1. Introduction
Raindrop size distribution (DSD) is a crucial factor in developing methods to accurately estimate the rainfall amount RA (mm) on the ground, known as quantitative precipitation estimation (QPE). DSD contains information about the microphysical processes of precipitation and includes the physical phenomena occurring in clouds due to the interaction between hydrometeors (Uijlenhoet et al. 2003; Jaffrain and Berne 2012). It also incorporates precipitation characteristics such as particle growth (e.g., Dolan et al. 2018), size sorting (e.g., Kumjian and Ryzhkov 2012), evaporation, and coalescence (Rutledge and Houze 1987; Houze 1997).
Most QPE schemes use the relationship between the ground rainfall rate R (mm h−1) and weather radar variables. Marshall et al. (1955) first proposed the radar reflectivity factor Z (mm6 m−3)–R relationship (i.e., Z = ARb) for stratiform precipitation. Various Z–R relationships have been proposed because two parameters (A, b) depend on the DSD, which varies with the type of rainfall (Sekhon and Srivastava 1971; Rosenfeld et al. 1993; Tokay and Short 1996; Le Loh et al. 2019), climatological conditions (Bringi et al. 2003; Göke et al. 2007; Ulbrich and Atlas 2007; Suh et al. 2016), geographical conditions (Suh et al. 2021), seasonal conditions (Suh et al. 2016; Krishna et al. 2016; Seela et al. 2018), and diurnal variations (Kozu et al. 2006; Suh et al. 2016; Villalobos-Puma et al. 2019; Suh et al. 2021).
Raindrop size distribution can also be influenced by fluid dynamics, which are primarily determined by orographic effects (e.g., Blanchard 1953; Uijlenhoet 2001; Campos et al. 2006; Marzuki et al. 2013; Massmann et al. 2017; Murata et al. 2020). For instance, large amounts of water vapor entering mountain slopes can trigger mechanisms that result in the formation of small raindrops (Rosenfeld and Ulbrich 2003). Approximately 85% of the world’s countries (237) contain mountainous areas, which cover about 26% of the total continental surface. In South Korea, about 70% of the land area is mountainous (Lee et al. 2015). Therefore, understanding the factors affecting DSD in orographic precipitation is essential for improving QPE in remote sensing (Ryzhkov and Zrnić 1995) and refining microphysical schemes in numerical models (Saleeby and Cotton 2004; Abel and Boutle 2012; McFarquhar et al. 2015).
The Froude number (Fr) can be used to explain airflow properties especially in mountainous areas (e.g., Chen and Lin 2005a,b; Kim and Doyle 2005; Chen et al. 2008; Panziera and Germann 2010; Lin et al. 2021; Phadtare et al. 2022). Theoretically, if Fr is less than 1, a region of upstream-flow deceleration forms, which propagates upstream over time, and the windward side is characterized by flow stagnation with horizontal rerouting of the low-level flow. However, when Fr is higher than 1, the air flows freely over the mountains. Smolarkiewicz and Rotunno (1989) conducted a numerical simulation of prevailing winds passing through a single bell-shaped mountainous area finding that lee vortices developed at Fr2 ∼ 0.05 in the leeward highlands, creating banner clouds, while an updraft developed in the leeward lowlands caused by the low-level convergence. At Fr2 ∼ 0.43, these features disappeared, and orographic lifting occurred on the windward side, resulting in updraft development up to the upper layers in the leeward highlands. Lee et al. (2010) analyzed the characteristics of orographic precipitation over Mountain Halla, the same mountain investigated in this study, using a cloud-resolving storm simulator. They showed that orographic effects increased RA on the leeward side under Fr2 ∼ 0.30, and Lee et al. (2014) found that the precipitation system near the coastline on the leeward side developed due to updraft.
Jeju Island provides an ideal setting for studying orographic precipitation (e.g., Lee et al. 2012, 2014; Lee et al. 2018; Kim et al. 2022; You et al. 2022). Jeju Island, located in the southern part of the Republic of Korea (126.08°–127.02°E, 33.02°–33.32°N, approximately 75 km in a horizontal length), is a volcanic island with Mountain Halla (mountain top altitude HM of 1950 m). The Korea Meteorological Administration (KMA) has examined orographic precipitation on Jeju Island, revealing significant regional differences in annual average cumulative precipitation for the normal year (1981–2010) attributable to orographic effects. These differences reached up to 824 mm, with Gosan in the windward lowlands receiving 1142.8 mm and Sungsan in the leeward lowlands receiving 1966.8 mm. Notably, regional differences in cumulative precipitation recorded by KMA’s tipping-bucket rain gauges on Jeju Island over a decade (2011–20) are associated with Fr (Fig. 1). As Fr increased, wind direction over the entire region became more consistent, even when Fr2 < 1. The variation of normalized cumulative RA with Fr in regions A and B is relatively minor, approximately 0.1, but the greatest impact is observed in region C, where normalized cumulative RA is 0.88 for 0.1 < Fr2 < 0.3 dropping to 0.59 under conditions of 1 < Fr2 < 2.
