Abstract

During 11–12 June 2012, heavy precipitation occurred over the northwestern Taiwan coast (~435 mm) and within the Taipei basin (~477 mm). With the presence of a midlatitude omega-blocking pattern, a persistent cold northerly wind component west of the northeast China low and west of the mei-yu frontal cyclone extends all the way to the subtropics and up to the 700-hPa level. At 2000 LST 11 June, the total precipitable water ahead of the front is elevated (>70 kg m−2) with horizontal southwesterly moisture fluxes >360 g kg−1 m s−1 at the 950-hPa level. The rainfall maximum along the northwestern coast mainly occurs before 0200 LST 12 June, as the convective activities in the frontal zone are enhanced by the localized convergence between the prefrontal southerly barrier jet and environmental airflow. After landfall, the relatively deep (~1.5 km) mei-yu front moves over the mountains (with peaks ~1121 m) along the northern coast and into the Taipei basin. During 0200–0800 LST 12 June, it stalls at the foothills of the Snow Mountains (with peaks ~3886 m) south of the basin under the postfrontal west-northwesterly flow. Rain cells associated with the mei-yu front are enhanced as they move southeastward toward the Snow Mountains. The barrier jet and the rainfall maxima over the northwestern coast and within the Taipei basin are well simulated using the high-resolution WRF Model. With the model terrain removed, the simulated mei-yu front continues to move southward after landfall without reproducing the barrier jet and both observed rainfall maxima.

1. Introduction

Heavy rainfall events are major meteorological disasters that occur around the globe. They pose a significant challenge for both scientific research and operational forecasts. Heavy rainfall events in diverse locations share essential similarities: copious moisture and destabilization effects due to lifting (Ogura et al. 1985; Wang et al. 1985; Kodama and Barnes 1997; Lin et al. 2001; Chiao et al. 2004; Medina et al. 2005; and others).

Taiwan is a mountainous island located off the southeastern China coast. It is subject to the northeast monsoon from September to April. The southwesterly monsoon dominates the rest of the year (Ramage 1971). Heavy rainfall in many parts of the world is frequently localized in nature due to terrain and local winds (Ogura et al. 1985; Grossman and Durran 1984; Ogura and Yoshizaki 1988; Buzzi et al. 1998; Zhang et al. 2005; Tu and Chen 2011; and others). Heavy rainfall events during the early summer rainy season over Taiwan are related to the arrival of subtropical cold fronts (or mei-yu fronts) (Trier et al. 1990; Chen et al. 1989; Yeh and Chen 1998; Chen 1993; Davis and Lee 2012), mesoscale cyclones (Wang and Orlanski 1987; Chen et al. 2010a; Lai et al. 2011), abundant moisture (Chen and Yu 1988; Chen and Li 1995a; Chen et al. 1997; Chen et al. 2007a,b; Tu et al. 2017; and others), orographic effects and local winds (Li et al. 1997; Yeh and Chen 2002; Akaeda et al. 1995; Teng et al. 2000; C.-S. Chen et al. 2005, 2010b, 2011; and others), and cold pools from rain evaporative cooling (Xu et al. 2012; Chen et al. 2013; Tu et al. 2014, 2017). The island-scale weather and precipitation over Taiwan are linked to the diurnal heating cycle (Johnson and Bresch 1991; Chen and Li 1995b; Kerns et al. 2010; Ruppert et al. 2013) and interactions among large-scale flow, mesoscale processes, and island-induced circulations (Chen 2000; Yeh and Chen 1998; Chen and Chen 2003; Tu et al. 2014; and others).

Chen (1993) showed that during the 1987 Taiwan Area Mesoscale Experiment (TAMEX) (Kuo and Chen 1990), prior to the seasonal transition in mid-June, all the mei-yu fronts over southern China were baroclinic in nature. A moist baroclinic process drives the secondary frontal circulation with a low-level jet (LLJ) in the lower troposphere with tropopause folding aloft (Chen et al. 1994, 1997; Chen and Chen 1995, 2002). During periods of heavy precipitation over Taiwan, the subsynoptic LLJ is frequently observed in the warm sector of the mei-yu front (Chen and Yu 1988; G. Chen et al. 2005).

For flow past a mountain range, the Burger number [B = Ro/Fr = (N/f)/(h/L)] characterizes the scaled mountain slope, where Ro (= U/fL) is the Rossby number, Fr (= U/Nh) is the Froude number, U is wind speed, f is the Coriolis parameter, L is the horizontal length scale, N is Brunt–Väisälä frequency, and h is the mountain height (Pierrehumbert and Wyman 1985; Overland and Bond 1995; Smolarkiewicz et al. 1988). For the subsynoptic LLJ flow over the Central Mountain Range (CMR), which is hydrodynamically steep, B > 1 and Fr = 0.2–0.4 (Li and Chen 1998). The flow deceleration and flow splitting occur off the southwestern coast with a windward ridge/leeside trough pressure pattern due to orographic blocking (Chen et al. 1989; Trier et al. 1990; Chen and Li 1995a), in agreement with theoretical studies (Smith 1982, 1989; Lin 2007; and others). The deflected airflow accelerates northward with a large cross-contour wind component down the pressure gradients along the west coast, which results in strong orographically induced winds along the northwestern coast (e.g., barrier jet) (Chen and Li 1995a; Li and Chen 1998; Yeh and Chen 2003). The barrier jet is also affected by the diurnal heating cycle due to variations in stability and is strongest in the early morning (Chen and Li 1995b; Lin et al. 2011).

In the past, we studied the statistics of heavy rainfall events (frequencies and spatial distribution), rainfall characteristics over Taiwan, and the effects of local circulations and terrain on rainfall occurrences and cloud distributions based on surface and satellite data (Chen and Chen 2003; Chen et al. 2007; Yeh and Chen 1998; Kerns et al. 2010). These studies provide basic background information for the case study approach. During the mei-yu season over Taiwan, climatological rainfall distributions have pronounced maxima on the windward slopes of the Snow Mountains and CMR (Yeh and Chen 1998). However, during frontal passages over northern Taiwan, rainfall distribution for each event may deviate from the climatological rainfall pattern. For example, during TAMEX IOP 3, the localized moisture convergence between the west-southwesterly monsoon flow and a southerly barrier jet caused the development of deep convection within the Taiwan Strait (Yeh and Chen 2002). During TAMEX IOP 13, the convergence between a prefrontal wind shear line and southerly barrier jet generated a rainband off the central-northwestern coast (Li et al. 1997). For both cases, the development of heavy rain cells due to interaction between the jet–front system and orographically induced flow occurred over coastal waters. These cells then drifted inland and caused coastal flooding.

