1. Introduction
The National Aeronautics and Space Administration’s (NASA) Global Precipitation Measurement (GPM) mission is designed to study the physics and space–time variability of global precipitation, which are key in tracing Earth’s water cycle across its weather, climate, and hydrological systems (Skofronick-Jackson et al. 2018). To accomplish this goal, the GPM program has identified the Level-I requirements which include the detection of falling snow and estimates of rainfall rate within prescribed uncertainty levels from the GPM Core Observatory’s active and passive sensors (Skofronick-Jackson et al. 2017). This raises a critical question: What is the reference for the validation of GPM precipitation products?
The GPM Ground Validation (GV) program selected the National Oceanic and Atmospheric Administration’s (NOAA) Multi-Radar Multi-Sensor (MRMS) precipitation estimates as one of the validation products (Zhang et al. 2016; Kirstetter et al. 2020). The MRMS integrates the operational weather radar observations across the conterminous United States (CONUS) and southern Canada with the environmental and climatological data and rain gauge observations and constructs the quantitative precipitation estimate at 1-km resolution with a 2-min update. The environmental data are used to identify the snowy pixels and an empirical relationship is used to estimate the snow water equivalent rate (SWER) from radar reflectivity (Ze) measurements.
The GPM GV program also operates a validation network (VN), which constructs a 3D mosaic of precipitation from several ground-based polarimetric radar networks, both operational and research, with coverage that expands beyond the United States (Petersen et al. 2020; Gatlin et al. 2020). The VN employs several precipitation retrieval algorithms, including empirical ones that relate the dual-polarization radar observables—horizontal reflectivity (ZH), differential reflectivity (ZDR), and differential phase (KDP)—to rainfall rate (R) given (e.g., Cifelli et al. 2011), but the VN does not currently include any SWER estimates. Accurately estimating snowfall from weather radar measurements can be more complicated than its liquid counterpart. SWER estimates can help in more than just validation of GPM snowfall estimates. For example, a comparison between the GPM Core Observatory and CloudSat radar snowfall products revealed the importance of the assumptions in deriving the SWER(Ze) relationship as well as in rain–snow delimitation algorithms (Skofronick-Jackson et al. 2019).
In addition to the inter- and intrastorm variability of the microphysical characteristics of falling snow (e.g., habit, density), the instrumentation and the derivation of the SWER(Ze) relationships play an important role in SWER estimates. Both Ze and SWER are functions of size, concentration, and the fall velocity of falling snowflakes. The PIP, which was developed by Dr. F. Larry Bliven of NASA Wallops Flight Facility over a decade of diligent work to measure individual precipitation-sized particles (Pettersen et al. 2020a), can measure these three attributes. Its cost effectiveness, ease of assembly, and low-maintenance operation in cold climate regimes (e.g., Souverijns et al. 2017; Shates et al. 2021; Schoger et al. 2021) makes the PIP a reliable device for measuring snowflakes.
This study evaluates the performance of operational- and research-based SWER(Ze) relationships utilizing PIP observations from the International Collaborative Experiment for Pyeongchang 2018 Olympic and Paralympic Winter Games (ICE-POP2018). The objective of this study is to evaluate several radar-based SWER(Ze) approaches for mapping precipitation during falling snow so that the VN can use them appropriately to validate spaceborne precipitation retrieval algorithms under the GPM program. Furthermore, more accurate quantitative precipitation estimates (QPE) is of great interest to the broader Earth science community, and the results have important implications for hydrometeorological applications and cloud-microphysical model validation studies.
This study is organized as follows: the measurement site, the instrumentation, and the events are summarized under observations in section 2. Section 3 presents the methodology under which the mathematical form of integral snowfall parameters, the derivation of SWER(Ze) relationship, and the evaluation statistics are defined. The operational and research-based SWER(Ze) relationships are given in sections 4 and 5, respectively. The latter section also defines the density and habit based classification algorithms. Section 6 is dedicated to the two case studies where the time series of PIP-calculated and SWER(Ze) estimated snow water equivalent (SWE) and SWER are presented. The scatter diagrams of the calculated and estimated SWER are also given. The performance of SWER(Ze) relationships for all events is evaluated through two popular statistics in section 7, followed by the conclusions in section 8.
