Retrieval of Snow Water Equivalent by the Precipitation Imaging Package (PIP) in the Northern Great Lakes
1. Introduction
Precipitation is a key component of the water cycle and its global distribution is measured through a multiplatform effort including ground-based, shipborne, airborne, and spaceborne observations. Among these four platforms, the spaceborne measurements are the primary source for mapping the precipitation globally while the remaining three are the component of the validation efforts.
The National Aeronautics and Space Administration (NASA) Global Precipitation Measurement (GPM) mission and its predecessor, the Tropical Rainfall Measuring Mission (TRMM), map the precipitation globally using their core observatories and constellation satellites, and the Ground Validation (GV) program is an integral component of these missions (Skofronick-Jackson et al. 2017). One of the main differences between the TRMM and GPM missions is the orbital inclination of Core Observatory of 35° and 65°, respectively. Field campaigns are integral components of the Earth-observing satellite missions. Several field campaigns were conducted in the tropics and subtropics during TRMM era (Lau et al. 2000) but moved toward mid- to high latitudes where precipitation falls in liquid, mixed, and solid phases during GPM era (Skofronick-Jackson et al. 2015).
Historically, much of our knowledge of mixed and solid phase microphysics relies on the optical array probes on board research aircrafts (Field et al. 2006), while the surface measurements of falling snowflakes have been based on sampling individual particles (Gunn and Marshall 1958) until optical disdrometers became available. Optical disdrometers measure the size and fall velocity of individual mixed and frozen particles with different degrees of uncertainty; however, the complex shape, composition, and orientation bring additional challenges in determining the equivalent diameter of the snowflakes. The commercially available laser-optical Particle Size Velocity (PARSIVEL) and Two-Dimensional Video Disdrometer (2DVD) were originally developed to measure the raindrops. Battaglia et al. (2010) showed the limitations of the snowflake size and fall velocity measurements of snowflakes by PARSIVEL. The 2DVD measures the size and fall velocity of snowflakes between the two orthogonal cameras more accurately, provided the particle is correctly matched between the two view planes, and has been used to determine the scattering properties of snowflakes (Brandes et al. 2007; Huang et al. 2010, 2015; Bukovčić et al. 2018, 2020). The Multi-Angle Snowflake Camera (MASC) is another dedicated instrument designed to measure the properties of falling snowflakes. It captures high-resolution photographs of hydrometeors from three angles from which the habit can be identified (Garrett et al. 2012).
The Precipitation Imaging Package (PIP), formerly called the Snow Video Imager (SVI) was developed to measure the size and fall velocity of snowflakes. It has been widely used since its introduction (Newman et al. 2009) and underwent several hardware and software upgrades by the instrument inventor, Dr. Larry F. Bliven of NASA Wallops Flight Facility (Pettersen et al. 2020a,b). Most of the studies used PIP observations to investigate the microphysical properties of falling snow (Tiira et al. 2016; Moisseev et al. 2017; von Lerber et al. 2017; Pettersen et al. 2020a,b; Kulie et al. 2021) and to simulate the retrieval of snow properties from dual- (Li et al. 2018) and triple-frequency radars (Kneifel et al. 2015; Falconi et al. 2018; Tyynelä and von Lerber 2019; Li et al. 2020) including GPM’s Dual-Frequency Precipitation Radar (DPR) (Liao et al. 2016). Additionally, Pettersen et al. (2020b) demonstrated that the PIP-based bulk liquid water equivalent was within 2.5% agreement when compared to the collocated snow stake field over many events. Chase et al. (2020) used the PIP observations to examine the precipitation rate (PR)–melted mass-weighted mean diameter (Dmass*) relationship in the presence of snow in the DPR algorithm and found out that the DPR power-law PR (Dmass*) relationship is not optimal for snow. Measurement uncertainties of the SVI and PIP were evaluated by Wood et al. (2013) and Souverijns et al. (2017), respectively.
Of particular interest, Wood et al. (2014, 2015, W1415 hereafter) and von Lerber et al. (2017, 2018, vL1718 hereafter) described the methodology to retrieve the bulk snowfall characteristics including the snow water equivalent rate (SWER) and radar reflectivity (Ze) and used PIP measurements to test their retrieval processes. Pettersen et al. (2020b) compared the W1415 and vL1718 based bulk snowfall characteristics for low and high snow-to-liquid ratio events separately. The PIP measurements were used for this comparative study and a good agreement was found between the two retrieval methodologies. Pettersen et al. (2020b) found out that the W1415 and vL1718 retrieved SWER compared well to the independent PIP produced values of SWER.
This study uses PIP measurements to calculate the bulk descriptors of falling snowfall, snowfall rate (SR), and SWER. It should be noted that the SR refers to the snow intensity without melting while the SWER is the intensity of the melted equivalent of snow. The SR and SWER and their integral quantities snow depth (DP) and snow water equivalent (SWE) are the components of the climate record and have a wide range of applications in atmospheric and hydrological sciences. Among those, SWE are used for the short (≤daily) and long-term global precipitation mapping, respectively. The measurements of SWE are collected by operational gauges at daily or higher time resolutions and these observations are often integrated with the remote sensing precipitation estimate such as the one done by Multi-Radar Multi-Sensor (MRMS) product (Zhang et al. 2016). The MRMS is a ground validation product for the GPM mission (Kirstetter et al. 2015). It has a rain–snow discrimination algorithm based on surface air and wet-bulb temperatures (Chen et al. 2016) and relies on a power-law relationship between Ze and SWER for snow.
This study evaluates the retrieved SWE from PIP observations through comparisons with a National Weather Service (NWS) reference observations (hereafter referred to as “snow stake field” measurements). It should be noted that the estimated SWE is referred as PIP-retrieved SWE for the rest of the paper. The measurement site, at Marquette, Michigan (MQT), and the instrumentation including PIP and precipitation gauges are summarized in section 2. Section 3 is devoted to retrieval methodology while the snow events that were determined based on PIP observations are listed in section 4. Section 5 compares collocated gauges and the catch efficiency of the gauges under windy conditions. The results of this study can be found in sections 6 and 7 for the detailed discussion of the two events and overall comparisons, respectively, followed by conclusions in section 8.