After TAMEX, the Central Weather Bureau, Taiwan (CWB), established a dense Automatic Rainfall and Meteorological Telemetry System (ARMTS) network over the island (Kerns et al. 2010) and completed a Doppler radar network. Chu (2013) showed that during 1993–2012, there were 13 heavy rainfall events with daily rainfall accumulation >200 mm recorded at one or more stations with elevation <250 m over northwest Taiwan (north of 24°N and west of 121.5°E). Among those cases, the 11–12 June 2012 case is the only widespread heavy precipitation event with maximum daily rainfall accumulation >400 mm over both the northwestern coast of Taiwan (~435 mm) and within the Taipei basin (~477 mm) (Chu 2013). For most stations within the Taipei basin, the heaviest rainy period for this case occurred during 0000–0800 local standard time (LST) 12 June. It is apparent that in addition to favorable large-scale settings, the interaction of the jet–front system with the terrain and orographic effects may be crucial for the development of this extreme precipitation event. However, in contrast to our previous studies on the interaction of the barrier jet and jet–front system within the Taiwan Strait, for this study, we will focus on the orographic effects during and after the landfall of a mei-yu front.

The large-scale, mesoscale, and local conditions prior to and during landfall of the mei-yu front are studied by analyzing synoptic, sounding, surface, rain gauge, and radar data and numerical modeling. The data used and design of the numerical model are described in section 2. A synoptic overview is given in section 3. Observational analyses of the favorable subsynoptic settings, evolution of the mei-yu front before and after landfall, and precipitation patterns over the Taiwan area are presented in section 4. In section 5, the results from high-resolution multinested Weather Research and Forecasting (WRF) Models with a horizontal grid as small as 1 km for the innermost domain are used to diagnose the effects of terrain on the jet–front system and mechanisms for the occurrence of extreme precipitation. Finally, the results are summarized in section 6.

2. Data and method

a. Data

There were 433 ARMTS stations in use during May–June 2012 (Fig. 1a). All of the ARMTS and conventional stations measure hourly rainfall at a precision of 0.5 mm. Rainfall is measured using tipping-bucket gauges. Among those stations, hourly wind observations are also recorded for 210 stations. Winds are recorded every second and averaged over a 10-min period with resolutions of 0.1 m s−1 and 1° for wind speed and direction, respectively. In addition, data from 24-hourly conventional surface weather stations, four rawinsonde stations, and four operational Doppler radars over the island of Taiwan are also available (Fig. 1b) (Tu et al. 2014). The hourly composite radar echoes produced by CWB are also used. The European Centre for Medium-Range Weather Forecasts (ECMWF) interim reanalysis (ERA-Interim) is used to delineate the subsynoptic weather patterns (Dee et al. 2011).

Fig. 1.

(a) Locations of 433 ARMTS rain gauge stations (solid blue circles) and hourly rainfall and wind stations (solid red circles) in 2012. The Shuei-Wei and San-Xia stations are denoted by a purple “×.” (b) Locations of 24 routine hourly surface stations (blue “+”); four Doppler radar sites (solid red circles), including Wu-Fen-Shan radar site; and four rawinsonde sites (purple triangle), including the Banciao rawinsonde site.

Fig. 1.

(a) Locations of 433 ARMTS rain gauge stations (solid blue circles) and hourly rainfall and wind stations (solid red circles) in 2012. The Shuei-Wei and San-Xia stations are denoted by a purple “×.” (b) Locations of 24 routine hourly surface stations (blue “+”); four Doppler radar sites (solid red circles), including Wu-Fen-Shan radar site; and four rawinsonde sites (purple triangle), including the Banciao rawinsonde site.

b. Model description

The Advanced Research core of the WRF Model (WRF-ARW, hereinafter WRF) uses the sigma (terrain following) hydrostatic pressure vertical coordinate (Skamarock et al. 2008; Laprise 1992). Four model domains with two-way nesting are used with horizontal grids of 27 (domain 1), 9 (domain 2), 3 (domain 3), and 1 km (domain 4) (Fig. 2). There are 38 vertical levels from the surface to the 50-hPa level with 13 levels below 2 km. In domains 1 and 2, Grell’s convective parameterization scheme and Goddard’s grid-resolvable microphysics are used (Grell and Dévényi 2002; Tao and Simpson 1993). For the 3- and 1-km grid domains, the convective parameterization scheme is turned off. The Rapid Radiative Transfer Model (RRTM), Dudhia’s shortwave schemes, Noah land surface model (LSM), and Yonsei University (YSU) planetary boundary layer scheme are used (Mlawer et al. 1997; Dudhia 1989; Chen and Dudhia 2001; Hong et al. 2006). The surface layer uses the fifth-generation Pennsylvania State University–NCAR Mesoscale Model (MM5) similarity scheme with stability functions from Paulson (1970), Dyer and Hicks (1970), and Webb (1970). For the lower-boundary conditions over Taiwan, the 1-km land-use data compiled by CWB are used.

Fig. 2.

The nested model domains. The horizontal grid sizes for domains 1–4 are 27, 9, 3, and 1 km, respectively.

Fig. 2.

The nested model domains. The horizontal grid sizes for domains 1–4 are 27, 9, 3, and 1 km, respectively.

A 36-h simulation initialized from the ERA-Interim analysis at 0800 LST (0000 UTC) 11 June 2012 is conducted. The ECMWF analysis is used to validate the model results from the 9-km grid domain. The evolution of the surface front and rainfall distribution over the Taiwan area from our model is compared with the analyses of surface data. Furthermore, the orographic effects on the convective systems as they move toward the northern Taiwan coast and the impact of terrain on heavy precipitation in the Taipei basin are investigated using the results from the 3- and 1-km domains. A model sensitivity test without Taiwan’s topography is performed (NT run) to assess the impact of terrain on localized heavy rainfall patterns. For the NT run, the 1-km land-use data compiled by CWB are also used.