Prevailing ground winds (red arrows) and normalized cumulated RA (vertical bars, colored according to their normalized amount) between 2011 and 2020 obtained by automatic weather systems for (a) 0.1 < Fr2 < 0.3, (b) 0.3 < Fr2 < 0.6, (c) 0.6 < Fr2 < 1, and (d) 1 < Fr2 < 2. The contour lines represent a 150-m elevation interval.
Citation: Journal of Hydrometeorology 25, 10; 10.1175/JHM-D-23-0087.1
Orographic effects influence not only regional differences in accumulated rainfall amounts but also QPEs due to local microphysical properties of precipitation (e.g., Rosenfeld and Ulbrich 2003). Previous research studies have primarily focused on case studies investigating the mechanism of severe weather phenomena causing heavy rainfall in mountainous areas. However, these studies face challenges in identifying the general microphysical features induced by orographic effects, which are essential for the development of QPE, due to variations in topography and airflow conditions. Consequently, statistical analyses of the microphysical properties of orographic precipitation under various airflow conditions, utilizing long-term ground-based disdrometer (i.e., DSD) data, are necessary.
Annual summer monsoon seasons, known as changma in Korea (e.g., Lee et al. 2017; Jung et al. 2022), mei-yu in China (e.g., Chen et al. 2013; Wen et al. 2016; Chang et al. 2022), and baiu in Japan (e.g., Karev et al. 2010; Oue et al. 2011; Chen et al. 2019), bring continuous frontal precipitation systems to East Asian regions. These systems contribute an average cumulative rainfall of 348.7 mm on Jeju Island. This study analyzed DSD characteristics during two changma periods (18 rainy days: 20 June–9 July 2013 and 28 June–13 July 2014) and their relationship with orographic effects via airflow conditions. Section 2 outlines the observation instruments used, the normalized gamma DSD model, data quality control (QC) measures, and the criteria for classifying cases and rainfall types. Section 3 presents the spatiotemporal features of regional variance in DSD and their relationships with radar variables influenced by orographic effects. In section 4, we discuss the mechanisms driving DSD characteristics due to orographic effects. Finally, section 5 summarizes the conclusions of the study.
2. Data and methods
a. Observation instruments
The study utilized four Parsivel disdrometers and two operational S-band single-polarization (hereafter “pol”) Doppler weather radars for case analysis (Fig. 2). The Parsivel disdrometer (OTT HydroMet) measures the diameter and fall velocity of hydrometeors using a laser-based optical signal, with a range from 0.31 mm and 0.2 m s−1 (third channel) to 25 mm and 20 m s−1 (32nd channel). It calculates the number concentration [N(D); mm−1 m−3] from raindrop data collected for each diameter channel. Both versions of the Parsivel disdrometers (Parsivel1 and Parsivel2) were employed. The four Parsivel disdrometers were strategically placed across Jeju Island in a zonal orientation to examine the orographic effects on precipitation on the windward lowland (WL) and leeward lowland (LL) and the windward highland (WH) and leeward highlands (LH), respectively (Table 1).
Locations of the weather radars (GSN and SSP; blue squares), radiosonde (R1 and R2; blue squares), and Parsivel disdrometers (WL, WH, LH, and LL; red bullets) operated on Jeju Island, South Korea. The contour lines represent a 150-m altitude H interval.
Citation: Journal of Hydrometeorology 25, 10; 10.1175/JHM-D-23-0087.1
Locations of the weather observation instruments.
The KMA operates 11 Doppler weather radars, among which two S-band single-pol Doppler weather radars, GSN (33.29°N, 126.16°E) and SSP (33.38°N, 126.88°E), were used to analyze the structural development of precipitation systems over Jeju Island. The radar scanning strategy consisted of 15 elevation angles with a 10-min volume scan time interval. Detailed specifications of the disdrometers and weather radars are summarized in Tables 2 and 3, respectively.
Specifications of Parsivel disdrometers.