2. Measurement site and instrumentation
a. Measurement site
The GPM Field Support Office augmented the existing precipitation observing site at MQT by deploying 10 OTT Pluvio2 200/400 weighing bucket gauges and an Autonomous PARSIVEL2 Unit (APU) at the beginning of December 2017. The master site (46.53°N, 87.55°W) adjacent to the NWS office is approximately 230 m above the nearby Lake Superior shoreline (Fig. 1) and has been equipped with a PIP and a K-band vertically pointing Micro Rain Radar (MRR) since January 2014 (Kulie et al. 2021; Pettersen et al. 2020a,b). The MRR provides the vertical structure of Ze and Doppler velocity (W) at 100-m gate spacing within 3 km above the ground. The daily PIP and MRR observations are posted online at https://www.ssec/wisc.edu/lake_effect/mqt/. The NWS office also operates a complete weather station and a manual snow stake field at the master site. Weather station and snow field observation details can be found in Pettersen et al. (2020a). The NWS Marquette Weather Surveillance Radar (KMQT) is located 80 m from the master site. The Pluvio2 gauges were distributed up to 17 km from KMQT and one of the Pluvio2 200 gauges (PL09) and APU are collocated with the other instrumentation at the master site.
Marquette (MQT) snowfall observatory data acquisition network. The master site includes the Precipitation Imaging Package (PIP), Pluvio2 200 weighing bucket gauge (PL09), complete weather station (WS) and NWS stake field, Micro Rain Radar (MRR), and Autonomous PARSIVEL2 disdrometer Unit (APU). The NWS-Marquette radar site (KMQT) with 10- and 20-km ranges, nine Pluvio2 200/400 gauge sites, and NWS Sawyer Airport and private weather station sites are also shown.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
Marquette (MQT) snowfall observatory data acquisition network. The master site includes the Precipitation Imaging Package (PIP), Pluvio2 200 weighing bucket gauge (PL09), complete weather station (WS) and NWS stake field, Micro Rain Radar (MRR), and Autonomous PARSIVEL2 disdrometer Unit (APU). The NWS-Marquette radar site (KMQT) with 10- and 20-km ranges, nine Pluvio2 200/400 gauge sites, and NWS Sawyer Airport and private weather station sites are also shown.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
Marquette (MQT) snowfall observatory data acquisition network. The master site includes the Precipitation Imaging Package (PIP), Pluvio2 200 weighing bucket gauge (PL09), complete weather station (WS) and NWS stake field, Micro Rain Radar (MRR), and Autonomous PARSIVEL2 disdrometer Unit (APU). The NWS-Marquette radar site (KMQT) with 10- and 20-km ranges, nine Pluvio2 200/400 gauge sites, and NWS Sawyer Airport and private weather station sites are also shown.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
b. PIP
PIP records the two-dimensional grayscale video images (see Figs. 6 and 10, Kneifel et al. 2015) of falling particles between a light source and a high-speed camera that are 2 m apart. The field of view (FOV) is calculated based on the 48 mm × 64 mm calibration image considering edge effects. The focal plane is about 1.3 m from the lenses and the depth of field (DOF) is size dependent. The sampling volume is a multiplication of FOV, DOF, and the number of frames over a given time period. Considering a single particle with 1 mm in equivalent diameter (Deq), the sampling volume is 3.95 m3 for a 1-min observation period. This is relatively larger than the corresponding sampling volumes of 2DVD and PARSIVEL2, 2.40 and 1.25 m3, respectively.
The PIP’s pixel size is 0.1 mm × 0.1 mm and the particles with less than 14 pixels are rejected. This effectively rejects the particles Deq < 0.2 mm. The standard sizing error for the SVI was reported as approximately 18% (Newman et al. 2009) and the current setup uses half of DOF reducing the uncertainty in the size measurements. The use of a higher speed camera enabled with particle tracking software allows the PIP to measure the fall velocity of individual particles (Pettersen et al. 2020b). This is one of the major improvements of the PIP from its original version, SVI. Depending on the direction of the particle entering and leaving the sample volume and particle size, particles have been photographed multiple times, which provide a unique information regarding the particle’s motion. The PIP’s measurement volume is not enclosed, and therefore, it is immune to the secondary particles due to splashing and undersampling in windy conditions. This is one of the advantages of PIP with respect to the 2DVD and PARSIVEL.
The PIP’s raw data have been grouped under particle, track, and velocity files. The record number and time stamp are included in each file that covers a 10-min time span. The particle file was generated following National Instruments Image Acquisition (IMAQ) software and outputs selected variables listed in Table 10-1 of IMAQ vision concepts manual (National Instruments 2004). The definitions of the various descriptors of the size parameters including Deq and maximum dimension of the particle (Dmx) are given in the appendix. It should be noted that Deq and Dmx are key for the retrieval assumptions and Fig. 1b of von Lerber et al. (2017) shows the schematic image of plane projection of the side view of PIP snowflake with Deq and Dmx.
The track files include, particle identification, record number, and Deq but do not include other descriptors of size parameters that can be found in particle file. A lookup table is generated where the record numbers are grouped by the particle identification number. Interestingly, a few particles had more than 20 records with a maximum of 59 records in our dataset. The user needs to combine particle and track files to determine the mean and maximum values of particle dimensions.
There are two velocity files. One is dedicated for the particles observed twice and the other is for the particles observed more than twice. The velocity files include the particle identification number from which the particle is matched, and the mean fall velocity is calculated. It is feasible that the particle may have negative (upward) fall velocity. Particles less than 0.5 m s−1 are excluded from the analysis (von Lerber et al. 2017).