The initial conditions of the meteorological data for the high-resolution model domains are interpolated horizontally from the pressure-level global analysis data and then converted to sigma levels using the surface pressure in the high-resolution model domains. For coastal grid points, the terrain outside the land mask is set to zero with water as the ground cover. After inserting the prescribed high-resolution (1 km) terrain for the CTRL run or removing the terrain in the NT run, the surface pressure within the high-resolution domains is computed using the hydrostatic relationship. For both the CTRL and NT runs, we let the interpolated meteorological data adjust to the prescribed static lower-boundary conditions (terrain and land surface parameters). For high-resolution model simulations over mountainous subtropical islands (e.g., Hawaii and Taiwan), the adjustment time scale to changes in model terrain is on the order of a few hours (Smolarkiewicz et al. 1988; Chen and Feng 2001; Yeh and Chen 2003). After 6-h model runs, the simulated high-resolution model results are well adjusted to the prescribed model terrain for both the CTRL and NT runs (not shown). Model results after 12 h of time integration (e.g., 1200 UTC 11 June) are presented in section 5.

3. An overview of weather patterns

a. Synoptic conditions

During 0000 UTC (0800 LST) 9 June–0000 UTC (0800 LST) 13 June, at the 300-hPa level, an omega blocking pattern (Chen et al. 2007) is present over East Asia with a blocking ridge over the Okhotsk Sea, sandwiched by a northeast China low (Du et al. 2014) and the Aleutian low (Fig. 3a). During this time of the year, a blocking ridge (or blocking high) over the Okhotsk Sea is common. A midlatitude Rex blocking pattern is also reported by Hsiao and Chen (2014) for the 10–14 June 1978 case studied by Chen and Chang (1980). At the 850-hPa level, an east-northeast (ENE)–west-southwest (WSW)-oriented trough over southern China is present between the midlatitude blocking pattern and west Pacific subtropical high (WPSH) (Fig. 3b). A rising motion is diagnosed ahead (southeast) of the trough (Fig. 3b).

Fig. 3.

Mean synoptic fields averaged over 0000 UTC 9 Jun to 0000 UTC 13 Jun 2012 from ERA-Interim (10°–60°N, 105°–170°E). (a) The 300-hPa-level geopotential heights every 50 gpm (solid). (b) The 850-hPa-level geopotential heights every 20 gpm (contoured) and 500-hPa-level vertical motions (Pa s−1; shaded).

Fig. 3.

Mean synoptic fields averaged over 0000 UTC 9 Jun to 0000 UTC 13 Jun 2012 from ERA-Interim (10°–60°N, 105°–170°E). (a) The 300-hPa-level geopotential heights every 50 gpm (solid). (b) The 850-hPa-level geopotential heights every 20 gpm (contoured) and 500-hPa-level vertical motions (Pa s−1; shaded).

Around 0000 UTC 10 June, a southwest vortex is generated on the lee side of the Tibetan Plateau (Chen et al. 1994, 1997; Chang et al. 2000) (not shown), propagates eastward, and develops into a mei-yu frontal cycle. At 1200 UTC 11 June, 2 h before the commencement of extreme precipitation over northern Taiwan, the 850-hPa mei-yu frontal cyclone has moved off the eastern China coast (Fig. 4b) with a trough axis extending southwestward just north of the northern Taiwan coast. A west-southwesterly LLJ is present south of the trough axis (Fig. 4b). Ahead of the trough axis, the winds turn clockwise with respect to height (Figs. 4a,b), indicating warm advection within the warm sector. At lower levels, both the 925-hPa trough axis (Fig. 4c) and mei-yu front (Fig. 4d) propagated southward and were just off the northern Taiwan coast at 1200 UTC 11 June.

Fig. 4.

Synoptic fields from ERA-Interim (10°–60°N, 105°–170°E) at 1200 UTC 11 Jun. (a) The 500-hPa-level geopotential heights every 50 m and winds (m s−1) (one pennant, full barb, and half barb represent 25, 5, and 2.5 m s−1, respectively). (b) As in (a), but for the 850-hPa level. Geopotential heights every 30 gpm, winds, and equivalent potential temperature every 3 K (color shaded). (c) As in (a), but for the 925-hPa level. (d) As in (a), but for sea level pressure (every 2 hPa), surface temperature (°C; color shaded), and surface winds.

Fig. 4.

Synoptic fields from ERA-Interim (10°–60°N, 105°–170°E) at 1200 UTC 11 Jun. (a) The 500-hPa-level geopotential heights every 50 m and winds (m s−1) (one pennant, full barb, and half barb represent 25, 5, and 2.5 m s−1, respectively). (b) As in (a), but for the 850-hPa level. Geopotential heights every 30 gpm, winds, and equivalent potential temperature every 3 K (color shaded). (c) As in (a), but for the 925-hPa level. (d) As in (a), but for sea level pressure (every 2 hPa), surface temperature (°C; color shaded), and surface winds.

The north–south vertical cross sections along 119.5°E constructed from ERA-Interim show that the mei-yu front is characterized by a marked vertical tilt with significant wind shift up to at least the 600-hPa level with an upper-level jet (>40 m s−1; ULJ) at the 250-hPa level (Fig. 5a). With a significant midlatitude omega blocking pattern, persistent northerlies from west of the northeast China low extended all the way to the subtropics (Fig. 4b). Furthermore, the low-level frontal system, including the midlevel wind shift associated with the trough axis at the 700-hPa level, reaches south of 27°N (Fig. 5).

Fig. 5.

Vertical cross section along 119.5°E for 1200 UTC (2000 LT) 11 Jun. (a) Equivalent potential temperature (solid white lines; every 5 K), relative humidity (%; color shaded), and horizontal winds (m s−1; one pennant, full barb, and half barb represent 25, 5, and 2.5 m s−1, respectively). (b) Vertical motion (Pa s−1; <0 Pa s−1, contoured every 0.3 Pa s−1) and horizontal moisture flux (vectors with magnitude color shaded every 30 g kg−1 m s−1).

Fig. 5.

Vertical cross section along 119.5°E for 1200 UTC (2000 LT) 11 Jun. (a) Equivalent potential temperature (solid white lines; every 5 K), relative humidity (%; color shaded), and horizontal winds (m s−1; one pennant, full barb, and half barb represent 25, 5, and 2.5 m s−1, respectively). (b) Vertical motion (Pa s−1; <0 Pa s−1, contoured every 0.3 Pa s−1) and horizontal moisture flux (vectors with magnitude color shaded every 30 g kg−1 m s−1).

