Abstract

This study investigates the statistical characteristics of extreme hourly precipitation over Taiwan during 2003–12 that exceeds the 5-, 10-, and 20-yr return values and 100 mm h−1. All the extreme precipitation records are classified into four types according to the synoptic situations under which they occur: tropical cyclones (TCs), fronts, weak-synoptic forcing, and vortex/shear line types. The TC type accounts for over three-quarters of the total records, while the front type and weak-synoptic forcing type are comparable (9%–13%). Extreme hourly precipitation is mostly caused by mei-yu fronts during May–mid-June and by TCs during July–October. The TC type tends to have a long duration time (>12 h) with a symmetrical evolution of hourly rainfall intensity, while the front type and weak-synoptic forcing type mainly occur over a short period (<6 h) with a slightly asymmetrical evolution pattern. The TC type is further divided into seven subtypes according to the location of the TC center relative to the island. When the TC center is over the island or near the coastline (distance <100 km), the spatial distribution of subtypes I–IV is largely determined by the interaction between the TC circulation and topography when a TC center is over the northwest, south, east, or northeast portion of Taiwan, respectively. When the TC center is far away (distance >100 km) from the island, the strength of the environmental southwesterly or northeasterly winds and the impingement of TC circulation on the east side of the Central Mountain Range are also key factors determining the spatial distribution of subtypes V–VII.

1. Introduction

Taiwan is a mesoscale island located in the East Asian monsoon region and is subject to the northeasterly monsoon during the cold season (September–April) and the southwesterly monsoon during the warm season (May–August) (Tao and Chen 1987). Severe weather systems embedded in the prevailing monsoonal flow passing through Taiwan include mei-yu fronts during the early summer, tropical cyclones (TCs) during May–October, cold fronts in spring or autumn, and cold surges in winter. Meanwhile, the Central Mountain Range (CMR) runs through Taiwan in a nearly north–south direction at an average height of about 2 km and with peaks near 4 km (Fig. 1). The mountainous topography further complicates the temporal and spatial variations of rainfall in Taiwan (Ramage 1971; Yeh and Chen 1998; Chen et al. 2007; Cheung et al. 2008; Lin et al. 2011).

Fig. 1.

Spatial distribution of the threshold values of extreme hourly rainfall with 5-yr return period (mm h−1) at 303 stations over Taiwan. Shading represents the topography. The cities of Taipei, Yilan, and Kaohsiung, as well as the location of Alishan, are labeled with black hollow circles. Two vertical intersecting axes separate Taiwan into four areas: northwest (NW), southwest (SW), southeast (SE), and northeast (NE). The westernmost, southernmost, easternmost, and northernmost locations of Taiwan along the two axes, denoted by black asterisks, are (23.98°N, 120.32°E), (23.20°N, 120.60°E), (23.52°N, 121.48°E), and (25.10°N, 121.75°E), respectively.

Fig. 1.

Spatial distribution of the threshold values of extreme hourly rainfall with 5-yr return period (mm h−1) at 303 stations over Taiwan. Shading represents the topography. The cities of Taipei, Yilan, and Kaohsiung, as well as the location of Alishan, are labeled with black hollow circles. Two vertical intersecting axes separate Taiwan into four areas: northwest (NW), southwest (SW), southeast (SE), and northeast (NE). The westernmost, southernmost, easternmost, and northernmost locations of Taiwan along the two axes, denoted by black asterisks, are (23.98°N, 120.32°E), (23.20°N, 120.60°E), (23.52°N, 121.48°E), and (25.10°N, 121.75°E), respectively.

TCs are the most threatening weather systems affecting Taiwan and the TC-related precipitation remains one of the most important and challenging issues for both research and forecast operations in Taiwan (Wu et al. 2016). A series of TCs with extraordinary amounts of rainfall have influenced Taiwan in the twenty-first century (Chang et al. 2013). The TC-related rainfall amount in Taiwan is closely associated with the TC duration time and the location of their tracks relative to the meso-α-scale terrain, but less associated with TC intensity (Chang et al. 2013; Wu et al. 2016). In addition, the topographic effect of the CMR (Chang et al. 1993; Wu et al. 2002), the interaction between TC circulations and the environmental northeasterly–southwesterly winds (Wu et al. 2009; Chen and Wu 2016; Yu and Cheng 2014), and the remote impact from other nearby TCs (Wu et al. 2010) are important factors as well. The mei-yu front, which periodically develops to the north of Taiwan during May–June, can shift southward and provide an effective triggering mechanism for intense and widespread rainfall over the island (Chen 1983; Chen et al. 2008; Lai et al. 2011). Copious rainfall can be produced by preexisting mesoscale convective systems (MCSs) that are embedded in the mei-yu frontal cloud band and drift toward the island to interact with the terrain and local winds (Kuo and Chen 1990; Chen et al. 2007; Xu et al. 2012; Tu et al. 2014; Chang et al. 2015). In early autumn heavy rainfall could also be produced across Taiwan under the influences of a cold front passing by the island from the northwest (Trier et al. 1990; Chien and Kuo 2006).

Previous studies mostly used the hourly rainfall data from about 20 conventional stations to study the long-term statistical features of precipitation in Taiwan, since these stations have kept continuous observations for over half a century (Lu et al. 2007; Chang et al. 2013). However, Wu et al. (2016) have documented that the uneven and very sparse number of conventional stations cannot accurately capture the main features of either precipitation extremes or the rainfall distribution, especially over the mountainous areas. In 1993, the Central Weather Bureau (CWB) of Taiwan began to install automatic stations and used them to aid in flash flood forecasting. To date, there are over 500 automatic stations in Taiwan. Using such a dense surface observation network, many systematic analysis and documentation efforts of the rainfall climatic phenomena over Taiwan have been made. The rainfall amount (light vs heavy) and type (stratiform vs convective) were found to be associated with the thermodynamic stratification and the available moisture content (Chen and Chen 2003). The seasonal variation in rainfall showed a geographical movement in the shape of a west–east seesaw between the summer rainfall over western Taiwan and the fall–winter rainfall over northeastern Taiwan (Chen et al. 1999). The diurnal cycle of rainfall in Taiwan, particularly during the early summer rainy season (mei-yu season), has been investigated extensively through the Taiwan Area Mesoscale Experiment (Kuo and Chen 1990; Johnson and Bresch 1991; Yeh and Chen 1998) and the Southwest Monsoon Experiment/Terrain-influenced Monsoon Rainfall Experiment (Jou et al. 2011; Kerns et al. 2010; Ruppert et al. 2013). Both a weak early morning maximum and a profound afternoon maximum have been identified in the diurnal cycle of precipitation. The weak early morning peak is mainly caused by the convergence between the offshore flow and incoming, decelerating southwesterly flow when the land surface is coldest. While during the day the offshore flow switches to onshore and upslope, deep convection developed in the coastal plains and windward slopes under the influence of strong solar heating.