2. Observations
a. Measurement site
The ICE-POP 2018 field campaign was an international effort with contributions from 29 agencies from 12 counties led by the Korean Meteorological Administration. One of the main goals of the field campaign was to understand the microphysical characteristics of falling snow in complex terrain (Kim et al. 2021). The field study was conducted over the mideastern region of the Korean Peninsula during the 2017/18 winter and included a wealth of ground sites both along the Pacific coast and inland in the mountainous regions. This study uses the in situ and remote sensing observations from a number of instruments at the MayHills supersite (MHS; 789 m above mean sea level, 37.6652°N, 128.6996°E). MHS was one of the inland sites and received abundant snowfall over a wide range of temperatures (0°C ≥ Twet-bulb ≥ −13°C; Twet-bulb: wet bulb temperature).
b. Instrumentation
The PIP was one of the primary instruments in this study (Fig. 1a) and is used to calculate the particle mass, particle size distribution (PSD), and bulk descriptors of snowfall (e.g., SWER, Ze; Pettersen et al. 2020a; Tokay et al. 2022). The Vaisala WXT520 weather station (Fig. 1b) outputs the temperature, relative humidity, atmospheric pressure, and wind direction and speed. The temperature and atmospheric pressure are employed to determine the density of air and dynamic viscosity, both of which are used in calculating the particle mass. The temperature, relative humidity, and atmospheric pressure are used to calculate the wet-bulb temperature which determines the snowing minutes (Twet-bulb ≤ 0°C). The wind rose is constructed based on the wind direction and speed for each event. A third key instrument in this study is the OTT PARSIVEL2, a laser-optical disdrometer (Tokay et al. 2014). PARSIVEL2 is a present weather sensor and is used here to verify the snowing minutes determined by the WXT520. It should be noted that PARSIVEL2 sometimes reports drizzle in the presence of light snow but this limitation should have minimal impact on this study. The METEK Micro Rain Radar (MRR) is a vertically profiling 24-GHz frequency Doppler radar (Klugmann et al. 1996) and is used to determine the echo-top-based classification. The MRR at the MHS site is configurated to profile the atmosphere to 4500 m above the ground with a vertical resolution of 150 m and temporal resolution of 30 s.
Picture of (a) Precipitation Imaging Package (PIP), (b) Vaisala WXT520 weather station, (c) OTT PARSIVEL2 disdrometer, and (d) Micro Rain Radar (MRR) from MHS supersite (courtesy of Kwonil Kim of Kyungpook National University).
Citation: Journal of Hydrometeorology 24, 4; 10.1175/JHM-D-22-0101.1
The instrumentation used in this study was previously employed for numerous field campaigns. Among those, the PIP is a relatively newer instrument and became a desired instrument to measure the microphysical properties of falling snow since its original version, Snow Video Images (SVI; Newman et al. 2009) was deployed during the Canadian CloudSat CALIPSO Validation Project in 2006 (Wood et al. 2013). The components and working principles of PIP have been documented in Pettersen et al. (2020a,b). In brief, PIP records the two-dimensional grayscale video images of falling particles between a light source and a high-speed camera that are 2 m apart. The focal plane is about 1.3 m from the lenses. The depth of field (DOF) is size dependent and is formulated as 0.117/2 × Deq, where Deq is the equivalent diameter. The field of view (FOV) is 48 mm × 64 mm and is formulated as (64 − Deq) × (48 − Deq) including particle’s edge effects. The sampling volume is a multiplication of the FOV, DOF, and the number of frames (380 frames per second) over a given time period. The image pixel size is 0.1 mm × 0.1 mm and any particles with the equivalent diameter (Deq) less than 0.2 mm are rejected to prevent camera resolution and image compression issues from contaminating the size distributions. The PIP’s measurement volume is not enclosed and therefore it is immune to both contamination by secondary particles associated with splashing as well as undersampling in windy conditions (Newman et al. 2009). The PIP’s velocity measurements include particle’s upward motion with negative fall velocity. Only particles with a downward vertical velocity greater than 0 m s−1 are included in the analysis.
c. Snow events
The PIP recorded 10 major snow events during the first three months of ICE-POP 2018. The events were separated from each other with minimum 1-h precipitation free periods based on PIP precipitation rate time series. The major events had at least 20-mm geometric snow depth and lasted 200 min or longer. Table 1 lists the event date, start and end hours in UTC, number of snowing minutes, maximum snowfall intensity (S_max), geometric depth of snow (S_total), and wet-bulb temperature statistics.
Snow event layout including the type (C, cold low; W, warm low; A, air–sea interaction), event date, start and end hour in UTC, number of snowing minutes, maximum snowfall intensity (S_max), geometric depth of snow (S_total), and median, maximum, and minimum wet-bulb temperature (°C).
The snowfall over the Pyeongchang area results from three different synoptic patterns. Jeoung et al. (2020) described these synoptic patterns as cold low (C), warm low (W), and air–sea interaction (A). Kim et al. (2021) listed the 9 out of 10 major events that are used in this study as three cold low, five warm low, and one air–sea interaction. Kim et al. (2021) also presented the MRR based reflectivity distributions for five sites, including the MHS site. The reflectivity distributions were composited for cold low, warm low, and air–sea interaction events and the echo-top heights were 3.0–3.5, ≥4.5, and 3.5–4.0 km for these three different synoptic patterns, respectively. The expected echo-top heights for the cold and warm low synoptic patterns were also present in the time series of MRR reflectivity at the MHS site during the cold low (e.g., Fig. 2a) and warm low (e.g., Fig. 2b) events. The echo-top heights ranged from 1.0 to 3.0 km in cold low events including event 01, which was not included in the Kim et al. (2021) study. The echo started to appear from the highest MRR gate for warm low events, indicating that the echo tops ≥ 4.5 km. The MRR observations were not collected during the air–sea interaction event.