In the lower troposphere, the strong (>15 m s−1), warm, moist LLJ with high equivalent potential temperature (>365 K) converges with the relatively cold, dry northeasterly flow with low equivalent potential temperatures (<350 K) in the postfrontal region (Figs. 5a,b). In the prefrontal region, the horizontal moisture fluxes mainly occur below 700 hPa with a maximum at the 950-hPa level. In the frontal zone, large-scale rising motions associated with the jet–front system exceed 0.9 Pa s−1 (Fig. 5b), bringing low-level warm, moist air vertically upward (Fig. 5a). It is striking that the horizontal fluxes from the northern South China Sea mainly occur below the 850-hPa level with a maximum >360 g kg−1 m s−1 at the 950-hPa level (Fig. 5b). This issue will be investigated further in the future.

b. Rainfall over Taiwan

On 10 and 11 June 2012, under the moist unstable prevailing southwesterly flow, daily rainfall accumulation of more than 350 mm is recorded on the windward side of the Snow Mountains and Ali Mountains (Fig. 1b) of CMR (Figs. 6a,b). In addition, heavy rainfall is recorded over the northwestern coast of Taiwan and the Taipei basin, with the maximum accumulated rainfall from 2200 LST 11 June to 1200 LST 12 June about 434.5 and 476.5 mm at Shuei-Wei (24.94°N, 121.08°E, z = 106 m) and San-Xia (24.94°N, 121.36°E, z = 55 m) (Fig. 1a), respectively (Chu 2013). The heavy rainfall occurs in northern Taiwan with an axis in the ENE–WSW direction (Fig. 6c). The reasons for the observed localized extreme precipitation maxima over the northwestern coast and within the Taipei basin (Figs. 6c,d) will be the main foci of this study.

Fig. 6.

(a) Daily (0000–2400 LST) rainfall accumulation (mm; color shaded) for 10 Jun. (b) As in (a), but for 11 Jun. (c) As in (a), but for 12 Jun. (d) Rainfall accumulation (mm) during 10–12 Jun. Terrain contours are 100 and 500 m.

Fig. 6.

(a) Daily (0000–2400 LST) rainfall accumulation (mm; color shaded) for 10 Jun. (b) As in (a), but for 11 Jun. (c) As in (a), but for 12 Jun. (d) Rainfall accumulation (mm) during 10–12 Jun. Terrain contours are 100 and 500 m.

4. Favorable conditions for the occurrences of heavy rainfall

a. The storm environment with high moisture content

The climatological TPW over the Taiwan area in early June is about 50–55 kg m−2 (Kerns et al. 2010). The horizontal distribution of daily (0000–2400 UTC) mean TPW on 11 June from ERA-Interim shows a moisture axis (TPW > 70 kg m−2) that is ~30% higher than the climatological values and extends from the southern China coast to over Taiwan and the western Pacific (Fig. 7a). The horizontal axis of the maximum low-level moisture fluxes reaches as high as 300 g kg−1 m s−1 (Figs. 7b,c). The maximum low-level moisture convergence (>2.5 × 10−4 g kg−1 s−1) occurs where the strong prefrontal southwesterly flow converges with the postfrontal northeasterlies over the southern China coast and northern Taiwan (Figs. 7a,b). For the 11 extreme precipitation cases (>350 mm day−1) over southwestern Taiwan in May–June during 1997–2006, the upstream maximum low-level moisture fluxes over Taiwan range from 120 to 270 g kg−1 m s−1 (Chen et al. 2007b). Thus, for this case, the low-level horizontal moisture transport toward the frontal zone is much higher than these 11 extreme torrential rain cases. During 10–12 June, heavy precipitation is recorded on the windward side of the Snow Mountains (>1000 mm) and Ali Mountains (>1500 mm) (Fig. 6d) as the warm, moist LLJ impinges on CMR at a relatively large angle (Fig. 4b). A potentially unstable LLJ with high moisture content impinging on steep terrain during the approach of a short-wave trough is favorable for the occurrence of extreme orographic precipitation (Lin et al. 2001).

Fig. 7.

The daily averaged (a) TPW (every 5 mm; color shaded), and 950-hPa horizontal divergence of water vapor (blue contours; <0 g kg−1 s−1, contoured every 2.5 × 10−4 g kg−1 s−1) from ERA-Interim (10°–60°N, 105°–170°E) for 11 Jun. (b),(c) As in (a), but for daily averaged geopotential height (gpm) and moisture flux (vectors with magnitude color shaded; g kg−1 m s−1) at 950- and 850-hPa level, respectively.

Fig. 7.

The daily averaged (a) TPW (every 5 mm; color shaded), and 950-hPa horizontal divergence of water vapor (blue contours; <0 g kg−1 s−1, contoured every 2.5 × 10−4 g kg−1 s−1) from ERA-Interim (10°–60°N, 105°–170°E) for 11 Jun. (b),(c) As in (a), but for daily averaged geopotential height (gpm) and moisture flux (vectors with magnitude color shaded; g kg−1 m s−1) at 950- and 850-hPa level, respectively.

b. Evolution of the subtropical cold front over the Taiwan area

At 1800 UTC 11 June (0200 LST 12 June), the leading edge of the surface front reached the Taipei basin (Fig. 8a). A secondary surface low was located at 25°N, 118.5°E over the southeastern China coast. At this time, the 850-hPa trough axis associated with the surface front is just off the northern Taiwan coast (Fig. 8b). This is in contrast to some of the frontal cases found during TAMEX cases (e.g., Chen et al. 1989; Chen and Hui 1990, 1992; Trier et al. 1990). For these cases, the 850-hPa trough axis remained over southern China as the low-level cold air penetrated and propagated southward with shallow (<1 km) postfrontal northeasterlies over the Taiwan area. Before 0800 LST, the mei-yu front stalls within the Taipei basin (Fig. 8c). Along the eastern coast of Taiwan, the mei-yu front propagates southward and is ~23°N at 0800 LST 12 June (Fig. 8c). In the meantime, the 850-hPa trough axis arrives at the northern coast of Taiwan (Fig. 8d).

Fig. 8.

Regional maps from ERA-Interim. (a) Surface map at 1800 UTC 11 Jun (0200 LST 12 Jun). Isotherms (color shaded; every 1°C), mean sea level pressure (green contours; every 2 hPa), and winds (m s−1; one full barb and half barb represent 5 and 2.5 m s−1, respectively). The heavy solid line denotes the approximate location of the surface front. (b) As in (a), but for 850-hPa-level geopotential heights every 15 m, equivalent potential temperature every 3 K (color shaded), and winds (m s−1). (c),(d) As in (a),(b), but for 0000 UTC (0800 LST) 12 Jun.

