively.

The averaged difference (f_j) between fall velocities calculated from the V-D relationship and 2DVD measurements was calculated by Eq. (3), according to the hydrometeor type. The value of f_j for dendrite, plate, needle and graupel were 0.10, 0.05, 0.21 and 0.18 m s^-1, respectively. In addition, the value of f_j for raindrop (0.41) was calculated by comparing with the V-D relationship (AT73) for rainfall events occurring g on 8 February 2010 (not shown).

For a comparison of the V-D relationships between PS and BS, the fall velocities in the V-D relationships were converted into at mean sea level (MSL) (1013 hPa) using Eq. (4), which requires consideration of the effect of air density changes due to differences in observing altitudes (Brandes et al., 2008): \begin{equation} V_{1013}=V_{\rm obs}\sqrt{\dfrac{\rho_{\rm obs}}{\rho_{1013}}} , \end{equation} where V _obs and V₁₀₁₃, expressed in m s^-1, indicate the fall velocity of each snowflake at observational altitude and MSL, respectively; ρ₁₀₁₃ (1.225 kg m^-3) and ρ _obs (1.112 kg m^-2) refer to the density of air at 1013 hPa and at an observational altitude (842 m MSL), where the air density is linearly interpolated in the vertical direction based on the air density profile of the standard atmosphere. In BS, the fall velocity of snowflakes was measured at an altitude of 1604 m MSL and a ρ _obs corresponding to 1.048 kg m^-3.

Table 3 and Fig. 6 illustrate the V-D relationships corresponding to snowflake types in PS (solid lines) and BS (dashed lines), both after and before applying a height reduction to obtain values corresponding to those at MSL, and in LH (dashed lines). The results of LH are mostly used as a reference in the community, although in their study the authors did not report temperatures and the pressure conditions when measuring the fall velocity. The difference in the observational height between PS and BS does not cause a difference in the value of the exponents between V-D relationships. Four types of snowflakes show similar trends in terms of the V-D relationships. In PS and BS, the V-D relationship for dendrite (graupel) is gentlest (steepest). The coefficient of the adjusted V-D relationship for dendrite in PS (0.79) is smaller than that in BS (0.91 for moderately rimed dendrite and 0.98 for densely rimed dendrite) and is close to that of LH (0.80 for unrimed dendrite and 0.79 for densely rimed dendrite), as shown in Table 3. The exponent for dendrite in PS (0.24) is equal to that for densely rimed dendrite in BS, and is between that of unrimed (0.16) and densely rimed dendrite (0.27) in LH. On the contrary, the coefficient for plate in PS (0.71) is smaller than that in BS (that for unrimed, moderately rimed, and densely rimed plate are 0.94, 1.12 and 1.26, respectively), and its exponent in PS (0.35) is between that of moderately rimed (0.26) and densely rimed plate (0.40) in BS. The coefficient for needle in PS (0.99) is between that for unrimed (0.90) and moderately rimed needle (1.17) in BS, and the exponent for needle in PS (0.71) is greater than that for densely rimed needle (0.35) in BS. Furthermore, the coefficient for graupel in PS is smaller (greater) than that for graupel in BS (LH), and its exponent in PS is greater than that in BS (0.61) and LH (range between 0.28 and 0.65). The temperature range for graupel is -1.2^°C to -1.0^°C in PS, whereas BS reported a temperature range of -5.0 to -1.0^°C for the 15 cases. Assuming the temperature for graupel is colder in BS than in PS, the density of graupel would be higher in PS than in BS (Garrett and Yuter, 2014), and thus the difference in power-law exponents between PS and BS would be caused by the differences in temperature.

For the entire ranges of diameters, the fall velocity of dendrite and plate in PS is smaller than that of dendrite and plate in BS, as shown in Fig. 6, and, in addition, the fall velocity of needle and graupel in PS is smaller than that of needle and graupel in BS, with a range in diameter of < approximately 1.5 mm. However, the fall velocity of needle and graupel in PS is greater than that of needle and graupel in BS, with a range in diameter of >1.5 mm, and the fall velocity increases more rapidly with increasing diameter than in BS. The V-D relationship of needle and graupel with increasing diameter in PS intersects that of needle and graupel in BS.