Relationships between extreme precipitation and the associated synoptic situation have been investigated for some regions globally. For example, Schumacher and Johnson (2005 ,2006) focused on extreme rainfall with daily amounts greater than the 50-yr recurrence threshold in the United States. They found that 65% of the events were associated with MCSs under weak synoptic forcing, 27% were caused by synoptic weather systems (i.e., extratropical cyclones and fronts), and 8% resulted from TCs and their remnants. Nearly all of the cold season events were caused by storms with strong synoptic forcing, while the MCSs were the dominant (74%) producer of the summertime extreme rainfall events. Luo et al. (2016) defined the 99.9th percentile of all rainy hours (with rainfall ≥0.1 mm h−1) during 1981–2015 as the threshold for selecting extreme hourly rainfall in China. They classified nearly 5800 records during 2011–15 into four types according to the relevant synoptic situations—TCs (8.0%), fronts (13.9%), vortex/shear lines (39.1%), and weak-synoptic forcing (39.0%)—and revealed distinctive characteristics in the regional distribution and seasonal or diurnal variations of each type. Both provide forecasters with valuable information of when and where extreme precipitation occurs under a specific set of weather conditions.

However, statistical studies of extreme rainfall in Taiwan are relatively limited in the literature, especially concerning its relationship with the large-scale atmospheric flow patterns. Using the hourly rainfall database derived from the densely distributed rain gauges over Taiwan, combined with weather maps and radar reflectivity images provided by the CWB, this study aims to examine the characteristics of extreme hourly precipitation in Taiwan over a 10-yr period (2003–12). The extreme hourly precipitation records are classified into four types according to the synoptic situations under which they occurred, namely, TCs, fronts, low-level vortex/shear lines, and weak-synoptic forcing. In section 2, the data and methods are presented. The temporal and spatial variations of each type are shown in section 3. Seven subtypes of the TC-related extreme precipitation are described in section 4. Section 5 provides a summary and our conclusions.

2. Data and method

a. Data

As mentioned above, the number of rain gauges in Taiwan has significantly increased since 1993, and there were 348 stations that covered roughly the entire island by the end of 1997 (Central Weather Bureau 1995). Later on, some of the rain gauges were discarded or relocated, as a result of urban construction, transport, railway projects, or other reasons. The total number of rain gauges with continuous observation decreased to 311 in 2012 and to 257 in 2013. For identifying extreme hourly rainfall that covers the same climatological period, 303 stations (Fig. 1) are ultimately selected, each with at least 90% valid records available annually during 1998–2012. Among the 303 stations, 43% are located below 100 m, 31% between 100 and 500 m, 10% between 500 and 1000 m, and the remaining 16% are located above 1000 m. The percentages of the four elevation categories remain largely unchanged since 1990 despite an increase in the total number of rain gauges in Taiwan (Wu et al. 2016).

To help classify the extreme hourly precipitation, the weather maps and radar reflectivity images provided by the CWB and collected by the Chinese Culture University (http://twister.atmos.pccu.edu.tw/ssl/sslbank/), and the TC best track data from the Japan Meteorological Agency Regional Specialized Meteorological Center in Tokyo are used. The weather maps, including the upper-air (500, 700, and 850 hPa) synoptic analyses performed twice daily (0000 and 1200 UTC) and the surface analyses run four times per day (0000, 0600, 1200, and 1800 UTC), are used to check whether there is a synoptic-scale weather system influencing Taiwan when the extreme hourly rainfall occurs. The radar reflectivity images are used to crosscheck with hourly precipitation data whether heavy rainfall truly occurs in that location, and to examine the scale/movement of the associated rainy system. The TC best-track data provide the 6-hourly (or 3 hourly when a TC center moves close to the Taiwan Island) estimates of TC position of all the TCs in the western North Pacific basin since 1951. Moreover, the ERA-Interim data with a spatial resolution of 0.125° × 0.125° (Dee et al. 2011) are used to show the composite environmental thermodynamic and dynamic conditions of extreme precipitation. The variables of the ERA-Interim data used herein include the horizontal wind direction and wind speed, geopotential height, temperature, relative humidity, and precipitable water.

b. Selection of extreme rainfall thresholds

The generalized extreme value (GEV) distribution is applied to model the annual maximum of the hourly precipitation amount (RAM) and estimate the extreme precipitation threshold, following previous studies (e.g., Coles 2001, 45–57; Li et al. 2013; Zheng et al. 2016). All the valid hourly rainfall data from the 303 stations are used for the period from 1998 to 2012 to obtain the historical maximum and to estimate the 5-, 10-, and 20-yr return values at each station. Below is a brief illustration of the methodology followed, using the Taipei station as an example. First, the empirical distribution function of RAM during the 15 yr is estimated according to the classical theory of extreme value using the following equation:

 
formula

where G is the distribution of the GEV and μ, σ, and are the location, scale, and shape parameters, respectively. In this case, G is obtained through maximum likelihood estimation; for example, at the Taipei station, the parameters have values of μ = 51.96, σ = 9.76, and = 0.027 (Fig. 2a). Second, the hourly rainfall amount for different return periods based on the inverse function of Eq. (1) is estimated. The estimated rainfall intensities at the Taipei station are 67.5, 74.1, and 81.5 mm h−1 with return periods of 5, 10, and 20 yr (as indicated by the dotted lines in Fig. 2b). For a 10-yr period, the expected frequencies of extreme hourly rainfall with return periods of 5, 10, and 20 yr are 2, 1, and 0.5, while the station-averaged frequencies are 2.47, 1.18, and 0.58, respectively. These results are close to the expected frequencies, which supports the validity of this methodology.