Fig. 8.

Regional maps from ERA-Interim. (a) Surface map at 1800 UTC 11 Jun (0200 LST 12 Jun). Isotherms (color shaded; every 1°C), mean sea level pressure (green contours; every 2 hPa), and winds (m s−1; one full barb and half barb represent 5 and 2.5 m s−1, respectively). The heavy solid line denotes the approximate location of the surface front. (b) As in (a), but for 850-hPa-level geopotential heights every 15 m, equivalent potential temperature every 3 K (color shaded), and winds (m s−1). (c),(d) As in (a),(b), but for 0000 UTC (0800 LST) 12 Jun.

Time series of wind and thermodynamic variables are constructed for Bancio rawinsonde data every 12 h from 1200 UTC 10 June to 1200 UTC 13 June. Prior to 0000 UTC 12 June, strong, low-level, warm, moist southwesterly winds with equivalent potential temperature >360 K are present (Fig. 9). The prefrontal southwesterly flow turns clockwise with respect to height and extends up to the 650-hPa level, indicating warm air advection. At 0000 UTC 12 June, the low-level winds were weak, cold, drier northeasterlies as the surface cold front arrives. Above the 950-hPa level, the wind shifts from northeasterlies to northwesterlies and turns counterclockwise with respect to height (Fig. 9a) as the trough axis arrives (Fig. 8d). After 0000 UTC, the postfrontal cold, dry air extends upward to above the 850-hPa level (Fig. 9a). The heaviest rainfall periods over northern Taiwan occur during the passage of the mei-yu front/850-hPa trough (Figs. 8, 9).

Fig. 9.

Time series of winds (one pennant, full barb, and half barb represent 25, 5, and 2.5 m s−1, respectively) and potential temperature (K; color shaded) profiles from 1200 UTC 10 Jun to 1200 UTC 13 Jun constructed from rawinsonde data collected at Banciao (Fig. 1b) every 12 h. (b) As in (a), but for water vapor mixing ratio (g kg−1; color shaded) and equivalent potential temperature (K; contoured).

Fig. 9.

Time series of winds (one pennant, full barb, and half barb represent 25, 5, and 2.5 m s−1, respectively) and potential temperature (K; color shaded) profiles from 1200 UTC 10 Jun to 1200 UTC 13 Jun constructed from rawinsonde data collected at Banciao (Fig. 1b) every 12 h. (b) As in (a), but for water vapor mixing ratio (g kg−1; color shaded) and equivalent potential temperature (K; contoured).

c. Evolution of precipitation patterns over northern Taiwan and its vicinity

1) Radar echoes

At 2000 LST 11 June, an ENE–WSW-oriented radar echoes line (L1) associated with the mei-yu front is off the northern coast of Taiwan (Fig. 10). To the south of L1, there are scattered prefrontal echoes (C1) over the northern part of the Taiwan Strait. There are persistent radar echoes on the windward side of the Snow Mountains and Ali Mountains as the moisture-laden LLJ impinges on CMR. The heaviest rainy period over the northwest coastal region (Shuei-Wei) occurs during 2200 LST 11 June–0100 LST 12 June as the prefrontal echo area (C1) and the radar echo line L1 move inland.

Fig. 10.

Composite radar reflectivities at 1200 UTC (2000 LST) 11 Jun. The heavy solid line denotes the approximate position of the surface front. The ENE–WSW-oriented radar echoes line is denoted by L1. The radar echoes that originated from the southwestern coast of China are denoted by C1.

Fig. 10.

Composite radar reflectivities at 1200 UTC (2000 LST) 11 Jun. The heavy solid line denotes the approximate position of the surface front. The ENE–WSW-oriented radar echoes line is denoted by L1. The radar echoes that originated from the southwestern coast of China are denoted by C1.

During 2000–2200 LST, the frequency distribution of radar echoes exceeding 40 dBZ at 3-km height shows a maximum associated with L1 over the adjacent ocean northwest of Taiwan (Fig. 11a). A secondary maximum related to prefrontal radar echoes (C1) is also evident. The frequency distribution of radar echoes exceeding 40 dBZ at 3-km height during 2200 LST 11 June–1300 LST 12 June (Fig. 11b) shows that the high-frequency area (exceeding 30%) extended from the northwest coast to the Taipei basin.

Fig. 11.

(a) Occurrences (%) of radar echoes from the Wu-Fen-Shan Doppler radar exceeding 40 dBZ at z = 3 km from 2000 to 2200 LST 11 Jun (color shaded). The solid black line represents the 30% of the occurrence of radar echoes exceeding 30 dBZ at z = 3 km. (b) As in (a), but from 2200 LST 11 Jun to 1300 LST 12 Jun. The terrain contours (gray line) are 500 m.

Fig. 11.

(a) Occurrences (%) of radar echoes from the Wu-Fen-Shan Doppler radar exceeding 40 dBZ at z = 3 km from 2000 to 2200 LST 11 Jun (color shaded). The solid black line represents the 30% of the occurrence of radar echoes exceeding 30 dBZ at z = 3 km. (b) As in (a), but from 2200 LST 11 Jun to 1300 LST 12 Jun. The terrain contours (gray line) are 500 m.

2) Hourly rainfall patterns

Prior to 2000 LST 11 June, no rainfall was recorded over northern Taiwan (Fig. 12a) before the arrival of C1 and L1 (Fig. 10). By 2200 LST 11 June, as the radar echoes associated with the mei-yu front moved southeastward inland, heavy rainfall commenced over the northern coast (Fig. 12b). The heaviest period over the northwestern Taiwan coast occurs before 0200 LST 12 June (Fig. 12c) due to the arrival of C1, followed by the arrival of L1 (Fig. 10). By 0000 LST 12 June, winds over the Taipei basin turn from southwesterlies to northerlies (Fig. 13c). The relatively deep (~1.5 km) cold front is able to move over the Yang-Ming Mountains (highest peak ~1121 m) over the northern tip of Taiwan into the Taipei basin.

Fig. 12.

Hourly rainfall (mm) and surface winds (one full barb and half barb represent 5 and 2.5 m s−1, respectively) over northern Taiwan: (a) 2000 and (b) 2200 LST 11 Jun; (c) 0000, (d) 0200, (e) 0400, (f) 0600, (g) 0800, and (h) 1000 LST 12 Jun. Terrain contours are 100 and 500 m, respectively.

Fig. 12.