The PIP also produces the higher-order products including estimates of effective density and precipitation rate as detailed in Pettersen et al. (2020b). The effective density is critical for the PIP derived SWER, which is used for a comparative study with W1415 and vL1718 retrieved SWE. Lee and Chandrasekar (2019), on the other hand, presented rain rate (RR) and SWER time series to demonstrate the mixed phase period as a validation tool for the precipitation phase algorithm.
c. Precipitation gauges
The OTT Pluvio2 200 is a heated weighing bucket gauge with a 200-cm2 orifice. It outputs real-time and non-real-time precipitation totals at 0.01-mm resolution for a predetermined sampling interval, which is typically 1 min. The non-real-time precipitation accumulation has a 5-min delay and is reliable for 10-min or longer observation periods.
The NWS snow stake field features an overflow can, collector funnel, and measuring tube and has a 324-cm2 orifice. When solid precipitation is expected, the collector funnel and measuring tube are removed and the snow is accumulated to the overflow can. The snowfall in the overflow can is first melted and then poured in the measurement tube. The water content corresponds to the nearest 0.01 inch (0.254 mm) reading in the measurement tube. The measurement is taken every 6 h at 0000, 0600, 1200, and 1800 UTC and at local midnight (0500 UTC). Snow board totals are also recorded at the same measurement cadence. The local NWS offices in the northern United States (e.g., MQT office) often map the annual totals of winter precipitation under their jurisdiction.
The CETF was applied to the Pluvio2 gauge whenever the gauge recorded precipitation. The mean wind speed and temperature were calculated from the data collected within ±15 min of the gauge measurement time. Snow stake field observations were manipulated to mimic the Pluvio2 gauge time stamps. A time series of the PIP SR is a reliable source for the intensity change at 1-min resolution. For the NWS snow measurement observational period (1 or 6 h since midnight falls in 0500 UTC during EST), a calibration constant was determined by taking the ratio of the stake field total to the PIP DP. The calibration constant was then multiplied with the PIP SR and the SR was accumulated from the beginning of the stake field observation period. Once the accumulation reached 0.01 mm, the time stamp (e.g., min) was saved and the accumulation was reset to zero. One-minute accumulations were as high as 0.13-mm accumulation in this study. The CETF was then applied to the manipulated stake field observations.
3. Retrieval methodology
This section describes the DP and SWE calculation procedure from PIP particle size and velocity measurements. The accuracy of PIP measurements including particle concentration, the choice of prescribed Dmx–Deq relationships, and four different approaches of particle mass calculation play an important role in determining the SWE.
a. SSD
Time series of size distribution are useful for characterizing the precipitation systems with different origins. In rain, the presence of an abundance of small drops in tropical cyclones and their absence in extratropical cyclones was shown in a study in mid-Atlantic region (Tokay et al. 2008). In snow, the shallow lake-effect events had fewer small particles than the deep synoptic events (Pettersen et al. 2020a). For rain, the +small, midsize, and large drops are separated with size thresholds of 1 and 3 mm such that the drops larger than 3 mm in diameter are considered as large (Tokay et al. 2014). For snow, the size threshold between the midsize and large flakes is considered as 5 mm in diameter since both aggregates and graupel often reach sizes above this threshold. Hence, the midsize flakes are considered between 1 and 5 mm in diameter in this study.
b. Snowflake mass
While this set of m–Dmx relationships have been used for the backscattering cross section calculations (Leinonen et al. 2012), it was recognized that m–Dmx relationship has a wider range due to the particle habit which diverges from a dry spheroid (Tyynelä and Chandrasekar 2014). Tiira et al. (2016) suggested
This study recognizes the dependency of the particle mass on the habit and uses the hydrometeor aerodynamics outlined by Böhm (1989, BM hereafter). A similar approach was used by Szyrmer and Zawadzki (2010, SZ hereafter) and von Lerber et al. (2017) and the process used in this study is explained in the following four steps.
The fitting was based on the median values of fall velocity (m s−1) and mass (g) in each size bin and bin midsize Dmx (cm). Each size bin should have at least 10 snowflakes to calculate the median values of velocity and mass and this condition should be satisfied for at least eight size bins; otherwise, the fitting was not applied.
c. Snow depth
The particle fall velocity in Eq. (10) is a function of Dmx and the DP are therefore calculated for the four values of α in the Dmx–Deq relationship. The NWS measures the geometric depth using a snow board that is cleared after every measurement interval. The main difference between the NWS measurement and geometric depth derived from Eq. (10) is the packing efficiency of the snowflakes and the snow compression. Tiira et al. (2016) pointed out the packing efficiency as 70% for the worst case scenario and the snow compression close to unity for a freshly fallen snow. These two factors should be considered if the DP is compared to the NWS measurement which is beyond the scope of this study.
d. Snow water equivalent
4. Snow events
The PIP SR time series were used to define the snow events. Precipitating periods were recognized when a minimum sample of 50 particles and a minimum intensity of 0.1 mm h−1 were observed over 1-min intervals. The collocated APU, which has a built-in algorithm for retrieving the precipitation phase (Yuter et al. 2006) and the wet-bulb temperature from collocated weather station were examined to determine periods with frozen precipitation. A total of 30 snow events were then identified based on following three conditions: 1) the time gap between the two consecutive events was longer than 12 h; 2) the DP was 3 mm or higher; 3) the event had at least 90 samples. Table 1 denotes the snow events with the event number, event date, start and end day of year (DOY) and hour (HHHH) in UTC, total number of snowy minutes, PIP DP, and median, minimum, and maximum values of wet-bulb temperature and wind speed. During the 2017/18 winter, PIP accumulated 2345.8 mm of geometric DP in 499 h. Event 11 was the longest, while event 30 had the highest accumulation. These two events are different in many aspects and this study uses these two events as representation of the two predominant snowfall regimes at MQT (see also Pettersen et al. 2020a,b; Kulie et al. 2021).
The list of the snow events. The columns are the event identification number, event date, event start and end day of year (DOY) and hour (HHHH) in UTC, number of snow minutes, PIP snow depth, and median, minimum, and maximum values of wet-bulb temperature and wind speed.