MRR Ze time series for events (a) 03 and (b) 08.
Citation: Journal of Hydrometeorology 24, 4; 10.1175/JHM-D-22-0101.1
The distinction in echo-top height between the cold low and warm low events was also evident in NASA’s dual wavelength (Ku and Ka band) dual polarization Doppler radar (D3R) observations. D3R was located at another ground supersite, Daegwallyeong (DGW), 2.16 km away from MHS site during ICE-POP (Munchak et al. 2022). Figure 1 of Munchak et al. showed the time–height plots of vertical profiles of Ku-band horizontal reflectivity, differential reflectivity, differential phase, copolar correlation coefficient, and Ku- and Ka-band dual-wavelength ratio for events 01, 06, and 08 in Table 1. The cold low event (01) was shallow, while two warm low events (06, 08) were deep according to the D3R observations.
The wind was from the west-southwest (WSW) in the cold low events including event 01, while the warm low events were dominated by east-northeast (ENE) winds except event 02 where the wind speeds predominantly were weak (<2 m s−1), as depicted in Fig. 3. The air–sea interaction event was also dominated by ENE winds. The wind direction was in a good agreement with Kim et al. (2021) study where selected soundings from warm low, and air–sea interaction events showed a transition of wind direction from northeast to southwest at around 700-mb height (1 mb = 1 hPa) and northwest at around 800-mb height, respectively. The selected sounding from the cold low event had southwesterly flow near the surface, veering to westerly flow at around 600 mb in their study. The wind speeds were relatively stronger in cold low events than in warm low events but the event median wind speed also had large variability within warm low event category, from 0.5 to 4.4 m s−1. Lim et al. (2020) attributed this difference to the position of the low pressure center. The synoptic low was closer to the Korean Peninsula for event 07 than for event 09 resulting in stronger pressure gradients and stronger winds for the former event.
Windrose for the 10 major events During ICE-POP 2018.
Citation: Journal of Hydrometeorology 24, 4; 10.1175/JHM-D-22-0101.1
The combination of the wet-bulb temperature and the low-level temperature profile is not only the key to separating snow and rain (Sims and Liu 2015) but is also an indicator for the wetness of the snow. The cold low events had mostly lower median Twet-bulb than the warm low events but there were significant differences in median Twet-bulb and the range between maximum and minimum Twet-bulb among the warm low events (Table 1). A cold low event (event 05) and a warm low event (event 10) had similar Twet-bulb trends while two warm low events (events 02, and 06) had the warmest Twet-bulb among all events (not shown).
3. Methodology
This section introduces the formulation of the integral snowfall parameters, the data processing to derive the SWER(Ze) relationship, and the statistics to evaluate the SWE and SWER estimates.
a. Integral snowfall parameters
b. SWER(Ze) relationship
Figure 4 depicts the two-dimensional (2D) histograms of SWER versus Ze and the corresponding SIFT-based orthogonal regressions for event 03 and event 08. The performance of the regression depends on the scatter of SWER at a given Ze in a 2D histogram. The paired SWER and Ze observations are relatively more distant from the best fit line in event 03 than in event 08 (Figs. 4b,d). This hints that the error in SWER estimation would be higher in the former event than the latter event. The best line seems to overestimate the paired Ze and SWER observations at the high end in both events. Unless it has been compensated by the lower range of the spectrum, the event SWE totals would be overestimated in these events.
(a),(c) The two dimensional histograms of SWER vs Ze and (b),(d) the corresponding SIFT-based orthogonal regressions for event 03 and event 08.
Citation: Journal of Hydrometeorology 24, 4; 10.1175/JHM-D-22-0101.1
The methodology of the retrieval of SWER from Ze described in this study is considered as a traditional method. Alternative statistical retrieval methods such as neural network (Chase et al. 2021) and random forest (Yu et al. 2022; King et al. 2022) have performed well in retrieving particle size distribution parameters (e.g., mass weighted mean diameter Dmass) as well as integral parameters (e.g., SWER).