Hourly rainfall (mm) and surface winds (one full barb and half barb represent 5 and 2.5 m s−1, respectively) over northern Taiwan: (a) 2000 and (b) 2200 LST 11 Jun; (c) 0000, (d) 0200, (e) 0400, (f) 0600, (g) 0800, and (h) 1000 LST 12 Jun. Terrain contours are 100 and 500 m, respectively.

Fig. 13.

Model results from the 9-km domain for 21°–30°N, 116°–130°E. (a) Sea level pressure (every 2 hPa), surface winds (one full barb and half barb represent 5 and 2.5 m s−1, respectively), and temperature every 1°C for 1200 UTC (2000 LST) 11 Jun. (b) Simulated 850-hPa geopotential heights every 15 gpm (blue solid lines), winds (m s−1), and equivalent potential temperature (K; shaded) for 1200 UTC (2000 LST) 11 Jun. The dashed line denotes the approximation position of the 850-hPa trough. The areas with ascending motion greater than 0.1 m s−1 are contoured in red; L denotes the location of the synoptic low pressure center. (c),(d) As in (a),(b), but for 0000 UTC (0800 LST) 12 Jun.

Fig. 13.

Model results from the 9-km domain for 21°–30°N, 116°–130°E. (a) Sea level pressure (every 2 hPa), surface winds (one full barb and half barb represent 5 and 2.5 m s−1, respectively), and temperature every 1°C for 1200 UTC (2000 LST) 11 Jun. (b) Simulated 850-hPa geopotential heights every 15 gpm (blue solid lines), winds (m s−1), and equivalent potential temperature (K; shaded) for 1200 UTC (2000 LST) 11 Jun. The dashed line denotes the approximation position of the 850-hPa trough. The areas with ascending motion greater than 0.1 m s−1 are contoured in red; L denotes the location of the synoptic low pressure center. (c),(d) As in (a),(b), but for 0000 UTC (0800 LST) 12 Jun.

During 0200–0400 LST 12 June, heavy rains continue over the northwestern coast after the frontal passage and extend eastward over the Taipei basin (Figs. 12d,e). An easterly offshore flow develops along the northwestern coast (Figs. 12c–e) due to combined cooling from rain evaporation and nocturnal cooling. After the frontal passage, localized convergence is present between the barrier jet and the offshore flow. In the early morning (0400–0800 LST), a well-defined heavy rainfall axis extends from the northwestern coast to the Taipei basin (Figs. 12e–g). The rain cells and surface cold front are anchored along the northwestern foothills of the Snow Mountains. After 0800 LST 12 June, the heavy rainfall area propagates southward (Fig. 12h) as the cold front advances southward.

In summary, the rainfall maximum along the northwestern coastal area during 2200 LST 11 June and 0200 LST 12 June is mainly related to the arrival of prefrontal radar echoes followed by the ENE–WSW-oriented convective line associated with the mei-yu front. As model results will later show, during this period, the convective activities over the northwestern coast are enhanced by the localized convergence between the southerly barrier jet along the northwestern coast and postfrontal west-northwesterly flow. The terrain further enhances the southeastward-propagating echoes. After the frontal passage, localized convergence is present between the barrier jet and the offshore flow. Over the Taipei basin, the heaviest rainfall period occurs during 0200–0800 LST 12 June as the mei-yu front arrives and stalls over the basin. During this period, the depth of the postfrontal air is deeper than the coastal terrain north of the basin with peaks of ~1120 m. Thus, the top of the postfrontal northwesterly-northerly flow is above the terrain over the northern tip of Taiwan. As a result, the postfrontal cold air is able to move into the Taipei basin and is held against the north-northwestern slopes of the Snow Mountains south of the Taipei basin. Rain cells propagate southeastward in the frontal zone and continue to produce heavy precipitation within the basin. The heavy precipitation within the Taipei basin diminishes after 0800 LST as the front advances southward. For this case, it appears that orographic effects are important for the timing and locations of the occurrences of heavy precipitation as the mei-yu front arrives and will be discussed further using the results of the model simulations.

5. Numerical simulations

In this section, model results are used to diagnose orographic interactions for the occurrences of heavy precipitation. First, the evolution of subsynoptic weather patterns and the surface cold front are simulated. Then, the impacts of terrain on the jet–front system and occurrences of heavy precipitation are diagnosed based on a model sensitivity test by comparing the results of the CTRL run with those of the NT run.

a. Simulated weather patterns

At 1200 UTC (2000 LST) 11 June, the simulated mei-yu front at the surface is off the northern Taiwan coast (Fig. 13a). The simulated winds immediately behind the cold front are west-northwesterlies and turn to northerlies farther to the north. The simulated 850-hPa trough in the 9-km domain (Fig. 13b) extends from a low pressure center over the East China Sea to the southeastern China coast. A secondary low is simulated over the southeastern coast of China. A warm, moist tongue with high equivalent potential temperature is simulated ahead of the 850-hPa trough axis (Fig. 13b). The simulated trough axis and warm, moist tongue in the warm sector are consistent with observations (Fig. 4b).

At 0000 UTC (0800 LST) 12 June, the simulated 850-hPa trough axis moves southeastward (Fig. 13d) and is off the northern Taiwan coast and northeastern Taiwan Strait with a secondary low along the southeastern China coast. Winds at the 850-hPa level have a large westerly component impinging on the northwesterly slopes of the Snow Mountains. The western part of the simulated frontal position at the surface is over the northwestern coast with northeasterly winds behind the cold front (Fig. 13c). The simulated northeasterly winds at the surface with northwesterly winds aloft are consistent with the wind profile observed at Bancio at this time (Fig. 9a). Along the eastern Taiwan coast, the mei-yu front moves southward to the southeastern coast. The simulated weather patterns at both the 850-hPa level and the surface (Figs. 13c,d) are in agreement with observations (Figs. 8c,d).

b. The simulated evolution of the subtropical cold front over the Taiwan area

The simulated model results of the evolution of the surface front over the Taiwan area from the 3-km domain are shown in Fig. 14. At 2000 LST 11 June, the simulated mei-yu front, represented by changes in surface wind direction and large temperature gradients, is just north of the northern Taiwan coast (Fig. 14a). Over the southwestern Taiwan coast, the incoming LLJ decelerates as a result of orographic blocking (Fig. 14a). Enhanced rising motion at the 850-hPa level is simulated off the northwestern coast. Along Line AB in Fig. 14a, the orographically deflected south-southwesterly flow along the west coast accelerates downstream (Figs. 14a, 15a). At 2200 LST 11 June, the enhanced rising motion is simulated in the convergence zone over the northwestern coast (Fig. 14b).