Event 11 had 3 days and 2 h of nearly continuous lake-effect snowfall. The storm started when a low pressure center was situated between Lake Superior and Lake Huron with a north–south elongated cold front and west–east arc shape warm front at 1500 UTC 3 January 2018 (Fig. 2a). This is a classical extratropical cyclone scenario frequently observed in upper Midwest in winter. The low pressure center moved northeast and a high pressure center penetrated to south, centering on southwest Ontario, Canada, at 1500 UTC 5 January 2018 (Fig. 2b); a perfect configuration for the northwesterly flow fetching from Lake Superior to MQT shore. The wet-bulb temperature ranged between −16° and −18°C for most of the event (Fig. 3a). The winds were moderate with a median wind speed of 3.5 m s−1 and blew from northwest for the entire event (Fig. 3b). Time series of the MRR Ze and W showed echo tops less 1.5 km with Ze ≤ 15 dBZ (Fig. 4a) and W ≤ 1 m s−1 (Fig. 4b) for the entire event.
The NWS surface analysis for (top) 1500 UTC 3 Jan and (bottom) 1500 UTC 5 Jan 2018.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
The NWS surface analysis for (top) 1500 UTC 3 Jan and (bottom) 1500 UTC 5 Jan 2018.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
The NWS surface analysis for (top) 1500 UTC 3 Jan and (bottom) 1500 UTC 5 Jan 2018.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
Time series of (a) air temperature and wet-bulb temperature and (b) wind direction and speed observations from the weather station at the master site for event 11.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
Time series of (a) air temperature and wet-bulb temperature and (b) wind direction and speed observations from the weather station at the master site for event 11.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
Time series of (a) air temperature and wet-bulb temperature and (b) wind direction and speed observations from the weather station at the master site for event 11.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
Times series of (a) equivalent reflectivity (Ze) and (b) Doppler velocity (W) from Micro Rain Radar at the master site for event 11.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
Times series of (a) equivalent reflectivity (Ze) and (b) Doppler velocity (W) from Micro Rain Radar at the master site for event 11.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
Times series of (a) equivalent reflectivity (Ze) and (b) Doppler velocity (W) from Micro Rain Radar at the master site for event 11.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
Event 30 was an example of a spatially variable storm. The event can be divided into different segments depending on synoptic and microphysical analyses, respectively. The event started when a low pressure centered over Indiana with a north–south elongated cold front at 1200 UTC 15 April 2018 (Fig. 5a). MQT, located well within the cold sector, received northeasterly flow. The low pressure center moved to the mid-Atlantic and a secondary low formed over Lake Huron at 1500 UTC 16 April 2018 (Fig. 5b). The wet-bulb temperature ranged between −5° and −7°C for most of the event (Fig. 6a). The winds were moderate with a median wind speed of 4.8 m s−1, while the wind direction shifted from northeast to northwest at around 1430 UTC April 16 (Fig. 6b). This coincided with the eastward movement of the low pressure system. Times series of MRR Ze and W exhibited three distinct segments of the storm. The first segment ending near 0000 UTC 16 April had radar echoes for the entire column with Ze > 20 dBZ (Fig. 7a) and W ∼ 2.5 m s−1 (downward) near the ground (Fig. 7b). The second segment ending 1800 UTC April 16 was a shallow period with echo tops mostly less than 1.5 km with Ze ≤ 15 dBZ and W ∼ 2.0–2.5 m s−1. The third segment was a mixture of brief deep and shallow periods of snowfall with echo tops ranging between 1.5 and 3.0 km. The shallow MRR reflectivity features and microphysical evolution associated with the second and third segments of this event indicate likely lake and orographic enhancement processes that frequently occur at this site (Kulie et al. 2021). The MRR Ze was bounded mostly between 10 and 20 dBZ while MRR W gradually decreased from 2 to <1 m s−1 until the last gap in the time series at 0100 UTC 17 April and increased to over 2 m s−1.
The NWS surface analysis for (top) 1200 UTC 15 Apr and (bottom) 1500 UTC 16 Apr 2018.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
The NWS surface analysis for (top) 1200 UTC 15 Apr and (bottom) 1500 UTC 16 Apr 2018.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
The NWS surface analysis for (top) 1200 UTC 15 Apr and (bottom) 1500 UTC 16 Apr 2018.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
Time series of (a) air temperature and wet bulb and (b) wind direction and speed observations from the weather station at the master site for event 30.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
Time series of (a) air temperature and wet bulb and (b) wind direction and speed observations from the weather station at the master site for event 30.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
Time series of (a) air temperature and wet bulb and (b) wind direction and speed observations from the weather station at the master site for event 30.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
Times series of (a) equivalent reflectivity (Ze) and (b) Doppler velocity (W) from Micro Rain Radar at the master site for event 30.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
Times series of (a) equivalent reflectivity (Ze) and (b) Doppler velocity (W) from Micro Rain Radar at the master site for event 30.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
Times series of (a) equivalent reflectivity (Ze) and (b) Doppler velocity (W) from Micro Rain Radar at the master site for event 30.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
5. Gauge measurements
Gauges provide direct precipitation measurements and are therefore used as a reference for evaluating the performance of disdrometers (Tokay et al. 2013, 2014). Indeed, this study used the gauge measurements to evaluate the PIP derived SWE with caution. Ideally, multiple heated weighing bucket gauges are operated within double fence intercomparison reference, but this is only feasible for a study focusing on gauge accuracy in winter precipitation (Rasmussen et al. 2012).
The comparison of collocated PL09 and snow stake field measurements revealed that PL09 underestimated event totals nearly in all events (Fig. 8). This was partly due to the PL09 malfunction. Stake field errors are primarily due to coarse resolution of 0.01 in (1 in. = 25.4 mm). Two-thirds of the events in December 2017 had less than 2 mm SWE where the PL09 and stake field totals differed by more than 25%. Such large differences between the two measurements were also evident for the low SWE events observed in 2018. About 80% of the events in 2018 had SWE more than 2 mm where the differences between the two were less than 20% nearly in all events, indicating a reasonable agreement. The events with high median wind speed (WSPmed > 4 m s−1) or low median wet-bulb temperature (WBmed < −10°C) did not necessarily have the large differences in precipitation totals (Fig. 8). This was also the case when the event maximum wind speed (WSPmax > 8 m s−1) or maximum wet-bulb temperature (WBmax < −5°C) was considered.