Fig. 2.

(a) Cumulative distribution function (CDF) of the annual maximum hourly precipitation during 1998–2012 at Taipei station: comparison between the gauge-based observation results (hollow circles) and the GEV estimation (curve). (b) Rainfall intensities with different return periods at Taipei station: comparison between the gauge-based observation results (hollow circles) and the GEV estimation (solid line; with dotted lines highlighting the estimation results for 5-, 10-, and 20-yr return periods).

Fig. 2.

(a) Cumulative distribution function (CDF) of the annual maximum hourly precipitation during 1998–2012 at Taipei station: comparison between the gauge-based observation results (hollow circles) and the GEV estimation (curve). (b) Rainfall intensities with different return periods at Taipei station: comparison between the gauge-based observation results (hollow circles) and the GEV estimation (solid line; with dotted lines highlighting the estimation results for 5-, 10-, and 20-yr return periods).

The threshold values for the 5-, 10-, and 20-yr return periods are compared with those of the 99.5th, 99.9th, 99.95th, and 99.99th percentile values of all rainy hours (≥0.1 mm h−1) during 1998–2012 (Fig. 3). The intensities of the 5- and 10-yr return values are stronger than those of the 99.95th percentile value, and the intensity of the 20-yr value is comparable to that of the 99.99th percentile value. This proves that the hourly rainfall records selected using the GEV method are truly “extreme” for their locations. The spatial distribution of the threshold values for the 5-yr return period is shown in Fig. 1, and the patterns of the thresholds for the 10- or 20-yr return periods are largely similar (figures not shown). The maximal threshold value (95 mm h−1) is almost 3 times that of the minimum one (33 mm h−1). The top 25% threshold values (78–95 mm h−1) are mainly located in western Taiwan and south of Yilan city in northeastern Taiwan (see Fig. 1 for location of Yilan); while the lower 25% values (33–65 mm h−1) are located in the central mountainous regions of the CMR, along the central eastern coast, and along the northwestern coast of Taiwan. Both the large range of threshold values and their inhomogeneous spatial distribution over the island highlight the important role of the complicated topography in the extreme rainfall distribution over Taiwan.

Fig. 3.

The intensity thresholds (mm h−1) of extreme hourly rainfall estimated using the GEV method for 5-, 10-, and 20-yr return periods (blue color) and the 99.5th, 99.9th, 99.95th, and 99.99th percentile values (black color), respectively. The middle of each bar represents the median value, the top (bottom) of each bar indicates the 75% (25%) value, the top (bottom) line denotes the 90% (10%) value, and the top (bottom) dot shows the maximum (minimum) value.

Fig. 3.

The intensity thresholds (mm h−1) of extreme hourly rainfall estimated using the GEV method for 5-, 10-, and 20-yr return periods (blue color) and the 99.5th, 99.9th, 99.95th, and 99.99th percentile values (black color), respectively. The middle of each bar represents the median value, the top (bottom) of each bar indicates the 75% (25%) value, the top (bottom) line denotes the 90% (10%) value, and the top (bottom) dot shows the maximum (minimum) value.

Apart from the relative thresholds above, a fixed threshold of 100 mm h−1 is also adopted to select the most extreme hourly rainfall records for all of Taiwan, since over 90% (75%) of both the 10-yr (20-yr) recurrence threshold values and the 99.95th (99.99th) percentile values are below that level of intensity (Fig. 3).

c. Classification of extreme hourly precipitation

The extreme hourly rainfall records are classified into four types based on the synoptic situation under which they occur, namely, the TC, front, low-level vortex/shear line, and weak-synoptic forcing types. In this classification analysis, we focus on 10 recent years (2003–12) as the weather maps and radar reflectivity images are most complete during this period.

First, the TC-type extreme rainfall in Taiwan is identified when a TC [or tropical depression (TD)] center is located within the key domain of 12°–34°N, 110°–132°E (Fig. 1a). The key domain is determined by extending about 10° (roughly 1000 km) from Taiwan. The selection of 1000 km follows the studies of TC precipitation in the Atlantic basin by Jiang et al. (2011) and Leppert and Cecil (2016). There are 45 TCs and 3 TDs that passed through the key domain and caused extreme hourly rainfall in Taiwan during 2003–12. Among them, there are 25 TCs with centers located within 100 km to the nearest coastline of Taiwan (gray tracks in Fig. 4). Information about these 25 TCs as they approached Taiwan, such as the track and duration time, has been well documented by Wu et al. (2016) and is also supplied in this study. The TC type is further classified into seven subtypes considering two factors: 1) the distance between the TC center and the nearest coastline of Taiwan and 2) the azimuth of the TC center relative to the island. Details of the subgrouping method are provided in section 4b. Then, the front type is identified when a surface front migrates to within 50 km of Taiwan on the surface weather map and the associated rainband on the radar reflectivity image reaches the island. Next, the vortex/shear line type is identified when there is no frontal system on the surface weather map, but a vortex or a shear line is present at the 850-hPa level over the island. In addition, the extreme-rain-producing rainy systems in the above three types, all associated with synoptic-scale ascent, should extend over 200 km on the radar reflectivity images, which is the lower limit of the meso-α scale (Orlanski 1975). Finally, the remaining extreme rainfall records are classified into the weak-synoptic forcing type.

Fig. 4.

Map of the key domain (12°–34°N, 110°–132°E), overlaid with the tracks (yellow lines) of 45 TCs and the central positions (triangles) of three TDs during 2003–12. The gray lines denote portions of the tracks when the TC centers are located within 100 km of Taiwan during their life period. The symbols as illustrated in the top-left corner denote the locations of TC centers belonging to each TC subtype (I–VII). The coastline of Taiwan is shown in boldface.