Specification of GSN and SSP weather radars.
b. Normalized gamma DSD and radar variables
c. QC of Parsivel data
The Parsivel1 (i.e., LL in 2013) tends to underestimate and overestimate the N(D) for small (D < 1 mm) and large (D > 3 mm) drops, respectively, compared to the Parsivel2. To ensure consistent performance across all four disdrometers, this study applied the version correction proposed by Raupach and Berne (2015).
d. Rainfall event and type classifications
The daily accumulated rainfall amounts recorded by the four Parsivel disdrometers during the entire sampling period are shown in Fig. 3. The year 2014 experienced more precipitation than the year 2013 due to a heavy rainfall event (on 6 July) and Typhoon Neoguri (on 9 July), although typical precipitation patterns were observed continuously, except for these two extreme cases. These extreme cases were excluded from the analysis.
Daily rainfall amounts for four ground observation sites obtained by Parsivel disdrometers for the periods (a) 20 Jun–9 Jul 2013 and (b) 28 Jun–13 Jul 2014.
Citation: Journal of Hydrometeorology 25, 10; 10.1175/JHM-D-23-0087.1
Time–height of the Fr (solid black line) and wind speed (blue contours) obtained by R1 from (a) 20 Jun to 9 Jul 2013 and from (b) 28 Jun to 13 Jul 2014.
Citation: Journal of Hydrometeorology 25, 10; 10.1175/JHM-D-23-0087.1
The selected data, spanning 18 days, were divided into precipitation analysis cases based on three conditions: 1) The analysis cases were classified into two groups using Fr2 as the criterion to investigate the characteristics of orographic precipitation based on airflow. The normalized fractions of Fr2 for the 10-yr radiosonde data (R1: January 2011–May 2016 and R2: June 2016–December 2020; see Fig. 2) were found to be more similar for the ranges of Fr2 < 0.1 (52%) and 0.1 ≤ Fr2 < 1 (46%) only during the precipitation period, compared to those of all days (Fig. 5).
Normalized fraction of the Fr2 for (a) all days and (b) rainy days during the 10 years from 2011 to 2020 obtained by R1 and R2.
Citation: Journal of Hydrometeorology 25, 10; 10.1175/JHM-D-23-0087.1
The orographic precipitation cases were divided into two categories based on the Fr2 value, namely, (i) those dominated by airflow moving primarily around the mountain (Fr2 < 0.1; labeled as F1) and (ii) those dominated by airflow moving over the mountains (0.1 ≤ Fr2 < 1; labeled as F2). This study did not consider severe weather phenomena that do not reflect common regional rainfall features, such as Typhoon Neoguri, which corresponds to Fr2 > 1. 2) Additionally, the cases were defined when precipitation persisted continuously for more than an hour at each site. These criteria were independently applied to each observation site, as the study focused on statistical analysis. 3) Finally, convective precipitation types such as heavy rainfall and typhoons were excluded to ensure that the cases had minimal spatiotemporal variability in precipitation and traversed all ground observation sites driven by westerlies. The stratiform precipitation types that met these conditions were identified using the criteria suggested by Bringi et al. (2003): Rainfall in which R > 0.5 mm h−1 and the standard deviation σ of R for 5 min < 1.5 mm h−1 was considered stratiform rainfall. Overall, the study identified 27 cases (11 cases for F1 and 16 cases for F2). Detailed results of the case classification are provided in Table 4.
The number of data samples and precipitation events observed from each Parsivel observation site.
3. Results
a. Spatial features of DSD over the mountainous area by orographic effects
The normalized N(D) demonstrates the relationship between orographic precipitation and Fr (Fig. 6). At all observation sites, the normalized N(D) was most consistent at D/Dm ∼ 0.8, irrespective of Fr. For F1 cases, the normalized N(D) showed differences at D/Dm > 1.2 or D/Dm < 0.7, indicating a dominance of smaller and larger particles at LH and LL, respectively. In contrast, under the F2 conditions, the normalized N(D) converged across all sites. The normalized N(D) for D/Dm < 0.5 was lower in F2 than in F1. At LH, the normalized N(D) was higher in F2 cases than in F1 cases for D/Dm > 1.4, suggesting that orographic effects on ground DSD diminish when airflow primarily moves over the mountain.
Average normalized N(D) for (a) F1 and (b) F2 cases at the four disdrometer stations. Vertical bars represent ±1σ for N(D)/Nw.