Comparison of Pluvio2 200 weighing bucket gauge (PL09) and NWS stake field snow water equivalent event totals as a function of (a) median wind speed (WSP), (b) maximum wind speed, (c) median wet-bulb (WB) temperature, and (d) maximum wet-bulb temperature.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
Comparison of Pluvio2 200 weighing bucket gauge (PL09) and NWS stake field snow water equivalent event totals as a function of (a) median wind speed (WSP), (b) maximum wind speed, (c) median wet-bulb (WB) temperature, and (d) maximum wet-bulb temperature.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
Comparison of Pluvio2 200 weighing bucket gauge (PL09) and NWS stake field snow water equivalent event totals as a function of (a) median wind speed (WSP), (b) maximum wind speed, (c) median wet-bulb (WB) temperature, and (d) maximum wet-bulb temperature.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
6. Two predominant events
a. Snow size distribution
SSD time series between events 11 and 30 were significantly different (Fig. 9; see also Table 2). Event 11 had a relatively uniform distribution with abundant small flakes, low concentrations of midsize flakes and an absence of large flakes. The low concentrations of midsize flakes were mainly due to the lack of flakes between 3- and 5-mm size range (Fig. 9a). Event 30 showed intraevent variability reflecting the three segments observed in MRR Ze and W time series. The abundant small flakes, high concentration of midsize flakes, and the presence of large flakes between 5 and 10 mm in Deq were the characteristic features of the first segment (Fig. 9b). The narrow size spectra, with maximum flake size less than 3 mm dominated the second segment. The concentration of small flakes was also less than the first segment particularly toward the end of the second segment. The third segment was dominated by the low concentrations of small flakes, but the midsize flakes were well represented and the large flakes were also present including aggregates as large as 15 mm.
Time series of snowflake size distribution for (a) event 11 and (b) event 30.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
Time series of snowflake size distribution for (a) event 11 and (b) event 30.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
Time series of snowflake size distribution for (a) event 11 and (b) event 30.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
The minimum, median, mean, and maximum values of total concentration (NT), mass-weighted mean diameter (Dmass), maximum particle diameter (Dmax), and the shape parameter of the gamma fitted distribution (μ) for events 11 (top value for each parameter) and 30 (bottom value).
b. Snowflake mass
Time series of the coefficients, aυ and am, of the υ–Dmx and m–Dmx relationships, respectively, reflected the characteristic differences between and within the events. In this study, time series of aυ was constructed for four different Dmx–Deq relationships while time series of am was presented for four different Best number approaches when Dmx =1.4Deq.
Time series of aυ in event 11 reflected the uniform nature of the event where the maximum and minimum aυ values ranged between 0.5 and 1.9 m s−1 cm−bυ (Fig. 10a). The maximum difference in aυ at a given time occurred between 1.3Deq and 1.5Deq and was 0.8 m s−1 cm−bυ. Time series of am in event 11 had uniform structure throughout the event but there were significant differences in am at a given time between the four methods (Fig. 10b). The am values were significantly lower for the HW method and the maximum difference in am at a given time, 0.005 g cm−bm, occurred between the HW and MH methods. The MH method resulted in slightly higher am values than the BM and KC methods.
Time series of (a) coefficient (aυ) of the υ–Dmx relationships for event 11 when PIP maximum particle dimension is equal to 1.2Deq, 1.3Deq, 1.4Deq, and 1.5Deq, (b) coefficient (am) of the m–Dmx relationship for event 30 when PIP mass estimate is based on BM, HW, KC, and MH methods when Dmx = 1.4Deq.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
Time series of (a) coefficient (aυ) of the υ–Dmx relationships for event 11 when PIP maximum particle dimension is equal to 1.2Deq, 1.3Deq, 1.4Deq, and 1.5Deq, (b) coefficient (am) of the m–Dmx relationship for event 30 when PIP mass estimate is based on BM, HW, KC, and MH methods when Dmx = 1.4Deq.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
Time series of (a) coefficient (aυ) of the υ–Dmx relationships for event 11 when PIP maximum particle dimension is equal to 1.2Deq, 1.3Deq, 1.4Deq, and 1.5Deq, (b) coefficient (am) of the m–Dmx relationship for event 30 when PIP mass estimate is based on BM, HW, KC, and MH methods when Dmx = 1.4Deq.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
Time series of aυ in event 30 reflected the three segments of the event discussed in section 5. The first segment had uniform structure where the maximum and minimum aυ values are bounded between 1.1 and 1.9 m s−1 cm−bυ (Fig. 11a). The second segments of the storm had high variability where the minimum and maximum aυ values ranged from 1.2 to 4.9 m s−1 cm−bυ. The third segment of the storm had moderate variability with a 0.6–2.7 m s−1 cm−bυ range in aυ. The maximum difference in aυ at a given time was observed between 1.2Deq and 1.5Deq during the second segment of the event and was 2.5 m s−1 cm−bυ. It should be noted that the exponent (bυ) of the υ–Dmx relationships was around 0.5 in the power-law relationships. For a 0.1 cm snowflake with aυ = 4.9 m s−1 cm−bυ and bυ = 0.5, PIP fall velocity is 1.55 m s−1. Indeed, the visual inspection of velocity tables (not shown) showed that the median PIP fall velocity for the bin centered at 1.1-mm diameter remained less than 2 m s−1 during the second segment of the event.