Fig. 4.

Map of the key domain (12°–34°N, 110°–132°E), overlaid with the tracks (yellow lines) of 45 TCs and the central positions (triangles) of three TDs during 2003–12. The gray lines denote portions of the tracks when the TC centers are located within 100 km of Taiwan during their life period. The symbols as illustrated in the top-left corner denote the locations of TC centers belonging to each TC subtype (I–VII). The coastline of Taiwan is shown in boldface.

3. Temporal and spatial characteristics of extreme hourly precipitation

The number of extreme hourly rainfall records and the contributions from each of the classified types are shown in Table 1. When using the 5-, 10-, and 20-yr return values, the longer the return period, the smaller the number of total records, but the percentage of each type stays relatively stable. The TC type accounts for approximately 75%–77% using the relative thresholds and 85% using the fixed threshold of 100 mm h−1, suggesting the dominating impacts of TCs on extreme hourly precipitation in Taiwan. The proportions of the front type and weak-synoptic forcing type are comparable, each accounting for roughly 9%–13% of the total records. There are few records (about 1%) caused by a low-level vortex or a shear line during 2003–12, and hence further analysis of this type will be excluded from the upcoming sections. For a frontal case and a TC case, a shear line is sometimes found to be a component in the associated synoptic patterns. This does not change the category of the extreme rainfall, as the front and the TC are considered to be the dominating synoptic system.

Table 1.

Numbers of extreme hourly precipitation records using four kinds of thresholds during 2003–12. Numbers in parentheses represent the fractional contributions (%) from each type to the total number.

Numbers of extreme hourly precipitation records using four kinds of thresholds during 2003–12. Numbers in parentheses represent the fractional contributions (%) from each type to the total number.
Numbers of extreme hourly precipitation records using four kinds of thresholds during 2003–12. Numbers in parentheses represent the fractional contributions (%) from each type to the total number.

a. Seasonal variation of extreme rainfall occurrence

The number of extreme hourly precipitation records in each half-month period is added up and then divided by the yearly total number to examine the fractional contribution (%) of extreme precipitation in each half-month (Fig. 5a). Note that there are very few extreme rainfall occurrences during November–April (less than 2%), so only the seasonal variation of extreme hourly rainfall during May–October is shown. Contributions from the extreme precipitation stay relatively small during May–June (less than 8%) and start to increase rapidly afterward with a prominent peak during 16–31 July. The extreme precipitation during 16 July–15 August accounts for about half of the yearly total records, suggesting that severe heavy rainstorms are most active during this period. The contribution decreases sharply to about 5% during 16–31 August and then shows less fluctuation afterward.

Fig. 5.

Temporal variation of the extreme hourly rainfall occurrence (%), calculated as the number of records in a half-month period divided by the total number of records during May–October: (a) all types, (b) TC type, (c) front type, and (d) weak-synoptic forcing type. The results for extreme hourly rainfall that correspond to the 5-, 10-, and 20-yr return period are represented using three different gray levels, while those for extreme rainfall exceeding 100 mm h−1 are shown using solid lines with asterisks. Note that the ranges of the y axis in (c),(d) differ from those in (a),(b).

Fig. 5.

Temporal variation of the extreme hourly rainfall occurrence (%), calculated as the number of records in a half-month period divided by the total number of records during May–October: (a) all types, (b) TC type, (c) front type, and (d) weak-synoptic forcing type. The results for extreme hourly rainfall that correspond to the 5-, 10-, and 20-yr return period are represented using three different gray levels, while those for extreme rainfall exceeding 100 mm h−1 are shown using solid lines with asterisks. Note that the ranges of the y axis in (c),(d) differ from those in (a),(b).

To illustrate the contributions from the three types with the greatest frequency of occurrence of extreme precipitation, the number of each type in each half-month is also divided by the yearly total number of all (four) types (Figs. 5b–d). The TC type shows a seasonal variation quite similar to that in Fig. 5a during July–October (Fig. 5b), with only two typhoons [Typhoon Soudelor (2003) and Chanchu (2006)] producing four records altogether in May. The very few occurrences of the TC-type extreme precipitation before July are due to a lack of landfalling TCs and the thermal atmospheric conditions that are insufficient for TCs to produce such intense rainfall over the island. The front type occurs during two discrete periods: from May to mid-June and during the first half of September, respectively. The front-type extreme hourly rainfall in the May–mid-June period is caused by mei-yu fronts and is the predominant type during this same period, while in the first half of September it is related to cold fronts (Fig. 5c). The weak-synoptic forcing type could occur throughout the warm season, but more frequently during mid-June–mid-August (Fig. 5d). This type is the predominant type during mid-June–mid-October when TCs are not present.

b. Diurnal variation of extreme rainfall occurrence

While the diurnal variation of precipitation over Taiwan has been previously analyzed, the diurnal cycle of extreme hourly rainfall in this region is not well documented in the literature. In this study, it shows three peaks at 0000–0200, 0900–1000, and 1500–1700 LST, respectively (Fig. 6a). The diurnal variation of the TC-type extreme rainfall is quite similar to that of the total records, except that the peak at 1500–1700 LST becomes less obvious (Fig. 6b). A number of studies have used satellite data to examine the diurnal cycle of TC precipitation over the oceans (Jiang et al. 2011; Dunion et al. 2014; Wu et al. 2015; Bowman and Fowler 2015; Leppert and Cecil 2016). Despite there being some disagreement among the results, a nocturnal/early morning rainfall peak has been identified in most of the observational studies, suggesting that our finding of the nocturnal peak of the TC-type extreme hourly precipitation is not by chance. On the other hand, compared to the large amount of data over the oceans, the amount of TC precipitation data over land is quite limited, which is a major reason for our insufficient understanding of the effects of land surface on the diurnal behavior of TC rainfall (Tuleya 1994; Bowman and Fowler 2015). Therefore, whether the features in the diurnal variation of the TC-type extreme precipitation in Taiwan are a random result arising from the selection of the samples or a general conclusion needs further investigation.