Citation: Journal of Hydrometeorology 25, 10; 10.1175/JHM-D-23-0087.1
In F1, the shape μ and slope Λ parameters for the lowlands were lower than those for the highlands (Fig. 7). Higher Λ compared to the southeastern China near Jeju Island (Chen et al. 2013; Huang et al. 2021) implies a more maritime-like climate with high N(D) in smaller raindrops. The LH site had the highest Λ, indicating a dominance of smaller particles (D < 1 mm), while the LL site had the lowest Λ. However, μ at LL was higher than at WL, despite both being coastal areas with similar geographical conditions. The average μ and Λ in F2 became consistent with those of WL in F1, where WL is expected to experience minimal orographic influence. The averages of μ and Λ in F2 were converged to approximately 10.5 and 18, respectively.
Average shape μ and slope Λ parameters of stratiform rainfall for the (a) F1 and (b) F2 cases at the four disdrometer stations. Vertical bars represent ±1σ for the slope values. The solid gray lines correspond to Λ = (4 + μ)/Dm. The gray and dark gray dashed curves represent the average curve for stratiform rainfall as defined by Chen et al. (2013) and Huang et al. (2021), respectively.
Citation: Journal of Hydrometeorology 25, 10; 10.1175/JHM-D-23-0087.1
The average logNw and Dm were lower than those found in midlatitudes (Bringi et al. 2003), but corresponded to those found in the southeastern coast of South Korea (Suh et al. 2021). Comparing the relationship between Dm and logNw in this region—adjacent to Jeju Island (∼315 km)—with the present study results helps investigate regional DSD features according to orographic effects and analyze regional DSD characteristics depending on the presence of mountainous areas (Fig. 8). High Dm values were found in the lowlands, with greater differences between F1 and F2 cases on the leeward sides. In F1, LL had the highest Dm and LH had the lowest Dm, but in F2, these values converged around those in the windward side, following the linear regression line suggested by Suh et al. (2021) (Fig. 8b). This suggests that the DSD range can be expected under similar climatological conditions regardless of topography and airflow condition. All σ values of logNw were lower in F2 than in F1. In F1, the σ of logNw was proportional to its mean value, but all σ values of logNw decreased and became consistent in F2. On the windward side, Dm variation was negligible (WL: 1.09–1.06 mm; WH: 0.99–0.98 mm) as Fr increased. However, Fr more significantly affected DSD on the leeward side. As Fr increased, Dm increased by 0.2 mm (from 0.84 to 1.04 mm) at LH but decreased by 0.17 mm (from 1.26 to 1.09 mm) at LL.
Average Dm vs logNw of stratiform rainfall for (a) F1 and (b) F2 cases at the four disdrometer stations—WL, WH, LH, and LL. Horizontal and vertical bars represent ±1σ for the Dm and logNw values, respectively. The solid black and broken gray lines correspond to the linear regression lines defined by Suh et al. (2021) at Busan and Bringi et al. (2003) at midlatitudes, respectively.
Citation: Journal of Hydrometeorology 25, 10; 10.1175/JHM-D-23-0087.1
One main reason for low Dm (and high Nw) under F1 can be found in the kernel density estimation (KDE) (Fig. 9; see the appendix). Second peaks at Dm < 0.7 mm and logNw > 4.5 (Figs. 9a,b) on the windward side are attributed to the coastal sea breeze (Suh et al. 2016, 2021). Consistent with expected orographic effects, the second peak did not appear in either Dm or logNw parameters at the LL site, despite its proximity to the coast. However, a primary peak corresponding to the ranges where the secondary peak is found at the other sites (Dm < 0.7 mm and logNw > 4.5) was identified in the KDE of LH.
Normalized probability density distribution with the function of KDE of (a) Dm for F1, (b) logNw for F1, (c) Dm for F2, and (d) logNw for F2 at the four disdrometer stations (WL, WH, LH, and LL). The shaded area represents the differences between KDE and the histogram, wherein the bandwidth and maximum frequency are synchronized with those of KDE. The values in parentheses, indicating each observation site, represent the mean and standard deviation of the frequency error for KDE, respectively.
