A Climatology Model for Forecasting Typhoon Rainfall in Taiwan

Natural Hazards (2006) 37:87–105 Springer 2006 DOI 10.1007/s11069-005-4658-8

CHENG-SHANG LEE1,2,w, LI-RUNG HUANG2, HORNG-SYI SHEN2 and SHI-TING WANG3 1Department of Atmospheric Sciences, National Taiwan University, Taipei, Taiwan, ROC; 2Meteorology Division, National S&T Center for Disaster Reduction, Taipei, Taiwan, ROC; 3Central Weather Bureau, Taiwan, ROC

Abstract. The continuous torrential rain associated with a typhoon often caused flood, landslide or debris flow, leading to serious damages to Taiwan. Thus, a usable scheme to forecast rainfall amount during a typhoon period is highly desired. An analysis using hourly rainfall amounts taken at 371 stations during 1989–2001 showed that the topographical lifting of typhoon circulation played an important role in producing heavier rainfall. A climatology model for typhoon rainfall, which considered the topographical lifting and the variations of rain rate with radius was then developed. The model could provide hourly rainfall at any station or any river basin for a given typhoon center. The cumulative rainfall along the forecasted typhoon track was also available. The results showed that the R2 value between the model estimated and the observed cumulative rainfall during the typhoon period for the Dan- Shui (DSH) and Kao-Ping (KPS) River Basins reached 0.70 and 0.81, respectively. The R2 values decreased slightly to 0.69 and 0.73 if individual stations were considered. However, the values decreased significantly to 0.40 and 0.51 for 3-hourly rainfalls, indicating the strong influence of the transient features in producing the heavier rainfall. In addition, the climatology model can only provide the average conditions. The characteristics in individual typhoons should be considered when applying the model in real-time operation. For example, the model could give reasonable cumulative rainfall amount at DSH before Nakri (2002) made landfall on Taiwan, but overestimated the rainfall after Nakri made landfall and weakened with significant reduction in convection. Key words: typhoon, typhoon rainfall, rainfall climatology, quantitative precipitation forecast, typhoon landfall, topographical effect

1. Introduction On average, about 80 tropical cyclones formed around the whole globe each year and about 30 of them formed in the western North Pacific (Gray, 1981). Taiwan is located on the main path of western North Pacific tropical cyclones and was affected by at least one system each year accord- ing to the official record of the Central Weather Bureau (CWB), Taiwan.

w Author for correspondence: Phone: +886-2-2392-8260, Fax: +886-2-2363-3642, E-mail: [email protected] gg gy

88 CHENG-SHANG LEE ET AL.

Table I. The occurrence of diﬀerent numbers of typhoons per year that aﬀected Taiwan and made landfall on Taiwan in 1961–2002

Number of year Number of typhoons

012 3 45 6789

Aﬀected Taiwan 0 1 2 11 7 13 2 4 1 1 Made landfall 9 9 11 10 2 0 1 0 0 0

In this paper, we use the term ‘‘typhoon’’ in representing tropical cyclone generally, including tropical storm and typhoon. Table I shows the distribution of occurrence of typhoons that affected Taiwan and made landfall on Taiwan each year during 1961–2002. Here a typhoon was considered to affect Taiwan if CWB issued the sea warning (or the storm force wind would affect the area as far as 100 km from the coast in the next 24 h). Taiwan was usually affected by three to five typhoons every year (maximum at nine), and the annual variation was large. The average number of typhoon affecting Taiwan in a year is 4.5, with 1.8 of them making landfall. Table I also indicates that there were nine years during 1961–2002 in which no typhoon made landfall. Although typhoons could form through- out the whole year in the western North Pacific, Taiwan was only affected by typhoons from April to November, with 74% of them occurred in July- September. Taiwan is a small island 140 km wide and 394 km long, and the average elevation of the Central Mountain Range (CMR) is above 2000 m (Fig- ure 1). A typhoon often experienced tremendous changes in motion and structure as it was approaching or moving across the island (Wang, 1992, Chang et al., 1993, Lee, 1993, Lin et al., 2001). On the other hand, the terrain slope lifting of the warm and moist air associated with a typhoon often caused continuous torrential rainfall on the windward side leading to serious flooding, landslide or debris flow. Official reports indicated that during the 10-year period of 1985–1994, typhoon-related disaster caused an eco- nomic loss of 403 million US dollars each year, which accounted for about 76% of the average total yearly loss or 534 million US dollars caused by all weather events. In the period 1996–2001, the average yearly property loss due to typhoon increased to 530 million US dollars (number adopted from the reports of Ministry of the Interior). Table II lists the top five typhoons that caused most serious damage to Taiwan in the past several years. In 1996, Typhoon Herb hit Taiwan and brought a total of 1,984 mm rainfall at Ah-Li Mountain located at the central mountain area, resulting in severe debris flows and flooding. The National Science & Technology (S&T) Pro- gram for Hazard Mitigation (the former program office of the National S&T Center for Disaster Reduction) was established after the event. In MODEL FOR FORECASTING TYPHOON RAINFALL 89