Fig. 6.

The diurnal variation of the extreme hourly rainfall occurrence (%). Here, the occurrence is calculated as the number of extreme-rainfall records within an hour of the day divided by the daily total number of records: (a) all types, (b) TC type, (c) front type, and (d) weak-synoptic forcing type. Note that the ranges of the y axes in (c) and (d) differ from those in (a) and (b).

Fig. 6.

The diurnal variation of the extreme hourly rainfall occurrence (%). Here, the occurrence is calculated as the number of extreme-rainfall records within an hour of the day divided by the daily total number of records: (a) all types, (b) TC type, (c) front type, and (d) weak-synoptic forcing type. Note that the ranges of the y axes in (c) and (d) differ from those in (a) and (b).

In our analysis, the extreme hourly rainfall associated with a front shows less coherent and more erratic diurnal variations (Fig. 6c). In contrast, the weak-synoptic forcing type occurs mostly in the afternoon with a prominent peak during 1500–1600 LST (Fig. 6d), which was observed in the average hourly rainfall amount over Taiwan under weak synoptic-scale forcing (Lin et al. 2011). This feature of extreme rainfall is also found over Hainan Island (in southern China, near the northwestern corner of the South China Sea), which has a more striking afternoon peak than those over other regions of the Chinese mainland (Luo et al. 2016). This is probably due to the combined effect of mountain–plain and land–sea circulations caused by the strong thermal contrast between the mountainous tropical islands and the surrounding sea. The sea-breeze circulation is therefore greatly promoted and convective showers occur on the windward slope as a result of the sea breeze advancing inland and being lifted by the topography during the daytime (Fovell 2005; Wang and Kirshbaum 2015; Liang and Wang 2017).

c. Temporal evolution of the hourly rainfall intensity

To examine the evolution of hourly rainfall intensity before and after the time of extreme rainfall (peak time), the ratios of the hourly rainfall amount 6 h before and after the peak time to that at the peak time are calculated for each extreme-rainfall record. The statistics of the ratios for each type are similar regardless of the thresholds (5-, 10-, and 20-yr return values), and thus only those exceeding the 5-yr recurrence threshold are shown in Fig. 7. For the TC type, the evolution of rainfall intensity is nearly symmetrical before and after the peak time (Fig. 7a). Six to three hours before the peak time, the intensity slowly increases but the median ratios remain below 25%, suggesting that half of the samples during these 4 h have less than one-quarter of the extreme hourly rainfall amount at the peak time. At 1 h before the peak time, the rainfall intensity increases more sharply, and the median ratio reaches 53%. On the other hand, the ratios within each hour cover a wide range. For example, at 1 h before the peak time, the lower quarter of the hourly rainfall amounts are less than 32% of the peak time extreme rainfall intensity, while the top quarter reaches about 80%. The wide ranges reflect the inhomogeneous features of the TC-induced precipitation at the hourly and station scales.

Fig. 7.

The temporal evolution of hourly rainfall intensity (%; relative to the extreme rainfall amount) 6 h before and after the time of extreme precipitation: (a) TC type, (b) front type, and (c) weak-synoptic forcing type. The middle of each bar represents the median ratio value, the top (bottom) of each bar indicates the 75% (25%) ratio value, and the top (bottom) line denotes the 90% (10%) ratio value. The median ratio values are connected by gray solid lines in each panel.

Fig. 7.

The temporal evolution of hourly rainfall intensity (%; relative to the extreme rainfall amount) 6 h before and after the time of extreme precipitation: (a) TC type, (b) front type, and (c) weak-synoptic forcing type. The middle of each bar represents the median ratio value, the top (bottom) of each bar indicates the 75% (25%) ratio value, and the top (bottom) line denotes the 90% (10%) ratio value. The median ratio values are connected by gray solid lines in each panel.

The front-type extreme rainfall exhibits shorter duration and more rapid change in its intensity before and after the peak time with a slightly asymmetrical evolution; that is, the decreasing trend is slower than the increasing trend (Fig. 7b). The time period with at least half of the samples recording nonzero hourly rainfall is shorter before the peak time than after (3 vs 6 h). These features of the front type can be seen more clearly in the weak-synoptic forcing type (Fig. 7c). About 90% of this type last no longer than 3 h, with the median rainfall intensity increasing by 7.7 times in an hour before the peak time and decreasing by 4 times in an hour after. The slightly asymmetrical evolution is probably associated with the organizational modes of the extreme-rain-producing storms that mostly consist of both convective and stratiform precipitation regions (Parker and Johnson 2000; Schumacher and Johnson 2005).

Taking advantage of the densely distributed gauges over the island, the relationship between the topography and the evolution of rainfall intensity is analyzed by grouping the extreme-rainfall samples into four categories according to their station elevations: 0–100, 100–500, 500–1000, and above 1000 m (Fig. 8). The evolutional patterns are generally similar among the four categories, reflecting the dominance of the TC type in each category. However, at higher station elevations, the rainfall duration tends to become longer with a more gradual change in hourly rainfall intensity before and after the peak time. This is due to the fact that the front-type or weak-synoptic forcing type extreme precipitation mostly occurs at the lower altitudes (Figs. 9a,b).

Fig. 8.

As in Fig. 7, but for four categories of station elevation: (a) 0–100, (b) 100–500, (c) 500–1000, and (d) >1000 m. The proportion of each category in the total number of extreme precipitation records is shown in parentheses.

Fig. 8.

As in Fig. 7, but for four categories of station elevation: (a) 0–100, (b) 100–500, (c) 500–1000, and (d) >1000 m. The proportion of each category in the total number of extreme precipitation records is shown in parentheses.

Fig. 9.

(a)–(c) Spatial distributions of the three types of extreme precipitation with 5-yr return periods: weak-synoptic forcing type, front type, and TC type. (d) As in (a)–(c), but for the extreme hourly rainfall exceeding 100 mm h−1. The colors denote the numbers of extreme hourly rainfall records occurring at each station and different symbols represent different types, which are all illustrated in the bottom-right corner in (a)–(c).