Citation: Journal of Hydrometeorology 25, 10; 10.1175/JHM-D-23-0087.1
In F2, the KDEs showed similar shapes across all sites, and the second peak at all sites except WL disappeared (Fig. 9b). The second peak at WH where the variation in average Dm and Nw was negligible with respect to Fr disappeared as Fr increased. The Dm gradually increased (and Nw gradually decreased) to the distance from the coastline at similar elevations (Suh et al. 2021). However, a lower Dm was seen at WH, which is relatively inland compared to the coastal WL site, suggesting that DSD in WH was influenced by orographic effects. At LH, the primary peak with Dm < 0.7 mm vanished in F2. Additionally, the peak for LL at Dm ∼ 1.2 mm decreased. A common feature of DSD in probability density functions (PDFs) for all sites except for LH was that the second peak weakened or disappeared in the low Dm (high logNw) ranges, while the primary peak for LH disappeared and the second peak became the primary peak in F2.
b. Temporal features of DSD and radar variables over the mountainous area by orographic effects
A statistical analysis of the temporal variations in DSD was conducted to investigate the temporal characteristics of orographic precipitation that are not discernible from a spatial perspective (see section 3a). Figure 10 presents the averaged time series of DSD parameters for all precipitation events with the precipitation initiation local time for each event considered as the reference time (i.e., t = 0). Intervals containing data from fewer than three cases for the same reference time were excluded from this analysis.
Time series of the average of (a) Dm for F1, (b) logNw for F1, (c) Dm for F2, and (d) logNw for F2 at the four disdrometer stations (WL, WH, LH, and LL).
Citation: Journal of Hydrometeorology 25, 10; 10.1175/JHM-D-23-0087.1
In F1, Dm decreased and logNw increased continuously for the initial 2 h at all sites due to the size sorting phenomenon (e.g., Kumjian and Ryzhkov 2012). The precipitation periods at site LH were the longest, with the minimum Dm of approximately 0.6 mm and maximum logNw of approximately 5.0, occurring from the second hour to the sixth hour from the reference time. Site LL exhibited the highest Dm, although it continuously decreased over time. In F2, the temporal variations in DSDs observed in F1 cases disappeared at all sites (Figs. 10c,d), indicating that the averaged DSD parameters under F2 represent the entire precipitation period.
Understanding the vertical structure of a precipitation system is crucial for interpreting the characteristics of DSD at the ground level. Orographic effects can be validated by the composite column maximum Cmax (dBZ), which is the vertical maximum of ZH within a 1-km2 horizontal range. This measure is valuable for identifying areas of convective activity where vertical motion or airflow disturbance can lead to precipitation system formation. Figure 11 depicts a time series of the averaged Cmax and its altitude Hc (km). The method for averaging the Cmax time series for each site is identical to that presented in Fig. 10.
Time series of the average composited column maximum Cmax and altitude of Cmax Hc over the entire duration of stratiform rainfall events for the (a) F1 and (b) F2 cases at the four disdrometer stations (WL, WH, LH, and LL). The size and color of the symbols correspond to the value of Cmax.
Citation: Journal of Hydrometeorology 25, 10; 10.1175/JHM-D-23-0087.1
In F1, the Cmax over the precipitation system’s lifetime was proportional to Hc, ranging from 6 to 9 km in height (Fig. 11a). A common feature across all sites was the increase in Cmax to more than 28 dBZ from the fourth to sixth hours, with Hc increasing from 6 to 9 km, between the third and sixth hours, respectively. At site LH, the Cmax and Hc decreased from 30 to 27 dBZ and from 9 to 6 km, respectively, at site LH between the 5th and 5.5th hours, a pattern not observed at other sites. All sites except LH exhibited consistent temporal variations in Cmax and Hc, suggesting a weak correlation between altitude above mean sea level (MSL) and Hc. At LH, Cmax correlated negatively with Dm from the third to seventh hours. Although ZH and Dm are generally positively correlated because Z is proportional to D6, the minimum Dm was observed during the same period when the maximum Cmax suggested the presence of a disturbance highly related to particle breakup in these precipitation systems.
In F2, no correlation was found between Hc and Cmax in F2, but both were positively correlated with the MSL of the sites (Fig. 11b). Compared to F1, the Hc in F2 was relatively lower (4–7 km) at higher Cmax (>28 dBZ), with the peak stage occurring earlier, within the second–fifth hours. A decrease in the averaged Dm at WL was associated with a decrease in Hc from 9 to 5–6 km as Fr increased, reducing the raindrop’s falling distance, which can affect particle growth. The highland sites reached strong Cmax levels (WH: ∼33 dBZ at 2.5th hour; LH: ∼32 dBZ at 4.7th hour), while WH exhibited weak variation in Dm, even at its strongest Cmax at 2.5th hour. Furthermore, the variations in Hc observed in F1 at LH between the 5th and 5.5th hours were absent in F2. Additionally, the Cmax at LL decreased in F2, suggesting that this induced the decrease in Dm observed at that site (Figs. 8–10). No strong Cmax higher than 28 dBZ was detected until the fourth hour, and weak Cmax, below 25 dBZ, was observed after the fifth hour at LL.
c. Geographical uncertainty in radar-based precipitation estimations caused by orographic effects
The dependence of orographic precipitation on airflow conditions was verified in the previous section using ground-based DSD and radar measurements, indicating that these characteristics are also related to QPE (i.e., Z = ARb). Note that the Z–R relationships were considered in the analysis owing to the use of single-pol weather radars and that these relationships were derived using a linear regression equation. The difference in Cmax with altitude became evident as Cmax increased at higher altitudes due to increasing Fr. Additionally, Cmax increased on the windward sides, while on the leeward side, it remained similar or decreased.