Fig. 14.

Simulated surface winds (one full barb and half barb represent 5 and 2.5 m s−1, respectively), temperature (every 1°C; blue solid lines), and 850-hPa vertical motions (m s−1; color shaded) for the 3-km grid domain: (a) 2000 and (b) 2200 LST 11 Jun; (c) 0200 and (d) 0800 LST 12 Jun.

Fig. 14.

Simulated surface winds (one full barb and half barb represent 5 and 2.5 m s−1, respectively), temperature (every 1°C; blue solid lines), and 850-hPa vertical motions (m s−1; color shaded) for the 3-km grid domain: (a) 2000 and (b) 2200 LST 11 Jun; (c) 0200 and (d) 0800 LST 12 Jun.

Fig. 15.

Vertical cross section along line AB (Fig. 14a) at 2000 LST (1200 UTC) 11 Jun. (a) Simulated meridional winds (m s−1; contoured) and simulated vertical motions (m s−1; color shaded). (b) As in (a), but for the NT run.

Fig. 15.

Vertical cross section along line AB (Fig. 14a) at 2000 LST (1200 UTC) 11 Jun. (a) Simulated meridional winds (m s−1; contoured) and simulated vertical motions (m s−1; color shaded). (b) As in (a), but for the NT run.

At 0200 LST 12 June, the simulated mei-yu front moves over the Yang-Ming Mountains along the northern coast and arrives at the Taipei basin (Fig. 14c). From 0000 to 0800 LST 12 June (Figs. 14b–d), the simulated mei-yu front stalls over the Taipei basin with persistent rising motion at the 850-hPa level. The simulated postfrontal west-northwesterlies impinge on the north-northwestern slopes of the Snow Mountains south of the basin (Figs. 14b,c). After 0800 LST 12 June, the postfrontal flow at the surface shifts to strong northeasterlies (Fig. 14d). Concurrently, the mei-yu front moves southward (Fig. 14d), ending this heavy rainfall episode over northern Taiwan.

c. Orographic effects on heavy rainfall occurrences over northern Taiwan

In the CTRL run, at 2000 LST 11 June, the maximum meridional wind component along the cross-sectional line AB (Fig. 14a) exceeds >20 m s−1 (Fig. 15a). Furthermore, the simulated convergence zone over the northwestern coast between the southerly barrier jet and postfrontal westerlies extends well above the 900-hPa level (Fig. 15a). In contrast, for the NT run, the maximum meridional wind component along the cross section is less than 12 m s−1 (Fig. 15b). The convergence zone in the NT run (Fig. 15b) is also much shallower, weaker, and farther south, compared to the CTRL run. At 2200 LST 11 June, the prefrontal southwesterly flow converges with the postfrontal westerly flow over northern Taiwan (Fig. 16a) without a barrier jet along the northwestern coast. As a result, the simulated radar reflectivities over the northeastern Taiwan Strait and northwestern coast of Taiwan (Fig. 17b are much weaker in the NT run than the CTRL run (Fig. 17a).

Fig. 16.

As in Fig. 14, but for the NT run at (a) 2200 LST 11 Jun and (b) 0200 LST 12 Jun.

Fig. 16.

As in Fig. 14, but for the NT run at (a) 2200 LST 11 Jun and (b) 0200 LST 12 Jun.

Fig. 17.

(a) Simulated 950-hPa-level winds (m s−1; vectors) and maximum radar reflectivity (every 5 dBZ; color shaded) for the 3-km grid domain at 2200 LST 11 Jun. Terrain contours are 200, 500, and 1500 m. (b) As in (a), but for the NT run. (c),(d) As in (a),(b), but for 0200 LST 12 Jun.

Fig. 17.

(a) Simulated 950-hPa-level winds (m s−1; vectors) and maximum radar reflectivity (every 5 dBZ; color shaded) for the 3-km grid domain at 2200 LST 11 Jun. Terrain contours are 200, 500, and 1500 m. (b) As in (a), but for the NT run. (c),(d) As in (a),(b), but for 0200 LST 12 Jun.

At 0200 LST 12 June, the simulated radar reflectivities associated with the mei-yu front in the CTRL run are over the Taipei basin as the mei-yu front stalls there (Fig. 17c). In addition to frontal lifting, radar echoes are anchored by persistent lifting over the north-northwestern slopes of the Snow Mountains under postfrontal north-northwesterlies (Fig. 17c). Note that with cold advection in the postfrontal region, at 0000 UTC 12 June, the low-level cold northeasterly wind turns counterclockwise with respect to height with a westerly wind component (Fig. 9a). After landfall, the simulated 850-hPa-level winds have a large westerly component impinging on the northwestern slopes of the Snow Mountains (Fig. 13b). In the NT run, however, the mei-yu front continues to move southward after landfall (Fig. 16b), with simulated radar echoes south of the Taipei basin (Fig. 17d).

d. Rainfall simulation from the nested 1-km grid domain

The simulated accumulated rainfall during 2000 LST 11 June–1500 LST 12 June from the 1-km grid domain exhibits a maximum rainfall axis oriented in an ENE–WSW direction (Fig. 18a). The simulated rainfall at Shuei-Wei over the northwestern coastal area is >400 mm, and it is >300 mm at San-Xia over the Taipei basin (Figs. 1a, 18a). The simulated rainfall amount over the northwestern coast is consistent with observations but less than the observed values within the Taipei basin and along the northwestern slopes of the Snow Mountains (Figs. 18a,c). For the NT run, the simulated maximum rainfall accumulation over northern Taiwan (Fig. 18b) is much lower than in the CTRL run (Fig. 18a) and does not have a rainfall maximum axis over the Taipei basin.

Fig. 18.

(a) The simulated rainfall accumulation (mm) during 2000 LST 11 Jun–1500 LST 12 Jun from the 1-km grid domain and winds at 1500 LST 12 Jun. Terrain contours (blue lines) are 200 and 500 m. The wind speed (m s−1) is specified at the bottom of the figure. (b) As in (a), but for the NT run. (c) As in (a), but for the observed rainfall accumulation (mm) from rain gauges.

Fig. 18.