Fig. 9.

(a)–(c) Spatial distributions of the three types of extreme precipitation with 5-yr return periods: weak-synoptic forcing type, front type, and TC type. (d) As in (a)–(c), but for the extreme hourly rainfall exceeding 100 mm h−1. The colors denote the numbers of extreme hourly rainfall records occurring at each station and different symbols represent different types, which are all illustrated in the bottom-right corner in (a)–(c).

d. Spatial characteristics of extreme hourly rainfall

Spatial distributions of the three types of extreme hourly rainfall using the 5-yr return value and the fixed threshold of 100 mm h−1 are shown in Fig. 9. The weak-synoptic forcing type tends to occur inland and near the mountain slopes (Fig. 9a), which is mainly a result of the orographic lifting enhanced by daytime anabatic winds in the afternoon (Yeh and Chen 1998). In contrast, the front type tends to occur in the coastal areas of Taiwan (Fig. 9b). Within this type, about 91.3% of the extreme precipitation is associated with a mei-yu front during May–mid-June (Fig. 5c). Examination of the radar reflectivity images suggests that the extreme precipitation is produced by convective storms moving from the northwest and southwest to influence Taiwan as shown in Figs. 10a and 10b, respectively. Under both situations, the composite environmental fields at 850 hPa show a shear line (i.e., a signal of the mei-yu front) situated north of Taiwan, with large horizontal gradients of equivalent potential temperature θe across the region. South of the shear line, there is a tongue of high θe influencing Taiwan. These characteristics of the environmental patterns are quite typical when Taiwan is under the influence of a mei-yu front (Chen 1993; Wang et al. 2011; Xu et al. 2012). When the rainy system comes from the northwest, the shear line is nearly west–east-oriented at about 27°N over southern China, and the tongue of high θe extends from southern China to northern Taiwan. When rainy systems come from the southwest, the shear line is located more toward the south with smaller θe gradients across the area, and a stronger southwesterly flow influencing southern Taiwan (cf. Figs. 10d and 10c).

Fig. 10.

(a),(b) Two distributional patterns of extreme hourly rainfall influenced by a mei-yu front. The colors of the dots denote the number of records occurring at each station. The number of records in each pattern and their fractional contribution (%) to the total number of the front-type records are shown in the top-left corner. The black arrows with dashed lines denote the directions of where the rainstorms come from. (c),(d) The composite environmental fields at 850 hPa corresponding to the patterns in (a) and (b), respectively. Shading represents the equivalent potential temperature θe, blue lines denote contours of wind speed ≥8 m s−1 (at intervals of 4 m s−1), and the thick dashed line denotes the shear line of the horizontal winds.

Fig. 10.

(a),(b) Two distributional patterns of extreme hourly rainfall influenced by a mei-yu front. The colors of the dots denote the number of records occurring at each station. The number of records in each pattern and their fractional contribution (%) to the total number of the front-type records are shown in the top-left corner. The black arrows with dashed lines denote the directions of where the rainstorms come from. (c),(d) The composite environmental fields at 850 hPa corresponding to the patterns in (a) and (b), respectively. Shading represents the equivalent potential temperature θe, blue lines denote contours of wind speed ≥8 m s−1 (at intervals of 4 m s−1), and the thick dashed line denotes the shear line of the horizontal winds.

The TC type is distributed extensively over the island but more frequently in southwestern Taiwan near the CMR (Fig. 9c). The prevailing southwesterly monsoon flow around Taiwan during the warm season enhances the moisture flux in the quadrant of the TC with southwesterly winds, which interacts with the mountain range and produces more intense rainfall than do the winds in other quadrants (Chang et al. 2013). Moreover, the TC-type records tend to occur along the southern edge and over northeast Taiwan, which a result of TCs crossing southern Taiwan and from the interaction between the TC circulation and environmental northeasterly winds, respectively. The hourly rainfall exceeding 100 mm h−1 is also distributed extensively over the island with a center at the foothills of southwestern Taiwan (Fig. 9d), being largely similar to the distribution of TC type in Fig. 9c. This similarity is unsurprising as most of the extreme precipitation records exceeding 100 mm h−1 belong to the TC type (85%).

4. Further analysis of the TC-type extreme rainfall

a. The TC ranking

The TC type is the major type of extreme hourly rainfall in Taiwan during 2003–12 (75%–85%; Table 1). There are 45 TCs and three TDs that passed the key domain and caused extreme hourly rainfall in Taiwan during this 10-yr period (Fig. 4). However, the majority (76%–82%) of the TC-type extreme precipitation is caused by 10 (8) typhoons, which are ranked in Table 2 by the number of records they produced. Typhoon Kalmaegi (2008) has the largest number of records regardless of the thresholds used. Typhoon Morakot (2009), with the highest accumulated rainfall ever recorded in Taiwan since 1960, ranks second. This is consistent with the findings of Shieh et al. (2009), who had compared Typhoon Morakot (2009) and Kalmaegi (2008) along with five other devastating typhoons that influenced Taiwan. They found the largest rainfall peak to be during Typhoon Kalmaegi (2008), but the longest duration of strong rainfall intensity was during Typhoon Morakot (2009). This shows that the rankings in Table 2 are based on the peak intensity of TC-related hourly rainfall rather than the averaged or accumulated rainfall amounts. Moreover, about half of the TCs in Table 2 pass through northern Taiwan, where the TCs would have the most exposure of westerly or southwesterly winds against the terrain and hence are more likely to cause extreme precipitation over the island. Furthermore, Typhoons Kalmaegi (2008), Morakot (2009), and Mindulle (2004) are the top three TCs in terms of the number of extreme rainfall records they generated, together accounting for over 47% of the TC type and 35% of the total records. One common feature of the three TCs is that the summer monsoonal southwesterlies are relatively stronger than those in other TCs (Lee et al. 2006; Ge et al. 2010). Therefore, the southwesterly flows interacting with the TC circulation are a key factor in determining the precipitation intensity of the TCs and the cause of the TC-type extreme in Taiwan.