A trend of high A and low b in the lowlands was observed in F1 (Fig. 12 and Table 5). On the windward side, the altitude of the observation sites and the coefficients of the Z–R relationship were negatively correlated, although this was not observed on the leeward side. A slight decrease in b and an increase in A were observed with altitude.
Mean coefficients A and b for the Z–R relationship (Z = ARb) at the four observation sites (WL, WH, LH, and LL). The blue arrows represent the transitions from F1 to F2 conditions. The size and color of the symbols correspond to the elevation MSL of the observation site and the composited column maximum Cmax, respectively. The dark gray square symbols represent the means for WSR-88D and M-P data and the mean from Suh et al. (2021), which are Z = 300R1.4, Z = 200R1.6, and Z = 152.8R1.6, respectively. The gray square symbols represent means from Fujiwara and Yanase (1968).
Citation: Journal of Hydrometeorology 25, 10; 10.1175/JHM-D-23-0087.1
Summary of coefficients A and b in the Z–R relationships and the correlation coefficient (CC) and root-mean-square error (RMSE) between measured and estimated R according to airflow conditions (F1 and F2).
The coefficients in F2 converged to around 155 < A < 201 and 1.50 < b < 1.54, which are similar to the range found in previous studies on stratiform precipitation (e.g., Marshall et al. 1955; Suh et al. 2021) and differ from results for convective precipitation data (Z = 300R1.6, WSR-88D). These findings indicate that orographic effects on DSD were more significant under F1 conditions. However, under F2, several notable characteristics were also observed: first, a tendency toward relatively lower coefficients A and b on the windward side of Mt Halla; second, coefficients A and b decreased with increasing elevation (e.g., Fujiwara and Yanase 1968), especially for the coefficient A. Coefficient A decreased and coefficient b increased at lowland sites (LL and WL) as Fr increased, with the most noticeable variation observed in LL. In the highlands, coefficient A consistently increased with increasing Fr.
In radar meteorology, RA is estimated by a unified Z–R relationship within the detectable range of weather radar without considering the major factors influencing atmospheric phenomena (i.e., geographical, climatological, and airflow conditions). However, even in smaller regions such as Mountain Halla with approximately 70 km in zonal length, regional differences in estimated RA due to orographic effects were confirmed. The cumulative RA of all precipitation events measured by the Parsivel disdrometer was highly dependent on Fr (Fig. 13). The regional differences in RA in F1 were greater than those in F2. Regardless of Fr, higher cumulative RA was recorded in the highlands compared to the lowlands: 69.9 mm at highland sites under F1 and 46.3 mm under F2. In F1, site LH recorded the highest amount of cumulative RA, 42.1 mm, which was 4.7 times higher than that of WL. The cumulative RA in highland sites was 2.3 times higher (69.9 mm) than that in the lowland sites (30.5 mm). Furthermore, 1.7 times more cumulative RA was recorded on the leeward side (63.7 mm) than on the windward side (36.7 mm). Under F2 conditions, cumulative RA at the windward sites (46.4 mm) was approximately 1.2 times higher than at the leeward sites (38.6 mm).
Barplot of the cumulative rainfall amount RA for the entire precipitation period considered in the present study. Gray, blue, and red color bars represent the cumulative RA obtained by the Parsivel disdrometers Rtrue, estimated by the Z–R relationship optimized for each site Rest, and estimated by the Z–R relationship optimized for WL RWL, respectively. The values at the top of each bar are the cumulative RA, which, for estimates, is followed in parentheses by the ratio expressed as a percentage of differences between the estimate and Rtrue.