c. Evaluation statistics
4. Operational SWER(Ze) relationships
The U.S. National Weather Service (NWS) employs five different SWER(Ze) relationships depending on the region in CONUS (Bukovčić et al. 2018). The A coefficient ranges from 40 to 222 and b exponent is 2.0 in these relationships (Table 2). Assuming that the measured reflectivity is 20 dBZ, the estimated SWER ranges from 1.58 to 0.67 mm h−1 for an A coefficient ranging from 40 to 222, respectively. If the intensity of the snowfall does not change in 1 h, the estimated SWE is 42% higher for the former A coefficient than the later A coefficient. The Canadian radar network uses the relationship derived by Sekhon and Srivastava (1970). Boudala et al. (2006) reported that this expression underestimates the precipitation rate even at warm temperatures. Indeed, the Canadian SWER(Ze) relationship results in only 0.27 mm h−1 SWER at 20 dBZ. The MRMS (Zhang et al. 2016) and Finnish Meteorological Institute (FMI) (Saltikoff et al. 2015) SWER(Ze) relationships use the same b exponent as the U.S. NWS but the A coefficients are aligned with the dry snow. At 20 dBZ, the SWER estimates are 1.15 and 1.00 mm h−1 for the MRMS and FMI SWER(Ze) relationships, respectively.
Operational SWER(Ze) relationships in the form of Ze = ASb (Ze in mm6 m−3 and S in mm h−1).
5. Research SWER(Ze) relationships
Four different approaches are taken to derive the SWER(Ze) relationships following the methodology presented in section 3b. First, the event-specific SWER(Ze) relationships are derived. Table 3 lists the A coefficients and b exponents of the event-based SWER(Ze) relationships. A wide range in both A coefficients and b exponents is evident between the events. This reflects the intervariability of the physical properties of the falling snow. Table 3 shows that the event 04 has an exceptionally high A coefficient and b exponent. At 20 dBZ, the derived SWER range from 0.30 mm h−1 for event 04 to 1.43 mm h−1 for event 08. This indicates that SWER in event 08 is 4.7 times the SWER in event 04 for the same reflectivity.
Event-specific SWER(Ze) relationships in the form of Ze = ASb (Ze in mm6 m−3 and S in mm h−1).
Second, the warm and cold low events describ2d in section 2c are grouped into a single SWER(Ze) relationships. Events 01 and 09 are included in cold and warm low, respectively, following the similarities in environmental variables (e.g., wet-bulb temperature, wind direction, and wind speed). Table 4 lists the A coefficient and b exponent of the synoptic setting–based SWER(Ze) relationships. Both the A coefficient and b exponent are higher in a cold low setting than in a warm low setting. This results in higher SWER in a warm low setting than in a cold low setting. For example, at 20 dBZ, SWER is 0.64 and 1.19 mm h−1 in cold and warm low settings, respectively.
Synoptic setting based SWER(Ze) relationships in the form of Ze = ASb (Ze in mm6 m−3 and S in mm h−1).
Third, a three-tier density classification is constructed based on PIP bulk density following Eq. (6). The low-density (ρsnow < 0.1 g cm−3) class comprises 29% of the PIP observations, while 34% of the observations are classified as the high density (ρsnow ≥ 0.2 g cm−3) class. The mid-density (0.1 ≤ ρsnow < 0.2 g cm−3) class has the highest occurrence with 37%. The occurrence of each density class is distinctly different between the cold and warm low events. All four cold events are dominated by the low-density class (Fig. 5). None of the density classes dominate the warm low events except in event 02 where the mid-density class is dominant. The mid-density class also has the highest occurrence in events 07 and 08 but the high-density class has a relatively high occurrence (32%–37%) in these events as well. The mid- and high-density classes have nearly the same occurrence in event 10 and the latter class is noticeably higher in air–sea interaction event. The low- and mid-density classes are nearly the same in event 06.
Percent occurrence of low-density (blue), mid-density (yellow), and high-density (red) classes for 10 events. Each density class starts from zero. This means that the high density had the highest occurrence in events 09 and 10. The mid-density had the highest occurrence in events 02, 07, and 08, while the remaining events (01, 03, 04, 05, and 06) received the highest contribution from low density.
Citation: Journal of Hydrometeorology 24, 4; 10.1175/JHM-D-22-0101.1
Table 5 shows the derived SWER(Ze) relationships for the three bulk density classes. The low-density class has the highest A coefficient and b exponent while vice versa is true for the high-density class. This results in higher SWER in high density than in low density. For example, at 20 dBZ, the SWER is 0.70, 1.38, and 2.26 mm h−1 in the low-, mid-, and high-density classes, respectively.
Bulk density based SWER(Ze) relationships in the form of Ze = ASb (Ze in mm6 m−3 and S in mm h−1).
The PIP based particle type classification algorithm resulted in only 6% wet snow/sleet. Among the four different snowflake habits, dendrite and plate had the highest two occurrences with 46% and 23%, respectively while the graupel and needle had the lowest two occurrences with 12% and 13%, respectively. The plates dominated the cold low events, while the dendrites had the highest occurrence in warm low events and air–sea interaction event (Fig. 6). The graupel had considerable contribution (25%) in the air–sea interaction event, while the needles occurred substantially (36%–37%) in events 02 and 10.