4.3.1. Rain-snow transition case

The performance of the HCA was examined using a transition case (between rain and snow on 9 February 2010), as shown in Table 2. Equations (10) to (13), given in Table 3, were applied as the reference V-D relationship corresponding to the type of snowflake in the HCA, and AT73 was used as the reference V-D relationship for raindrops.

Figure 7.  Scatter plots of fall velocity vs. diameter, and the front and side views from the 2DVD according to particle type: (a) rain; (b) needle; (c) wet snow. The solid line represents the relationship for rain; dotted lines the relationships for snow; red numbering is the surface temperature from an automatic weather station.

The two-dimensional distribution between the fall velocity and diameter corresponding to the precipitation types in the 2DVD measurements was investigated (Fig. 7) prior to a performance test of the HCA. The class intervals in the two-dimensional normalized frequency distribution were 0.1 mm and 0.1 m s^-1, as shown in Fig. 7. The solid line refers to AT73, and the blue, red, purple and green dashed lines represent the V-D relationship for the snowflake types of dendrite, plate, needle and graupel, respectively, in this study.

Results show that, although AT73 was slightly higher than the measured fall velocity over the entire diameter range, the fall velocity of raindrops in 2DVD agreed well with AT73. In addition, the V-D relationship for raindrops increased remarkably as its diameter increased (Fig. 7a). In this study, the fall velocity of snowflakes (needle) increased less remarkably than that of raindrops with increasing diameter, according to the V-D relationship for needle (Fig. 7b). For wet snow/sleet, the fall velocity was widely distributed between the V-D relationships of raindrops and graupel (Fig. 7c). The V-D relationship of considerably (relatively) melted small (large) ice crystals was particularly close to AT73 (apart from the V-D relationship of graupel). Hence, an optimal V-D relationship for wet snow/sleet was impossible to derive, due to the large variation in fall velocity, which depends on the ratio between the water and ice contents in the precipitation particles. (Thurai et al., 2007) found similar results, i.e., that the fall velocity and diameter data from 2DVD deviated slightly from the Gunn-Kinzer (G-K) curve during a period of rain, while the fall velocities distributed below the G-K curve in the case of wet snow, and the fall velocities of dry snow were less than about 2.8 m s^-1.

In the HCA, wet snow/sleet can be classified based on the difference in the V-D relationships of raindrops and snowflakes. The value of f_j, 0.60, applied as a threshold, is larger than the maximum f_j (0.41) among the values of f_j for the five hydrometeor types (raindrop, and the snowflake types of plate, dendrite, needle, and graupel) in the previous section. In other words, if the minimum f_j is larger than 0.6, the event can be classified as a wet snow/sleet event.

Figure 8 illustrates the time series of five f_j s derived from the HCA and the final classification by applying the threshold value of 0.6 for the transition case of rain and snow on 9 February 2010. The reference classification of hydrometeor types based on photo-interpretation and 2DVD measurements by experts is presented in the upper part of Fig. 8b.

Figure 8.  Time series of results from the hydrometeor classification for 9 February 2010: (a) f_j for five hydrometeor types; (b) final classification from the algorithm and reference; (c) time series of surface temperature from an automatic weather station. The hydrometeor types at the top of (b) indicate the reference from snow pictures and 2DVD measurements. The symbols of plus (+), cross (×), diamond (\(\lozenge\)), rectangle (\(\square\)), circle (\(\bigcirc\)), and triangle (\(\triangle\)) denote rain, wet snow, and the snowflake types of dendrite, plate, needle and graupel, respectively.

The type of precipitation was found to frequently turn from rain into wet snow/sleet, from wet snow/sleet into snow, and from snow into wet snow/sleet prior to 0800 UTC, after which it became rain. The minimum f_j during the wet snow/sleet period was larger than that during the rain and snow period. Although the HCA correctly classified the type of precipitation, its performance diminished during the transition period of the dominant particle types.