Citation: Journal of Hydrometeorology 25, 10; 10.1175/JHM-D-23-0087.1
The cumulative RA estimated by the Z–R relationships calculated for each observation site based on its airflow conditions consistently underestimated the ground truths. The differences in cumulative RA were particularly noticeable in F1, with differences ranging from −3.6% at LL to −7.0% at LH. In F2, relatively better estimation performance was observed, with differences ranging from −3.9% at WL and LL to −4.5% at WH. To assess the impact of orographic effects on radar-based QPEs, the differences in RA between the ground truth measurements and the Z–R relationship-based estimates for WL were analyzed. Among the observation sites, WL was considered to have no orographic effects on the precipitation, as confirmed by the smallest difference in its Z for the same R estimated using the Z–R relationship (Table 5). When the parameters used to estimate cumulative RA for WL were applied to all sites, underestimations compared to the ground truth were observed. In LH, where a lee vortex would be expected in F1, the estimation error was significant (−28.2%). This discrepancy may occur when QPE estimation is not optimized for the geographical characteristics of a mountainous area.
4. Discussion
An understanding of the prevailing airflow around mountainous areas and cloud microphysical phenomena is required to interpret the key results of this study, as DSDs depend on various physical processes, such as drop breakup/coalescence, vertical air motion, and evaporation/condensation (Testik and Barros 2007). Several previous studies have analyzed the dominant features of airflow based on Fr in single bell-shaped mountainous areas using observational data and numerical models (e.g., Smolarkiewicz and Rotunno 1989; Jiang and Smith 2003; Kunz and Kottmeier 2006; Lee et al. 2010, 2014; Kim et al. 2019). Additionally, variations in the coefficients of the Z–R relationship due to airflow conditions can help interpret the microphysics of raindrops (e.g., Rigby et al. 1954; Gunn and Marshall 1955; Atlas and Chmela 1957; Srivastava 1971; Rosenfeld and Ulbrich 2003). Based on previous finding, the DSD features observed in the present study can be interpreted as summarized in Fig. 14. The prevailing airflows and microphysics of precipitation at four observation sites are discussed except for at site WL where no orographic precipitation was identified.
Schematic representation of orographic precipitation according to the airflow conditions found in this study. (a) The mean ZH from site WL to site LL for R = 5 mm h−1. The red solid and blue dashed lines represent F1 and F2 conditions, respectively. Diagrams showing wind and precipitation over Mountain Halla during a theoretical precipitation event proceeding from (left) the windward side to (right) the leeward side under (b) F1 and (c) F2 conditions. The thick pink arrows in (b) and (c) above each observation site represent the expected dominant airflow condition; small, light-blue dots (small drops) and large, dark-blue dots (large drops) represent the DSD. The light and dark gray zones represent the composited column maximum Cmax for 20 < Cmax (dBZ) < 30 and Cmax > 30 dBZ, respectively. The abbreviations of references have the following meaning: S71 (Srivastava 1971), SR89 (Smolarkiewicz and Rotunno 1989), G92 (Geerts 1992), JS03 (Jiang and Smith 2003), RU03 (Rosenfeld and Ulbrich 2003), KK06 (Kunz and Kottmeier 2006), L10 (Lee et al. 2010), L14 (Lee et al. 2014), S16 (Suh et al. 2016), TP17 (Testik and Pei 2017), K19 (Kim et al. 2019), T20 (Tilg et al. 2020), and S21 (Suh et al. 2021).
Citation: Journal of Hydrometeorology 25, 10; 10.1175/JHM-D-23-0087.1
a. Windward highlands
As the elevation increased, the increase in Fr on the windward side negligibly affected ground DSD variation, but it did verify the development of the precipitation system: The term Cmax increased from 29.5 to 33 dBZ. The Froude number is proportional to low-level wind speed (see Fig. 4), which can induce upslope winds (i.e., increases in Cmax; Smolarkiewicz and Rotunno 1989; Lee et al. 2010) and particle breakup processes (i.e., decreases in Dm; Testik and Pei 2017; Tilg et al. 2020). The decrease in coefficient b in the Z–R relationship with increasing Fr might be influenced by a combination of updraft (an increase in A and a decrease in b) and aerodynamic breakup processes (a decrease in A and b; Srivastava 1971; Rosenfeld and Ulbrich 2003).
b. Leeward sides
1) Highlands
Further particle breakup can be induced by airflow disturbances, such as lee vortices, which are also related to the development of banner clouds (Smolarkiewicz and Rotunno 1989; Geerts 1992). Kim et al. (2019) identified unstable atmospheric conditions that exhibit a continuous development of updrafts in the upper layer (H > 3 km) and a downward flow in the lower layer (H < 3 km) under Fr2 ∼ 0.04 on the leeward highlands of Mountain Halla. These phenomena are associated with the highest Cmax (31 dBZ) and the lowest Dm (0.84 mm) in F1. However, unstable airflows under F1 can be eliminated as Fr increases due to the formation of mountain waves in the leeward highlands (Jiang and Smith 2003). This can explain the leap of Dm to 1.04 mm and the drop of Λ from 33.5 to 9.5 in F2. The weakening of the particle breakup mechanism associated with these microphysical features matches the increases in coefficients A and b in the Z–R relationship as Fr increased (Srivastava 1971).