Percent occurrence of dendrite (light blue), plate (orange), needle (green), graupel (dark blue), and wet snow/sleet (red) classes for 10 events. Each habit class starts from zero. This means that the plates had the highest occurrence in events 01, 03, 04, and 05, while dendrites had the highest occurrent for the rest of the events (02, 06, 07, 08, 09, and 10).
Citation: Journal of Hydrometeorology 24, 4; 10.1175/JHM-D-22-0101.1
Table 6 shows the derived SWER(Ze) relationships for the five-tier particle type classes. The graupel class has the lowest A coefficient and b exponent while the opposite is true for the plate class. This results in higher SWER in graupel than in plates. For example, at 20 dBZ, the SWER is 0.59 mm h−1 for the plate class and 2.52 mm h−1 for the graupel class. The SWER is also relatively high for wet snow/sleet (2.03 mm h−1) and is relatively low for dendrite (1.07 mm h−1) and needle (1.74 mm h−1) classes.
Particle type based SWER(Ze) relationships in the form of Ze = ASb (Ze in mm6 m−3 and S in mm h−1).
6. Case studies
This section presents the time series and scatter diagrams of PIP-calculated and SWER(Ze) relationship-based SWER and SWE for events 03 and 08. These two events were the longest cold and warm low events, respectively (Table 1). The operational and research-based SWER(Ze) relationships, listed in Table 2 and Tables 3–6, respectively, are evaluated for estimating the event SWE total and SWER utilizing bias and MAE presented in section 3c.
Among the eight operational SWER(Ze) relationships, the NWS North Plains and Upper Midwest and MRMS SWER(Ze) relationships had the best performance for events 03 and 08, respectively. The best performance was determined by the minimum MAE. The SWE underestimated by 9.1% and 12.1% in events 03 and 08, respectively (Fig. 7). This is mainly due to that fact that the estimated SWER could not match the peaks of PIP-calculated SWER in early segments of both events (Figs. 7a,b). The scatter diagrams of estimated and PIP-calculated SWER shows the SWER regimes where the under- and overestimation occurs (Figs. 7c,d). The SWER was overestimated when SWER < 0.1 mm h−1, while it was underestimated for SWER > 1 mm h−1 in both events. The underestimation at heavier precipitation was the main reason for the negative bias in SWE.
Time series of SWER and SWE for (a) NWS North Plains and Upper Midwest SWER(Ze) relationship for event 03 and for (b) MRMS SWER(Ze) relationship for event 08. The scatter diagrams of the estimated and PIP calculated SWER are given for (c) event 03 and (d) event 08.
Citation: Journal of Hydrometeorology 24, 4; 10.1175/JHM-D-22-0101.1
Event-specific SWER(Ze) relationship had much lower A coefficient and slightly lower b exponent than the synoptic cold low SWER(Ze) relationship in event 03. This means that SWER is higher in event-specific SWER(Ze) relationship for a given reflectivity. Overall, the event-specific SWER(Ze) relationship overestimated the SWE total by only 2.7%. This might be interpreted as a very good performance for the event-specific SWER(Ze) relationship but this is not the case. The time series show multiple periods of over- and underestimation of PIP-calculated SWER by both event-based and synoptic SWER(Ze) relationships (Fig. 8a). A wide scatter on both side of the 1:1 line was evident in corresponding scatter diagrams (Figs. 8e,f). The event-specific and synoptic SWER(Ze) relationship resulted in MAEs higher than that of the best operational SWER(Ze) relationship.
Time series of SWER and SWE for (a) event-specific (purple) and synoptic cold low (blue), (b) density-based, (c) habit-based SWER(Ze) relationships for event 03. (d) Time series of temperature and wet-bulb temperature for the same event. The scatter diagrams of estimated and PIP calculated SWER are given for (e) event-based, (f) cold low, (g) density-based, and (h) habit-based SWER(Ze) relationships.
Citation: Journal of Hydrometeorology 24, 4; 10.1175/JHM-D-22-0101.1
The low-density observations occurred 61% of the time especially during the first half of event 03 where the precipitation was heavier (Fig. 8b). The mid- (30%) and high-density (9%) observations were primarily present toward the end of the event when the precipitation was lighter. The density-based SWER(Ze) relationship underestimated the SWE total 1.6% and the MAE of SWER was the second lowest among the four research based SWER(Ze) relationships. This highlighted the advantage of physically based multiple SWER(Ze) relationships over a single SWER(Ze) relationship for a given event. Misclassification is the main caveat of the physically based SWER(Ze) relationships, however. In this event, the high-density observations at the very early stage of the event may result from misclassification. A close look to the scatter diagram showed that the high-density observations underestimated SWER, while the low-density observations mostly overestimated SWER (Fig. 8g).