Table 2.

The top 10 (or top 8) TCs during 2003–12 ranked by the number of extreme hourly rainfall records they produced.

The top 10 (or top 8) TCs during 2003–12 ranked by the number of extreme hourly rainfall records they produced.
The top 10 (or top 8) TCs during 2003–12 ranked by the number of extreme hourly rainfall records they produced.

b. Subgrouping of the TC-type extreme rainfall

Many studies concerning the TC impact on precipitation in Taiwan (e.g., Chang et al. 2013; Wu et al. 2016) focused on a time period when the TC center was within a distance of 100 km from the nearest coastline. During this time period, the terrain’s influence is so dominant that the location of the TC center almost determines the rainfall distribution (Chang et al. 2013). When the TC center is far away from the island, heavy rainfall could also be brought to Taiwan by monsoonal flows that are enhanced or modified by the TC circulation (Lee et al. 2006; Wu et al. 2009). In our analysis, about 66.5% of the TC-type records (using the 5-yr recurrence thresholds) occur when the TC center is within 100 km of the nearest coastline of Taiwan (gray tracks in Fig. 4). These records are further classified into subtypes I–IV according to the four azimuths of the TC centers relative to the island: northwest, south, east, and northeast, respectively (dots in Fig. 4). There are another 28.5% records that occur when the TC center is within the key domain but at least 100 km away from the island (yellow tracks in Fig. 4). These records are further classified into subtypes V–VII, corresponding to the TC’s interaction with the environmental southwesterly winds, the topography of Taiwan, and the environmental northeasterly winds, respectively. The locations of the corresponding TC centers are shown in Fig. 4 (squares). The remaining 5% of the TC-type records occur when the TC centers are at least 100 km away from the island, similar to those of subtype V–VII, but the relation between the extreme rainfall distribution and the TC center’s location is quite different. These records are excluded from further discussions herein.

c. Subtypes I–IV influenced by TCs

Careful examination reveals that, when the TC center is on the island or near the coastline (≤100 km), the azimuth of the TC center relative to Taiwan largely determines where the most intense rainfall occurs on the island. When the TC center is located around the northwest, south, east, and northeast of the island, respectively, the associated extreme rainfall is classified as subtypes I–IV, each accounting for 32.6%, 14.1%, 15.8%, and 4.0% of the TC type’s total population, respectively (Fig. 11). Extreme rainfall of subtype I (Fig. 11a) is located mostly to the west of CMR, near Alishan (see Fig. 1) in particular. This subtype is produced after the TC center has climbed over the central or northern CMR and moved to the northwest of the island. The subtype II records are distributed mostly over the southern part of the island, when the TC center moves to this region (Fig. 11b).

Fig. 11.

(a)–(d) Spatial distribution of subtypes I–IV in the TC-type extreme precipitation (colored dots), and the corresponding TC tracks. The colors of the dots denote the number of records occurring at each station. The location of the TC center, when extreme hourly rainfall occurs, is highlighted by typhoon symbols in black. The name and year of each TC are labeled. The number of records in each subtype and their fractional contribution (%) to the total number of the TC type are labeled in the box inside each panel. In (c) the typhoon symbols in rose red represent the centers of Typhoon Kalmaegi (2008) and Typhoon Morakot (2009), and triangles denote the extreme precipitation records they produced.

Fig. 11.

(a)–(d) Spatial distribution of subtypes I–IV in the TC-type extreme precipitation (colored dots), and the corresponding TC tracks. The colors of the dots denote the number of records occurring at each station. The location of the TC center, when extreme hourly rainfall occurs, is highlighted by typhoon symbols in black. The name and year of each TC are labeled. The number of records in each subtype and their fractional contribution (%) to the total number of the TC type are labeled in the box inside each panel. In (c) the typhoon symbols in rose red represent the centers of Typhoon Kalmaegi (2008) and Typhoon Morakot (2009), and triangles denote the extreme precipitation records they produced.

The subtype III extreme rainfall, which is produced by eight TCs, is distributed over both the southwestern and northeastern areas of the island (triangles and dots in Fig. 11c). The southwest records are produced by two TCs [Typhoon Kalmaegi (2008) and Morakot (2009)] under the substantial influences of the environmental westerly and southwesterly winds. A quasi-west-to-east-oriented shear line is noticed in the southern Taiwan Strait, along which the northerly typhoon airflow converges with the westerly or southwesterly winds (Figs. 12a,b). The enhanced moisture flux convergence favors the production of extreme hourly rainfall across southwest Taiwan. The extreme rainfall records in northeast Taiwan are produced on the windward side of the CMR where the TCs’ internal low-level flow impinges on the terrain directly, while the northerly flow dominates across western Taiwan (Figs. 12c–h).

Fig. 12.

(a)–(h) The fields of horizontal wind (barbs) and geopotential height (gray contours at interval of 2 dgpm) at the 850-hPa level, when each of the eight TCs shown in Fig. 11c caused extreme hourly rainfall across Taiwan. A full barb is 5 m s−1, and the wind direction between 225° and 270° (i.e., southwesterly to westerly) is highlighted using blue. The tracks of the TCs are also shown by light blue solid lines. The brown solid lines in (a) and (b) denote the wind shear lines.

Fig. 12.

(a)–(h) The fields of horizontal wind (barbs) and geopotential height (gray contours at interval of 2 dgpm) at the 850-hPa level, when each of the eight TCs shown in Fig. 11c caused extreme hourly rainfall across Taiwan. A full barb is 5 m s−1, and the wind direction between 225° and 270° (i.e., southwesterly to westerly) is highlighted using blue. The tracks of the TCs are also shown by light blue solid lines. The brown solid lines in (a) and (b) denote the wind shear lines.