Time series of (a) coefficient (aυ) of the υ(Dmx) relationships for event 30 when PIP maximum particle dimension is equal to 1.2Deq, 1.3Deq, 1.4Deq, and 1.5Deq, (b) coefficient (am) of the m(Dmx) relationship for event 30 when PIP mass estimate is based on BM, HW, KC, and MH methods when Dmx = 1.4Deq.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
Time series of (a) coefficient (aυ) of the υ(Dmx) relationships for event 30 when PIP maximum particle dimension is equal to 1.2Deq, 1.3Deq, 1.4Deq, and 1.5Deq, (b) coefficient (am) of the m(Dmx) relationship for event 30 when PIP mass estimate is based on BM, HW, KC, and MH methods when Dmx = 1.4Deq.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
Time series of (a) coefficient (aυ) of the υ(Dmx) relationships for event 30 when PIP maximum particle dimension is equal to 1.2Deq, 1.3Deq, 1.4Deq, and 1.5Deq, (b) coefficient (am) of the m(Dmx) relationship for event 30 when PIP mass estimate is based on BM, HW, KC, and MH methods when Dmx = 1.4Deq.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
Time series of am in event 30 had a similar trend as the time series of aυ for the same event (Fig. 11b). The uniformity and high variability were evident during the first and second segment of the event, respectively, and am ranged between 0.002 and 0.06 g cm−bm during the second segment. The exponent (bm) of the m–Dmx relationship was around 2.6 when am had the highest value in this segment. For a 0.1 cm snowflake with am = 0.06 g cm−bm and bm = 2.6, mass is 0.000 15 g matching well with the mass table (not shown). It should be noted that the HW method resulted in distinctly lower am values throughout the event. The maximum difference in am at a given time, 0.39 g cm−bm, was observed between the MH and HW methods during the highly variable second segment and was significantly higher than the difference in event 11. The dependency of the PIP-retrieved mass to the method of derivation has a clear role on the PIP-retrieved SWE that will be discussed later in this paper.
c. Snow water equivalent
Time series of PIP-retrieved and stake field-measured SWE show different degrees of agreement on an event-by-event basis. The PIP-estimated SWE was more sensitive to the method of Re–X numbers relationship than to the choice of Dmx–Deq relationship. A separate figure was therefore generated for each of the four Re–X numbers relationships for each event. Each figure includes PIP-retrieved SWE for Dmx = 1.2Deq and Dmx = 1.5Deq. Given the fact that PL09 gauge malfunctioned in several events, the uncorrected and wind-corrected stake field records were taken as a reference.
The two events presented in detail in previous sections showed significant differences for the performance of the PIP-retrieved SWE. Table 3 presents the performance of PIP-retrieved SWE in terms of absolute bias (%). The absolute bias is the difference between the PIP-retrieved and stake field-measured SWE divided by stake field-measured SWE multiplied by 100. The level of agreement is given for each Re–X relationship and the range of the absolute bias represents the agreement among the four different Dmx–Deq relationships. For event 11, the PIP-retrieved SWE had better agreements with the wind corrected stake field measurements; the best agreement with the absolute bias of 2.4% occurred when SWE was retrieved with the HW method and Dmx = 1.5Deq (Fig. 12).
Time series of accumulative snow water equivalent (SWE) for event 11 for uncorrected and wind-corrected NWS snow stake field observations and for (a) BM, (b) HW, (c) KC, and (d) MH method-based PIP calculations and when PIP maximum dimension is equal to 1.2Deq and 1.5Deq.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
Time series of accumulative snow water equivalent (SWE) for event 11 for uncorrected and wind-corrected NWS snow stake field observations and for (a) BM, (b) HW, (c) KC, and (d) MH method-based PIP calculations and when PIP maximum dimension is equal to 1.2Deq and 1.5Deq.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
Time series of accumulative snow water equivalent (SWE) for event 11 for uncorrected and wind-corrected NWS snow stake field observations and for (a) BM, (b) HW, (c) KC, and (d) MH method-based PIP calculations and when PIP maximum dimension is equal to 1.2Deq and 1.5Deq.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
Performance of PIP-retrieved SWE with respect to uncorrected (first row for each event) and wind corrected (second row) stake field measurements. The absolute bias (abs_bias) is given for the range based on Dmx–Deq relationships for X–Re relationships. The event lowest absolute bias is shown in boldface font. The rows for the two events (11 and 30) discussed in detail are in italics.
The PIP-retrieved SWE agreed better with the uncorrected stake field data than the wind corrected stake field data for event 30 (Fig. 13). If the absolute biases ≤ 15%, 10%, and 5% are considered as good, very good, and excellent agreements, respectively, PIP-retrieved SWE using the BM method had a very good performance with respect to uncorrected stake field record for all Dmx–Deq relationships (Table 3). In fact, three of the Dmx–Deq relationship in the BM method and Dmx = 1.2Deq in the KC method resulted in excellent performance for the PIP-retrieved SWE. It was expected that the PIP-retrieved SWE would have a better agreement with the wind corrected gauge records in windy conditions. Event 30 was moderately windy with higher median and maximum wind speeds than the event 11. Yet the PIP-retrieved SWE agreed better with the uncorrected stake field record.
Time series of accumulative snow water equivalent (SWE) for event 30 for uncorrected and wind-corrected NWS snow stake field observations and for (a) BM, (b) HW, (c) KC, and (d) MH method-based PIP calculations and when PIP maximum dimension is equal to 1.2Deq and 1.5Deq.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
Time series of accumulative snow water equivalent (SWE) for event 30 for uncorrected and wind-corrected NWS snow stake field observations and for (a) BM, (b) HW, (c) KC, and (d) MH method-based PIP calculations and when PIP maximum dimension is equal to 1.2Deq and 1.5Deq.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
Time series of accumulative snow water equivalent (SWE) for event 30 for uncorrected and wind-corrected NWS snow stake field observations and for (a) BM, (b) HW, (c) KC, and (d) MH method-based PIP calculations and when PIP maximum dimension is equal to 1.2Deq and 1.5Deq.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
7. Overall comparisons
An overall performance of the PIP-retrieved SWE was evaluated based on its absolute bias with respect the uncorrected and wind corrected stake field records for the 30 events. Additionally, time series of each event were visually inspected to ensure that any agreement at the end of the event was result of cancellation between two disagreements (i.e., the gauge was higher in one segment and PIP was higher in another segment of event). The minimum absolute bias was sought among the four Dmx–Deq relationship based on the PIP-retrieved SWE and stake field record for a given Re–X method in each event.