Following Lee et al. (2015), plates dominated the event 03 with 73% occurrence (Fig. 8h). The dendrites were observed to have 23% occurrence, mostly at the early stage of the event. Wet snow was scattered within plate observations and was attributed to a misclassification. The habit-based SWER(Ze) relationship underestimated the SWE total by 4.9% resulting in the lowest MAE among the four research SWER(Ze) relationships; the best performance for this event.
The wet-bulb temperature was steady at −3°C until 1200 UTC and gradually dropped to −18°C with time (Fig. 8d) in event 03. The heavier precipitation with dendrites and low density was observed during the period of steady wet-bulb temperatures early in the event. The lighter precipitation with plates and mid- and high-density occurred during the drop in wet-bulb temperature later in the event. It should be noted that the temperature where the hydrometeors form aloft plays a more significant role than the surface wet-bulb temperature at the surface. Sims and Liu (2015) relied first on surface wet-bulb temperature but later added the temperature profile in the lower atmosphere to partition snow from rain.
There were similarities between the events 03 and 08 for the performance of research based SWER(Ze) relationships even though the event’s characteristics were drastically different. The event 08 was 2.3 times longer than the event 03 (Table 1). For the geometric depth of snow, the event 08 was 1.58 times deeper than the event 03, but the former event accumulated 3.54 times greater SWE than the latter event. This is a direct consequence of the difference in bulk density of snowflakes and was one of the key differences between cold and warm low events.
Event-specific SWER(Ze) relationships had lower A coefficients and b exponents than the synoptic warm low SWER(Ze) relationship. As a result, several peaks in the PIP-calculated SWER time series were underestimated to a lesser extent by the event-specific SWER(Ze) relationship than the synoptic warm low one (Fig. 9a). The SWE totals were therefore underestimated only 1.3% and 16.2% by the event-specific and synoptic SWER(Ze) relationships, respectively. A wide but similar scatter on both sides of the 1:1 line reflected the under- and overestimation of SWER at different segments of the time series (Figs. 9e,f). The MAEs of the event-specific and synoptic SWER(Ze) relationships differed by less than 2% and about the same best operational SWER(Ze) relationship but noticeably higher than the physical based SWER(Ze) relationships.
Time series of SWER and SWE for (a) event-specific (purple) and synoptic warm low (blue), (b) density-based, (c) habit-based SWER(Ze) relationships for event 08. (d) Time series of temperature and wet-bulb temperature for the same event. The scatter diagrams of estimated and PIP calculated SWER are given for (e) event-based, (f) cold low, (g) density-based, and (h) habit-based SWER(Ze) relationships.
Citation: Journal of Hydrometeorology 24, 4; 10.1175/JHM-D-22-0101.1
The mid-density observations dominated the first half of event 08 with 50% overall occurrence (Fig. 9b). The high-density observations mostly occurred during the second half the event with 30% overall occurrence. The low-density observations at the beginning of the event could result from misclassification. Indeed, these low-density observations overestimated SWER when SWER < 0.3 mm h−1 and underestimated SWER when SWER ≥ 0.3 mm h−1 (Fig. 9g). The mid- and high-density observations followed the 1:1 line with a narrow scatter on both side of the line. The density-based SWER(Ze) relationship had higher SWE bias than the event-specific and synoptic SWER(Ze) relationships and this is mainly due to the overestimation of low-density observations at high SWER. The MAE of the density-based SWER(Ze) relationship, on the other hand, was the lowest among the four research based SWER(Ze) relationships, highlighting the success of the physical-based SWER(Ze) relationships.
Following the Lee et al. (2015) classification, dendrites dominated the event 08 with 69% occurrence (Fig. 8c). The graupel was observed during the second half of the event with 19% overall occurrence. The needles (9%) were present over brief periods, mostly during the early segment of the event. The plates at the beginning of the event were a result of misclassifications. Indeed, these plate observations overestimated SWER (Fig. 9h). The graupel observations were on both sides of the 1:1 line when SWER < 0.5 mm h−1 but SWER was underestimated above this threshold. The dendrites and needles were scattered on both sides of the 1:1 line with a slight underestimation of SWER. The SWE bias was 16%, higher than the best operational, event-specific, and density-based SWER(Ze) relationships but the habit-based SWER(Ze) has the second lowest MAE of SWER after the density-based SWER(Ze) relationship.
The wet-bulb temperature oscillated from −1°C during daytime hours to −5°C during nighttime hours (Fig. 9d). A majority of the precipitation occurred during the colder nighttime hours. The peak wet-bulb temperature between 0200 and 0300 UTC (1100 and 1200 LST) coincided the transition from mid- to high density. The graupel is observed after the mid-event peak in wet-bulb temperature.