For a quantitative evaluation of the HCA's performance, it is necessary to predetermine the reference classification by using the particle shape from 2DVD measurements and from the photo-interpretation by human experts. The hydrometeor types were classified into raindrop, wet snow/sleet, and snowflakes (dendrite, plate, needle, and graupel). The performance of the HCA was then evaluated using three skill scores (probability of detection, POD; false alarm ratio, FAR; critical success index, CSI) derived from the 3× 3 contingency table for three categories (raindrop, wet snow/sleet, and snowflakes) (Wilks, 2006, Fig. 9). The symbol "O" implies the reference hydrometeor types determined by human experts, and "P" stands for the hydrometeor types classified with the HCA in Fig. 9. Moreover, "r"-"z" represents the number of classifications for each type category; for example, "r" and "u" represent the number of rainfall events that are classified by the HCA correctly as raindrop events, and incorrectly as wet snow/sleet events, respectively. To derive the skill score for individual precipitation types, the 3× 3 contingency table was reduced to 2× 2 (Fig. 9), and the performance was then evaluated by using the score of the three skills (POD, FAR, and CSI), as follows:

\begin{eqnarray} {\rm POD}&=&\dfrac{e}{e+f} ,(4)\\ {\rm FAR}&=&\dfrac{f}{e+f} ,(5)\\ {\rm CSI}&=&\dfrac{e}{e+f+g} , (6)\end{eqnarray}

where e is the number of wet snow/sleet events correctly classified by the HCA; f is the number of other events incorrectly classified; and g is the number of wet snow/sleet events incorrectly classified as other types by the HCA. The skill scores according to the type of precipitation are listed in Table 4. PODs for both raindrops and wet snow/sleet (0.90) are larger than that of snow (0.71). The low skill score for snow is due to the large variation in the fall velocity of snowflakes, and hence snowflakes with a large fall velocity are incorrectly identified as wet snow. The FAR of wet snow/sleet (0.35) is larger than that of rain (0.03) and snow (0.00). Precipitation types were mostly misclassified during transition periods (e.g., snow to wet snow/sleet, wet snow/sleet to rain, etc.), due to the large variations in velocities during transitions. The CSI of wet snow/sleet (0.61) is smaller than that of rain (0.89) and snow (0.71).

Figure 9.  Reduction of the 3× 3 contingency table to a 2× 2 contingency table. The 2× 2 contingency table is constructed for wet snow as an event being forecasted, and the remaining rain and snow events are combined as complementary information.

4.3.2. Snowfall case

The performance of the HCA for four snowflake types (dendrite, plate, needle, and graupel) was evaluated by comparing with photo-interpretation by human experts using the snowfall cases (cases 2-4) listed in Table 2. Representative examples are shown in Fig. 10.

The skill scores for four snowflake types are listed in Table 5. POD, FAR, and CSI for dendrite were 1.00, 0.00, and 1.00, respectively, and for plate were 1.00, 0.00, and 1.00, respectively. All the dendrite and plate of snowflakes were, therefore, correctly classified. The POD, FAR, and CSI for needle were 0.67, 0.00, and 0.67, respectively. CSI and POD of needle were relatively smaller than those of dendrite and plate because the coefficient and exponent values of the V-D relationship for needle were between those of graupel and dendrite, and because the fall velocity of needle may strongly depend on the degree of riming under different growth regimes. The POD of graupel was 1.00, and its CSI was smaller than that of the other snowflake types due to its high FAR (0.50). The misclassification of needle to graupel in the HCA results with a high value of FAR is considered to have occurred because the fall velocity of densely rimed needle may be similar to that of graupel.

The V-D relationships by snowflake type were derived, and the HCA was developed using snow particle photographs taken at intervals of 10 minutes and 2DVD measurements at CPOS from 9 January to 9 April 2010.