Figures 14 and 15 present the scatter diagrams of PIP-retrieved SWE and stake field totals without and with wind corrections, respectively, when the BM, HW, KC, and MH methods are used. The Pearson correlation coefficient, bias, and absolute bias are included. Considering the uncorrected stake field record as a reference, the Dmx = 1.2Deq relationship had the minimum absolute bias for most of the events when the BM, KC, and MH methods were used (Fig. 14). For the HW method, the minimum absolute bias was obtained when Dmx = 1.5Deq was used for most of the events. Overall, the PIP-retrieved SWE was overestimated when BM, KC, and MH methods were used and underestimated when HW method was used. The BM method based PIP-retrieved SWE had the best performance with an absolute bias of 19%, while the absolute biases were 2.4%, 3.5%, and 8.3% higher when the KC, HW, and MH methods were used.
Comparison of PIP-retrieved and NWS stake field–measured (without wind correction) snow water equivalent (SWE) event totals for (a) BM, (b) HW, (c) KC, and (d) MH method-based PIP calculations and for the best agreement among the four PIP Dmx–Deq relationships (1.2Deq, 1.3Deq, 1.4Deq, and 1.5Deq). The correlation coefficient (cc), bias, and absolute bias between the two estimated and observed variables are also in given.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
Comparison of PIP-retrieved and NWS stake field–measured (without wind correction) snow water equivalent (SWE) event totals for (a) BM, (b) HW, (c) KC, and (d) MH method-based PIP calculations and for the best agreement among the four PIP Dmx–Deq relationships (1.2Deq, 1.3Deq, 1.4Deq, and 1.5Deq). The correlation coefficient (cc), bias, and absolute bias between the two estimated and observed variables are also in given.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
Comparison of PIP-retrieved and NWS stake field–measured (without wind correction) snow water equivalent (SWE) event totals for (a) BM, (b) HW, (c) KC, and (d) MH method-based PIP calculations and for the best agreement among the four PIP Dmx–Deq relationships (1.2Deq, 1.3Deq, 1.4Deq, and 1.5Deq). The correlation coefficient (cc), bias, and absolute bias between the two estimated and observed variables are also in given.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
Comparison of PIP-retrieved and NWS stake field–measured (with wind correction) SWE event totals for (a) BM, (b) HW, (c) KC, and (d) MH method-based PIP calculations and for the best agreement among the four PIP Dmx–Deq relationships (1.2Deq, 1.3Deq, 1.4Deq, and 1.5Deq). The cc, bias, and absolute bias between the two estimated and observed variables are also in given.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
Comparison of PIP-retrieved and NWS stake field–measured (with wind correction) SWE event totals for (a) BM, (b) HW, (c) KC, and (d) MH method-based PIP calculations and for the best agreement among the four PIP Dmx–Deq relationships (1.2Deq, 1.3Deq, 1.4Deq, and 1.5Deq). The cc, bias, and absolute bias between the two estimated and observed variables are also in given.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
Comparison of PIP-retrieved and NWS stake field–measured (with wind correction) SWE event totals for (a) BM, (b) HW, (c) KC, and (d) MH method-based PIP calculations and for the best agreement among the four PIP Dmx–Deq relationships (1.2Deq, 1.3Deq, 1.4Deq, and 1.5Deq). The cc, bias, and absolute bias between the two estimated and observed variables are also in given.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
The absolute biases were higher except for the MH method when the wind corrected gauge record was considered as a reference. The MH method based PIP-retrieved SWE had the best performance with absolute bias of 20.7% (Fig. 15). Overall, PIP-retrieved SWE was underestimated with respect to the wind corrected gauge record regardless of which of the four method was used. The bias difference between the uncorrected and corrected gauge references was the lowest for the HW method (28.9%) and highest for the MH method (38.2%). In terms of absolute bias difference, however, the HW and KC methods resulted in the maximum (18%) and minimum (2.1%) differences between the two references, respectively.
Figure 16 presents the scatter diagrams of PIP-retrieved SWE and stake field totals without and with wind correction, respectively. In these figures, the PIP-retrieved SWE method that had the best agreement with respect to the reference gauge was chosen. For most of the events, the HW and MH methods resulted in the best agreement with respect to uncorrected and wind corrected gauges, respectively. The agreement was better with respect to the uncorrected gauge totals with an absolute bias of 7.1%. The comparison of PIP-retrieved SWE with either uncorrected or wind corrected stake field records resulted in an excellent agreement with an absolute bias of 2.0%. On event-by-event basis, the PIP-retrieved SWE was in a good agreement, ≤15%, with respect to either uncorrected or wind corrected stake field measurements (Table 3). Realistically, the wind corrected gauge record should be used above a certain wind speed threshold. In this study, 12 out of 30 events had a better agreement when uncorrected gauge record was the reference and half of those events occurred when the median wind speed was moderate (3–6 m s−1) (Table 3).
Comparison of PIP-retrieved and NWS snow stake field–measured SWE event totals (a) without wind correction, (b) with wind correction, (c) with or without wind correction for the best agreement among the four PIP mass estimation methods (BM, HW, KC, and MH) and the four PIP Dmx(Deq) relationships (1.2Deq, 1.3Deq, 1.4Deq, and 1.5Deq, not shown). The cc, bias, and absolute bias between the two estimated and observed variables are also in given.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
Comparison of PIP-retrieved and NWS snow stake field–measured SWE event totals (a) without wind correction, (b) with wind correction, (c) with or without wind correction for the best agreement among the four PIP mass estimation methods (BM, HW, KC, and MH) and the four PIP Dmx(Deq) relationships (1.2Deq, 1.3Deq, 1.4Deq, and 1.5Deq, not shown). The cc, bias, and absolute bias between the two estimated and observed variables are also in given.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
Comparison of PIP-retrieved and NWS snow stake field–measured SWE event totals (a) without wind correction, (b) with wind correction, (c) with or without wind correction for the best agreement among the four PIP mass estimation methods (BM, HW, KC, and MH) and the four PIP Dmx(Deq) relationships (1.2Deq, 1.3Deq, 1.4Deq, and 1.5Deq, not shown). The cc, bias, and absolute bias between the two estimated and observed variables are also in given.