7. Overall statistics
This section presents the SWE bias and SWER MAE for (i) eight operational SWER(Ze) relationships and for (ii) four research and best operational SWER(Ze) relationships for 10 events. The performance of the operational SWER(Ze) relationships is drastically different between the cold and warm low events. For the warm low events including the air–sea interaction event, the operational SWER(Ze) relationships with the lowest two A coefficients had the least SWE bias for three events each (Fig. 10a). This is also true for the MAE except that the third lowest A coefficient was the best performance in one of the warm low events (Fig. 10b). For the cold low events including event 01, the operational SWER(Ze) relationships with higher A coefficients had the least bias and minimum MAE. Among cold low events, events 04 and 05 had the highest bias and MAE among the best operational SWER(Ze) relationships. Recall from Table 3, the event-based SWER(Ze) had exceptionally high A coefficient and b exponent for event 04. The operational SWER(Ze) relationship with the highest A coefficient had the best performance, consequently.
(a) SWE Bias and (b) SWER MAE for eight operational SWER(Ze) relationships for 10 events.
Citation: Journal of Hydrometeorology 24, 4; 10.1175/JHM-D-22-0101.1
The performance of four research-based and best operational SWER(Ze) relationships varied from one event to another (Fig. 11). The event-specific SWER(Ze) relationships had the lowest bias for four events, while synoptic warm/cold low SWER(Ze) relationships had the lowest bias for three events. Interestingly, the best operational SWER(Ze) relationships had lower bias than the research-based SWER(Ze) relationships for two events. The density-based based SWER(Ze) relationships had the lowest bias for the remaining one event. More importantly, the best performing SWER(Ze) relationships had bias < ±6% for all events except event 04. The second best performing SWER(Ze) relationships, on the other hand, had bias ≤ ±18% for nine events. For MAE, the density-based SWER(Ze) had the best performance for all warm low events except event 02. The habit-based SWER(Ze) relationships had the lowest MAE for three events, while the best operational and event-specific SWER(Ze) relationships had the lowest MAE in one event each. The MAE was less than 30% for the best performed SWER(Ze) relationship in half of the events, while it exceeded 40% in events 04 and 05.
(a) SWE Bias and (b) SWER MAE for four research and best operational SWER(Ze) relationships for 10 events.
Citation: Journal of Hydrometeorology 24, 4; 10.1175/JHM-D-22-0101.1
These statistics reveal two main conclusions: which classification method based SWER(Ze) relationships has the best performance for SWE and SWER estimates and how well SWE and SWER can be estimated from SWER(Ze) relationships. For operational purposes, the radar based SWER estimate should be based on a handful of SWER(Ze) relationships. As noted earlier, there is a significant intervariability for the physical properties between the events and the regional SWER(Ze) relationships listed in Table 2 and those used by the NWS are not adequate. This is also shown by the drastic differences in the performance of operational SWER(Ze) relationships in a given event.
The MRMS SWER(Ze) relationship is used in GPM ground validation program and is therefore of particular interest. It underestimated SWE by less than 30% in warm low events except a slight overestimation of 1.2% in event 10, and overestimated SWE 41%–167% in cold low events. It also resulted in MAE of 32%–46% in warm low events, and of 53%–177% in cold low events. These findings conclude that the MRMS SWER(Ze) relationship should not be used for cold low events. For warm low events, its performance is compared to the performance of the synoptic SWER(Ze) relationship presented in Table 4. Except event 08, the synoptic SWER(Ze) relationship performed better than the MRMS SWER(Ze) relationship for SWE total. The synoptic SWER(Ze) relationship resulted in higher MAE with respect to the MRMS SWER(Ze) relationship for two events only.
It seems that cold versus low events can easily be identified by a forecaster in the Korean Peninsula. If the precipitation is snow, it is practical to adopt the one of the two synoptic SWER(Ze) relationships presented in Table 4. The synoptic warm low SWER(Ze) relationship results in bias within ±17% but MAE ranges from 26% to 55%. The synoptic cold low SWER(Ze) relationship, on the other hand, resulted in 21%–22% bias and 31%–47% MAE except for event 04.
The density-based SWER(Ze) relationships performed well for the majority of the events. Except for three events (01, 04, and 05), the SWE bias was within ±16%. The MAE was under 40% except for events 04 and 05. The habit-based SWER(Ze) relationships also performed well. The bias was within ±21% except for the same three events listed for density-based SWER(Ze) relationships. The MAE was under 50% except for event 04. The main issue for these two physically based SWER(Ze) relationships is the misclassification due to subjectively defined bulk density boundaries and the effectiveness of the Lee et al. (2015) habit classification algorithm.
8. Conclusions
This study evaluated the performance of operational and research-based SWER(Ze) relationships utilizing the PIP-based observations from the ICE-POP 2018 field campaign. The PIP can accurately measure size, concentration, and fall velocity of the snowflakes from which Ze and SWER are calculated using hydrometeor aerodynamics outlined by Böhm (1989). This ICE-POP PIP dataset consists of 10 events, including 4 synoptically classified as cold low and 6 warm low events.