2) Lowlands
The precipitation system on the leeward side lowlands can be attributed to updraft enhancement under conditions of Fr < 1 (Kunz and Kottmeier 2006; Lee et al. 2014; Kim et al. 2019). This updraft enhancement can increase particle growth, with the largest Dm reaching 1.26 mm at LL under F1 conditions. In F2, upper-layer Cmax decreased from approximately 30 to 28 dBZ, and Dm on the ground decreased to 1.09 mm with a slight decrease in μ from 11.5 to 10.5. These microphysical features correspond to the disappearance of the updrafts. The weakening of the updraft due to increasing Fr is consistent with the decrease in A and the increase in b (Rosenfeld and Ulbrich 2003).
5. Summary and conclusions
Analyzing the microphysics of precipitation is crucial for developing QPE, but it is heavily dependent on meteorological conditions. The DSD characteristics are determined by climatological, geographical, and orographic effects. However, few studies have examined the orographic effects on QPE. This study is the third in a series, following investigations into the effects of climatological (Suh et al. 2016) and geographical (Suh et al. 2021) conditions on DSD. Here, we present findings from a 2-yr field campaign on Mountain Halla—a single bell-shaped mountainous area—serving as an ideal case study to explain how orographic processes affect DSD characteristics. Our findings can be summarized as follows:
-
Regional features in the mountainous area: In the F1 cases, Dm was higher on the leeward side than on the windward side. Specifically, the particle breakup effect due to lee vortices is assumed to have caused the lowest Dm at LH, while the enhanced updraft led to the highest Dm observed at LL. Variations in Dm on the windward side were negligible regardless of Fr. However, the weakening of the lee vortex in F2 corresponds to an increase in Dm at LH, while a decrease in Dm was found at LL. Consequently, variations in Dm on the leeward sides decreased remarkably from 0.42 to 0.05 mm as Fr increased.
-
Features of orographic precipitation in QPE: The importance of DSD analysis for orographic precipitation is evident in the Z–R relationship. In F1, cumulative RA was significantly underestimated by up to −28.2% at LH when estimated by using the Z–R relationship for WL, where minimal orographic effects were observed. However, the underestimation error was reduced to −8.2% at WH in F2. Regional differences in the estimated ZH at R = 5 mm h−1, which is the maximum value in stratiform rainfall, were high under F1, particularly in the highlands. Estimated ZH at WL showed negligible differences (F1: 32.3 dBZ; F2: 32.4 dBZ), but the significant differences were apparent at LH (F1: 30.1 dBZ; F2: 32.7 dBZ) due to airflow conditions. An increase in Fr induces a particle breakup process due to enhanced wind speeds in the lower layer, which can decrease Dm, thereby decreasing the estimated ZH at WH (F1: 33.2 dBZ; F2: 31.8 dBZ). The highest Dm was found at LL, corresponding to the high estimated ZH (34.0 dBZ) in F1, when updraft enhancement was expected, but it was only slightly reduced to 33.6 dBZ in F2.
The outcomes of this study demonstrate an imperative need to develop QPE scheme that considers orographic effects with prevailing wind conditions. This study focused on the statistical analysis of DSDs measured by ground-based Parsivel disdrometers positioned evenly in a mountainous region. However, examining how airflow influences the microphysics of raindrops is also necessary. Additionally, this study did not consider severe weather phenomena that can cause spatially discontinuous ground rainfall amounts, such as heavy rainfall, mesoscale convective systems, and typhoons (i.e., Fr2 > 1). Therefore, a follow-up study will be conducted to address these limitations.
Acknowledgments.
We would like to express our gratitude to the members of the Group of Environmental Atmospheric Research (GEAR) working with Professor Dong-In Lee at Pukyong National University, Korea. They provided valuable observational data during the 2012–14 Jeju Island intensive observation periods (IOPs), which played a decisive role in the success of this study. This research study was supported by the NARO Space Center Advancement Project of Ministry of Science and ICT (MSIT).
Data availability statement.
The data obtained by the Parsivel disdrometers in this study are available on request from Professor Dong-In Lee.
APPENDIX
Kernel Density Estimation
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