(a) The simulated rainfall accumulation (mm) during 2000 LST 11 Jun–1500 LST 12 Jun from the 1-km grid domain and winds at 1500 LST 12 Jun. Terrain contours (blue lines) are 200 and 500 m. The wind speed (m s−1) is specified at the bottom of the figure. (b) As in (a), but for the NT run. (c) As in (a), but for the observed rainfall accumulation (mm) from rain gauges.

Our results attest that under favorable large-scale conditions, localized convergence over the northwestern coast between the barrier jet and the postfrontal northerly wind component during landfall of the mei-yu front is the main reason for the observed coastal rainfall maximum over northwestern Taiwan. The propagating mei-yu front is slowed down by the island terrain and stalls within the Taipei basin. Anchoring of the relatively deep (>1.5 km) mei-yu front at the foothills of the Snow Mountains under postfrontal west-northwesterlies at the 850-hPa level along with persistent orographic lifting aloft are the main factors to account for the occurrence of localized heavy rainfall within the Taipei basin. A schematic diagram showing the front–terrain interactions over the Taipei basin is given in Fig. 19.

Fig. 19.

Schematic front–terrain interaction for a relatively deep (>1.5 km) mei-yu front that moved over the terrain along the northern coast and stalled within the Taipei basin for more than 6 h. The schematic diagram shows the surface flow patterns (solid arrows) and frontal position and 850-hPa postfrontal wind direction over northern Taiwan (red arrows).

Fig. 19.

Schematic front–terrain interaction for a relatively deep (>1.5 km) mei-yu front that moved over the terrain along the northern coast and stalled within the Taipei basin for more than 6 h. The schematic diagram shows the surface flow patterns (solid arrows) and frontal position and 850-hPa postfrontal wind direction over northern Taiwan (red arrows).

The back building (BB) process of the linear rainband associated with this mei-yu front case is investigated by Wang et al. (2016) from radar PPI data over the ocean, ocean surface winds, and high-resolution (1.5 km) modeling. The BB rainbands during the mei-yu season have been previously reported by Li et al. (1997) and Xu et al. (2012). For the case studied by Xu et al. (2012), cold pools from evaporative cooling play an important role for the initiation of new cells. For this case, Wang et al. (2016) suggest that the new cell initiation in the BB process could possibly occur without the cold pool dynamics.

6. Conclusions

During this extreme precipitation event, the large-scale airflow is characterized by a midlatitude omega blocking pattern with a blocking ridge over the Okhotsk Sea sandwiched between a northeast China low and Aleutian low for more than 4–5 days (9–13 June 2012). At the 850-hPa level, an ENE–WSW-oriented monsoon trough is located over southern China between the midlatitude blocking pattern and WPSH.

Around 0000 UTC 10 June, a southwest vortex is generated on the lee side of the Tibetan Plateau, migrates eastward, and develops into a mei-yu frontal cyclone. It moves off the southeastern China coast around 1200 UTC 11 June with a trough axis extending southwestward just north of the Taiwan coast. At the surface, the mei-yu front is just off the northern Taiwan coast. It is characterized by a marked vertical tilt with an upper-level jet (>40 m s−1) at the 250-hPa level. In the lower troposphere, the prefrontal potentially unstable WSW flow (>15 m s−1) converges with the postfrontal cold northeasterly flow with rising motions (>0.9 Pa s−1) in the frontal zone. With a significant midlatitude omega blocking pattern, persistent northerlies west of the northeast China low and west of the mei-yu frontal cyclone extend all the way to the subtropics and up to the 700-hPa level. The frontal system, including the trough axis associated with the frontal cyclone at the 700 hPa, reaches south of 27°N.

During 10–12 June 2012, a moist axis with TPW > 70 kg m−2, which is more than 30% higher than the climatological values during this time of the year, extends from the southern China coast to over Taiwan and farther eastward over the western Pacific. In addition, the horizontal axis of the maximum low-level moisture fluxes at the 950-hPa level reaches as high as 360 g kg−1 m s−1. Under favorable large-scale settings, a strong (>15 m s−1) persistent LLJ with elevated TPW impinges on the steep terrain at a relatively large angle. As a result, heavy orographic precipitation occurs on the windward side of both the Snow (>1000 mm) and Ali Mountains (>1500 mm) during 10–12 June.

During 11–12 June, heavy precipitation occurs over the northwestern Taiwan coast (~435 mm) and within the Taipei basin (~477 mm) as the mei-yu front arrives. The rainfall maximum along the northwestern coast mainly occurs during the landfall of the mei-yu front and before 0200 LST 12 June. The convective activities in the frontal zone are enhanced by the localized convergence between the prefrontal barrier jet and the postfrontal cold air along the northwestern coast. After the frontal passage, localized convergence is present between the barrier jet and the offshore flow, which is caused by combined nocturnal cooling and rain evaporative cooling.

Over the Taipei basin, with a relatively deep (~1.5 km) mei-yu front, the top of the postfrontal air is above the Yang-Ming Mountains (with peaks ~1120 m) along the northern Taiwan coast. As a result, postfrontal cold air is able to move into the Taipei basin and is held against the northwestern end of the Snow Mountains. With cold advection behind the cold front, the low-level northeasterly winds turn counterclockwise with respect to height and become northwesterlies at the 850-hPa level. The mei-yu front stalls over the Taipei basin during 0200–0800 LST 12 June with persistent heavy showers as the postfrontal northwesterly flow impinges on the northwestern slopes of the Snow Mountains. After 0800 LST 12 June, the postfrontal flow at the surface shifts to strong northeasterlies. Concurrently, the mei-yu front moves southward, ending this heavy rainfall episode over northern Taiwan. In contrast, along the east coast, the leading edge of the mei-yu front reaches 23°N off the southeastern coast at 0800 LST 12 June.

The barrier jet along the coast and rainfall maxima over the northwestern coast and within the Taipei basin are all well simulated using the high-resolution (1 km) WRF Model with two-way nesting procedures. With the model terrain removed, the simulated mei-yu front continues to move southward after landfall without reproducing the barrier jet and the observed rainfall maxima along the northwestern coast and within the Taipei basin.

Acknowledgments

This work is jointly funded by the Taiwan Ministry of Science and Technology (MOST) under Grant MOST 104-2923-M-008-003-MY5 and the Featured Areas Research Center Program within the framework of the Higher Education Sprout Project by the Ministry of Education (MOE) to the National Central University and the National Science Foundation under Grant AGS-1142558 to the University of Hawai‘i at Mānoa. We thank May Izumi for editing the text.

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