The subtype IV is produced by four TCs when their centers are located around the northeast corner of the island. This subtype includes 23 extreme precipitation records, among which 17 records are located along the northern edge of the island and 6 are over the northwest of the island (Fig. 11d).

d. Subtypes V–VII influenced by TCs

When the TC centers are far away (>100 km) from the island, they are located mostly to the northwest/north or southwest/south of Taiwan (Figs. 13d–f). In cases where TC centers are to the northwest/north, a total of 95 extreme precipitation records are distributed mostly over western Taiwan from the CMR to the western coastline (Fig. 13a). This subtype V is similar to subtype I, except for the longer distance between the TC center and the island. The composite field at 850 hPa shows a southwest–northeast-oriented band of high θe extending from the northern South China Sea and south China toward the East China Sea (Fig. 13d), suggesting that the strong southwesterly flow transports the moist and convectively unstable air northeastward to support extreme rainfall production over western Taiwan.

Fig. 13.

(a)–(c) Distribution of subtypes V–VII of the TC-type extreme precipitation. The number of records in each subtype and their fractional contribution (%) to the total number of the TC type are shown in the top-left corner. The name, year, and month of each TC are labeled in the box inside each panel. (d)–(f) As in (a)–(c), but for the composite environmental fields at 850 hPa. Shadings represent the equivalent potential temperature θe, and blue lines denote contours of wind speed ≥12 m s−1 (at intervals of 4 m s−1). The locations of the TC centers, when the TC produced extreme hourly rainfall across Taiwan, are highlighted using typhoon symbols in blue.

Fig. 13.

(a)–(c) Distribution of subtypes V–VII of the TC-type extreme precipitation. The number of records in each subtype and their fractional contribution (%) to the total number of the TC type are shown in the top-left corner. The name, year, and month of each TC are labeled in the box inside each panel. (d)–(f) As in (a)–(c), but for the composite environmental fields at 850 hPa. Shadings represent the equivalent potential temperature θe, and blue lines denote contours of wind speed ≥12 m s−1 (at intervals of 4 m s−1). The locations of the TC centers, when the TC produced extreme hourly rainfall across Taiwan, are highlighted using typhoon symbols in blue.

When the TC center is located over the Bashi Channel to the southwest and south of Taiwan, 36 and 31 records of extreme hourly rainfall are distributed along the eastern coastline and along the northern edge of the island (especially south of the city of Yilan), respectively, each belonging to subtypes VI and VII (Figs. 13b,c). The two patterns of the extreme hourly rainfall distribution are attributed to two different controlling factors: topography and the monsoon (Wu et al. 2009). Subtype VI occurs mainly during the summer and early September. The strong southerly flow in the TC circulation turns to easterly when approaching the island and impinges on the east slope of the CMR (Fig. 13e), resulting in extreme hourly rainfall there. In contrast, extreme precipitation in subtype VII (Fig. 13f), occurring in late autumn or early winter, is the result of the low-level convergence between the cold, dry winter-monsoonal northeasterly flows and the warm and moist air in the TC circulation around northern Taiwan (Cheung et al. 2008; Wu et al. 2009).

5. Summary and conclusions

Synoptic analysis of extreme hourly precipitation in Taiwan during a 10-yr period (2003–12) is conducted using the densely distributed rain gauge observations, weather maps, radar images, and ERA-Interim data. The intensity thresholds of extreme hourly rainfall are estimated through a GEV distribution with 5-, 10-, and 20-yr return periods, while a fixed threshold of 100 mm h−1 is also used. All the extreme rainfall records are classified into four types according to the synoptic situations under which they occur: the TC, front, weak-synoptic forcing, and vortex/shear line types. The seasonal/diurnal variations, the evolutions of rainfall intensity, and the spatial distributions of the first three types that account for about 98% of the total occurrences of extreme precipitation are investigated. Our main conclusions are summarized as follows.

  1. The TC type is the dominant type that accounts for more than three-quarters of the total records, while the front type and weak-synoptic forcing type are comparable, each contributing roughly 9%–13% to the total records. Extreme hourly precipitation is mostly caused by mei-yu fronts during May–mid-June and by TCs during July–October.

  2. The temporal evolution of hourly rainfall intensity before and after the time of extreme rainfall is nearly symmetrical for the TC type, but slightly asymmetrical for the front and weak-synoptic forcing types, with a decreasing trend after extreme rainfall that develops more slowly than the increasing trend before. The TC type tends to have a long duration time (>12 h), while the front type and weak-synoptic forcing type occur mainly over a short period (<6 h).

  3. The front type mostly occurs in the coastal areas of southwestern and northwestern Taiwan, respectively, with notable differences in the corresponding thermodynamic and dynamic conditions. The weak-synoptic forcing type tends to occur inland and near the mountain slopes.

  4. When the TC center is over Taiwan or near the coastline (distance <100 km), the spatial distribution of extreme hourly precipitation over the country is largely determined by the azimuth of the TC center relative to the island (i.e., the interaction between the TC circulation and the topography). When the TC center is far away (>100 km) from the island, the spatial distribution of extreme hourly rainfall in Taiwan is also determined by the strength of the environmental southwesterly or northeasterly winds, and by the impingement of TC circulation on the CMR from its east side.

These results provide useful information not only for understanding the relationship between the extreme precipitation in Taiwan and the associated atmospheric flow patterns, but also for evaluating model forecast results. In the future, synoptic analysis for extreme rainfall over a longer time period from 3 h to daily could be conducted to compare with the present study. The complex multiscale interactions among the synoptic background, mesoscale convective systems, and cloud microphysical processes need more investigation using integrated observations and numerical experiments to help further our understanding of the mechanisms governing the production of the extreme precipitation influencing Taiwan.

Acknowledgments

This research is supported by The National Natural Science Foundation of China (91437104) and the Basic Research and Operation Funding of Chinese Academy of Meteorological Sciences (CAMS) (2017Z006). CCW and THY are supported by the Ministry of Science and Technology of Taiwan under Grant MOST 105-2628-M-002-001. The ERA-Interim data were downloaded from the European Centre for Medium-Range Weather Forecasts (ECMWF; http://apps.ecmwf.int/datasets/data).

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