Citation: Journal of Atmospheric and Oceanic Technology 39, 1; 10.1175/JTECH-D-20-0216.1
8. Conclusions
One of main achievements of precipitation related field studies is to collect sufficient samples of data. There are perhaps two common obstacles that may prevent the collection of sufficient data: 1) an unexpected drought and 2) instrument malfunction. During the 2017/18 winter, the PIP functioned nearly uninterrupted collecting 2345.8 mm of geometric DP in 499 h under frigid weather conditions where the wet-bulb temperature dipped below −20°C. PIP is a low-cost and robust disdrometer. Considering its continuous and unattended operation, it is expected that PIP would be very useful for operational use as part of the automated surface stations.
This study focused on the methodology for deriving SWE from PIP particle size and fall velocity measurements. The motivation was to construct the validation product for the GPM active and passive sensor-based precipitation estimate in snow. The GPM algorithms also seek an appropriate Ze(SWER) relationships for the DPR measurements. This is a challenging task due to the complexity of the physics of a snowflake considering its size, density, habit, composition, and related scattering properties. Despite measurement uncertainties and the assumptions in calculations of snowflake mass, it is remarkable to achieve a very good agreement between the PIP-retrieved and stake field-measured SWE. The absolute bias between the estimate and reference SWE was less than 15% for at least one of the Re–X relationship and Dmx–Deq pair for all of the 30 events used in this study.
The diversity between the two events and within the different segments of the second event are the evidence of the complex nature of falling snow. The nearly nonstop falling snow over 3 days with northwesterly wind, the absence of large flakes (Deq ≥ 5 mm) in PIP observations, and the shallow (<1.5-km height) reflectivity in MRR observations were the characteristics of the first event. These features coincided with the 19–20 November 2016 lake-effect snowstorm that was reported in Kulie et al. (2021). The high accumulations with abrupt wind direction change from northeast to northwest, the presence of large flakes in PIP observations, and the combination of deep and shallow MRR reflectivity regimes were the characteristics of the second event. These features coincided with the 10–12 November 2014 lake-enhanced snowstorm that was reported in Kulie et al. (2021).
This study boosts our confidence to derive the Ze(SWER) relationship using PIP measurements. Perhaps one caveat in PIP measurements is the determination of the habit and composition (i.e., degree of riming) of the individual snowflakes. Collocated PIP and MASC measurement would be beneficial to derive more robust Ze(SWER) relation for different habits and composition.
Acknowledgments.
Comments from S. Joseph Munchak and Robert Meneghini of NASA Goddard Space Flight Center, Charles (Chip) Helms of Universities Space Research Association, and Liang Liao of Morgan State University are highly appreciated. Discussions with Norm Wood of University of Wisconsin–Madison on PIP data processing were very helpful. Leo Pio D’Adderio of National Research Council of Italy provided Fig. 1 of this study. Thanks to the National Weather Service in Marquette, Michigan, for hosting and maintaining the suite of instruments used in this work and sharing meteorological data. Thanks to the National Aeronautics and Space Administration Goddard Space Flight Center Wallops Flight Facility and the Global Precipitation Measurement (GPM) program for providing the PIP, Pluvio, and PARSIVEL instruments used in this work. Acknowledgments extend to three anonymous reviewers for their constructive comments. This study is partially supported by the NASA award (80NCCS19M0139) under Patrick N. Gatlin of NASA Marshall Space Flight Center, principal investigator. The instrument deployment and data processing for the observations from the Marquette snowfall suite are supported by NASA Grant 80NSSC18K0701 and NOAA Grant NA15NES4320001. Claire Pettersen’s efforts on this work are supported by NASA Grant 80NSSC19K0712, and Mark Kulie’s efforts are supported by NASA PMM Grant 80NSSC20K0982. Annakaisa von Lerber is funded by the Academy of Finland postdoctoral scholarship (333901). The scientific results and conclusions, as well as any views or opinions expressed herein, are those of the authors and do not necessarily reflect those of NOAA or the Department of Commerce.
APPENDIX
Variable Definitions
a. Descriptors of particle size
Deq: Equivalent diameter; it is a Waddel disk diameter that was described as the diameter of the disk with the same area as the particle in National Instruments IMAQ manual, which describes Deq equal to 2(area/π)0.5, where area is the total area of shadowed pixels bounded by a box
Dmin: Minimum particle size based on Deq measurements
Dmax: Maximum particle size based on Deq measurements
Dmx: Maximum dimension of the particle; it is prescribed as a function of Deq as in Eq. (5) in this study
Dmass: Mass weighted mean diameter
Dmass*: Melted value of Dmass as in Liao et al. (2016) and Chase et al. (2020)
b. Size distribution and integral parameters
NT: Total particle concentration that is given as number of particle per cubic volume of air
μ: Shape parameter of gamma size distribution
SR: Snow rate; this is intensity of falling snow without melting
DP: Snow depth; this is accumulative snowfall without melting or compression on the ground
SWER: Melted equivalent snow rate
SWE: Melted equivalent of falling snow
RR: Rain rateR: Precipitation rate
Ze: Radar reflectivity calculated by a disdrometer
c. Velocity, mass, and related parameters
υ: Fall velocity of a snowflake
Aυ: Coefficient of the υ–Dmx power-law relationship
Bυ: Exponent of the υ–Dmx power-law relationship
M: Mass of a snowflake
Am: Coefficient of the m–Dmx power-law relationship
Bm: Exponent of the m– Dmx power-law relationship
Re: Reynolds number
η: Dynamic viscosity
ρa: Density of air at the ground level
X: Best number
δ0: Boundary layer thickness
C0: Drag coefficient
G: Gravitational constant
Ae: Effective particle area
A: The area of the smallest circle or ellipse which contains Ae
d. Environmental variables
WSPmed: Median wind speed
WSPmax: Maximum wind speed
WBmed: Median wet-bulb temperature
WBmax: Maximum wet-bulb temperature
U: 30-min surface average wind speed
Ta: 30-min-average surface air temperature
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