Mismatched and/or minor-type particles were removed during the quality control procedure. The V-D relationships for four snowflake types (dendrite, plate, needle and graupel) were derived from 2DVD measurements based on photo-interpretations by human experts. Finally, a classification algorithm for six precipitation particles, including raindrops and wet snow/sleet, was developed using the 2DVD measurements. The HCA is based on the difference between the fall velocity from the predetermined V-D relationship for a given diameter and that of particles captured by 2DVD. For the classification of raindrops, AT73 was applied, and wet snow/sleet was classified using the threshold value of the averaged difference of fall velocities.

The fall velocities of dendrite and plate were narrowly ranged between 0.6 and 1.3 m s^-1 and slowly increased with increasing diameter due to the aerodynamic effects caused by their low density and flat shapes. Note that the diameter range of dendrite (0.0-4.0 mm) was twice as large as that of plate (0.0-2.0 mm), whereas both snowflakes had a similar fall velocity. It is considered that, in this study, dendrite grew under aggregation and deposition regimes. In addition, the fall velocities of needle and graupel were distributed within a range of 0.6-2.2 m s^-1, and had a larger range than those of dendrite and plate. The coefficient and exponent of both needle and graupel were larger than those of dendrite; that is, the fall velocity of needle and graupel increased more rapidly with increasing diameter than that of dendrite, due to growth under riming regimes.

The derived V-D relationships were adjusted with respect to the reference height (1013 hPa) and, then, compared with the V-D relationships in BS. The fall velocities of both dendrite and plate in this study were consistently smaller than those of BS over the whole diameter range; for needle and graupel, the fall velocities in this study increased more rapidly with increasing diameter than those of BS. It is considered that instrumental and geographical differences may have caused the discrepancy of the V-D relationships between the two studies.

Figure 10.  Scatter plots of fall velocity vs. diameter, and examples of photographs taken by the Nikon D80 for the snowflake types of (a, b) dendrite, (c, d) plate, (e, f) needle, and (g, h) graupel.

We then calculated the averaged difference between the fall velocities, which were calculated using empirical V-D relationships and observed 2DVD measurements according to hydrometeor type. The averaged differences of the fall velocities according to hydrometeor type were used to discriminate wet snow/sleet from other hydrometeor types. The HCA was applied to alternating transition cases of snow and rain. It was found that the fall velocity of wet snow/sleet varied significantly according to the ratio of air and water in particles. Therefore, it is impossible to determine an optimal, single V-D relationship for wet snow/sleet that can be discriminated from other hydrometeor types, based on the minimum average difference (f_j) between the fall velocity derived from the V-D relationship and the fall velocity measurements. In this study, a threshold value of f_j, 0.6, was used to identify wet snow/sleet. We then evaluated the performance of the HCA using the skill scores from a 3× 3 contingency table. The CSI for raindrops (0.89) and snow (0.71) was larger than that for wet snow/sleet (0.61). However, the FAR for wet snow/sleet (0.35) was larger than both rain (0.03) and snow (0.00). The V-D relationship of needle was located between that of dendrite and graupel, and the POD and CSI (0.67 and 0.67) of needle were smaller than those (1.00 and 1.00) of both dendrite and plate due to fluctuations in the fall velocity based on the degree of riming of needle. The CSI of needle (0.5) was the smallest.

(Yuter et al., 2006) suggested a classification algorithm for precipitation particles based on the fall velocity and diameter of particles. However, this algorithm can only distinguish snow from rain and mixed rain using a two-dimensional frequency distribution, which is not suitable for snowflake types. In contrast, our HCA is able to classify hydrometeors into six different types of precipitation: rain, wet snow/sleet, and the snowflake types of dendrite, plate, needle, and graupel.

The derived V-D relationships in this study can be used as a reference relationship for snowfall events over the Korean peninsula and, in addition, the HCA can be utilized for future studies related to snowfall estimation and V-D relationships. However, it is considered that the classification of precipitation particles needs to be further categorized by taking into consideration the growth regime of precipitation particles. In addition, our HCA could be further improved by considering surface temperature, or by using the vertical profile of temperature from a model.