Prior to evaluation of SWER(Ze) relationships, two physically based classification algorithms were developed. One of these physically based classification SWER retrieval algorithms uses three-class bulk density of PIP observations, which reveal that low-density class dominated cold low events, while mid- and high-density classes are largely observed in warm low events. The other physically based classification algorithm adopted the Lee et al. (2015) habit algorithm, which showed dendrites and plates dominating the warm and cold low events, respectively. The event-specific and synoptic cold/warm low SWER(Ze) relationships are the other two research-based SWER(Ze) relationships evaluated in this study, resulting in four new estimates for SWE and SWER.
This study reveals that inter- and intravariability of falling snow dominates the performance of SWER(Ze) relationships. It is clear that a single SWER(Ze) relationship is not the best solution for radar-based snowfall estimation on the Korean Peninsula. The intervariability among the events is highlighted by the wide range of A coefficients and b exponents of the event-specific SWER(Ze) relationships derived from the large sample of PIP observations. The intravariability of falling snow, which was observed mostly on relatively longer events revealed that a single SWER(Ze) relationship may not be appropriate for all the events.
Among 10 events, event 04, a cold low event, was exceptional. The event specific A coefficient and b exponent of the SWER(Ze) relationship were substantially higher than the other events and the vast majority of the literature (e.g., Table 3 of von Lerber et al. 2017). It is clear that the event-specific SWER(Ze) relationship performs relatively better than all other research and operational SWER(Ze) relationships, but the bias and MAE are still high for the event-specific relationship. This indicates that there will be rare events where neither the operational nor the physical-based SWER(Ze) relationships will estimate SWE and SWER accurately.
The relatively poorer performance of the research-based SWER(Ze) relationships is particularly interesting in events 01 and 05, both cold low events. The best operational SWER(Ze) relationship had lower bias and MAE than the four research based SWER(Ze) relationships in event 01. If the bias of ±15% and MAE of 30% are considered as the thresholds for the reasonable performance of the SWER(Ze) relationships, all of the research-based SWER(Ze) relationships had poor performance for event 01. The event-specific SWER(Ze) also performed well in event 05. The SWE was underestimated by <1% but MAE exceeded 40%, as being one of two least successful SWER(Ze) relationships for SWER. This emphasizes the importance of the purpose for which these relationships are being applied as this can differ between hydrologists and meteorologists. Hydrologists seek the best estimate of event SWE total, while the SWER estimate is more important for meteorologists.
The remaining cold low event (event 03) and all warm low events demonstrated that the physically based SWER(Ze) relationships are superior to a single SWER(Ze) relationship for a given event. The density-based SWER(Ze) relationships yield a ≤15% bias in SWE and ≤30% MAE in SWER except for two events of the events in which they had higher MAE. The habit based SWER(Ze) relationships also performed reasonably well but misclassification is an issue for both physically based algorithms. This suggests that physically based SWER(Ze) relationships are favorable for a majority of the events but the classification algorithms are subject to improvement. During ICE-POP 2018, the Multi-Angle Snowflake Camera (MASC), which provides very high resolution images of snowflakes that can be used to more precisely determine particle habit (Garrett et al. 2012), was collocated with the PIP, but did not operate continuously (Gehring et al. 2021). MASC images could refine the habit-based SWER relationship presented herein.
For operational purposes, there is an outstanding question: How can one apply the density or habit based SWER(Ze) relationships to the radar observations? It is suggested that the PIP based classification algorithms are first compared with collocated radar-based hydrometeor identification (HID) algorithms (e.g., Thompson et al. 2014). It is expected that this will lead to HID based SWER(Ze) relationships. A long record of falling snow with all the in situ instrumentation used in this study as well as a MASC and a nearby scanning radar is perhaps the best suite for such a follow-up study.
Acknowledgments.
First and foremost, acknowledgments go to Kwang Deuk Ahn of the Korean Meteorological Administration and GyuWon Lee of Kyungpook National University for their leadership during ICE-POP 2018. Specifically, the authors wish to thank their South Korean colleagues for operating the NASA’s PIP and PARSIVEL disdrometers and providing the Vaisala WXT520 weather station and MRR-2 database. Dr. Helm’s contribution to this study was supported by an appointment to the NASA Postdoctoral Program at NASA Goddard Space Flight Center, administered by Universities Space Research Association and Oak Ridge Associated Universities under contract with NASA. This study is funded through NASA’s Internal Scientist Funding Model for Precipitation Measurement Mission via Grant NNX16AE88G, Will McCarty, Program Manager, NASA Headquarters, George Huffman, Project Scientist, NASA Goddard Space Flight Center.
Data availability statement.
The data used in this study were extracted though a secure file transfer site where the IP address, username, and password were set by the ICE-POP 2018 field campaign organizers. To access the database, please contact Kwonil Kim (kwonil.kim.0@gmail.com).
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