Table II. A list of the top ﬁve typhoons that caused the most damages to Taiwan in the past eight years

Typhoon name (year/month) Brief description of damage and rainfall

Life loss Life injured Property loss (million US dollars)

Herb (1996/7) 73 463 978 Severe disaster around whole island. 1984 mm (1095 mm daily) rainfall at Ah-Li Mountain (central)

Toraji (2001/7) 214 188 531 Landfall period at 10 h. 147 mm hourly (390 mm 3-hourly) and 141 mm (333 mm 3-hourly) rainfall at Hua-Lien (east) and Nan-Tou (central)

Nari (2001/9) 104 265 454 Landfall period at 51 h. Severe disaster around western Taiwan. 1051 mm (425 mm daily) at Taipei and 1142 mm at Chia-Yi (south)

Zeb (1998/10) 38 27 297 Severe ﬂood at Taipei Metropolitan Area. 921 mm rainfall at Yang-Ming Mountain (north), 506 mm at Taipei and 805 mm at Hua-Lien (east)

Billis (2000/8) 15 110 251 Maximum wind speed 78 m s)1. 912 and 824 mm rainfall at Hua-Lien (east) and I-Lan (northeast)

2001, Taiwan was affected by nine typhoons with some really damaging ones. For example, Typhoon Nari stayed on land for 51 h and brought continuous torrential rain to many areas around the whole island. The daily rainfall reached 425 mm (1051 mm in total for the entire impact period) in Taipei city, leading to severe inundation at many places including the main station of the Taipei Metropolitan Rapid Transit System. Since most of the disasters caused by typhoons in Taiwan were due to the torrential rain that caused floods, landslides or debris flows, a useful scheme for quantitative precipitation forecast (QPF) during typhoon period is highly desired. The purpose of this study is to investigate the features of precipitation and to develop a usable scheme for forecasting rainfall amounts during the typhoon period. In Section 2, the rainfall characteristics in Taiwan during a typhoon period are analyzed. The development and the evaluation of the typhoon rainfall climatology model are discussed in Sections 3 and 4, respectively. Finally, Section 5 gives the discussions and conclusions. 90 CHENG-SHANG LEE ET AL.

2. The Characteristics of Typhoon Rainfall in Taiwan To study the rainfall characteristics associated with typhoons affecting Tai- wan, we collected all hourly rainfall data taken at 371 stations (Figure 1a) during 1989–2001 (the data time periods for some stations were shorter). These stations include 21 conventional surface stations and 319 automatic rain gauges of CWB, 8 rainfall stations of Taiwan Water Resource Bureau and 23 rainfall stations of different Reservoir Administration Bureaus. Note that the spatial distribution of these stations is not uniform with 80% of them located on the western side of CMR. The elevation of the stations ranges from 1 to 3845 m. The 6-hourly fixes of the Joint Typhoon Warning Center (JTWC) best tracks were interpolated to obtain hourly center positions. However, when typhoon was around Taiwan, mesoscale analysis (as that of Wang, 1992) was performed to provide hourly center positions. In 1989–2001, there were 58 typhoons affecting Taiwan. Fig- ure 1b shows the hourly center positions of these typhoons around Taiwan. The average maximum intensity of these typhoons when their centers were located within the domain (shown in Figure 1b) was 38.8 m s)1. But the average of all 6-hourly intensities (when the typhoons were within the domain) was only 31.8 m s)1 because typhoons often weakened significantly when moving across Taiwan. Figure 2 shows that the rain rate associated with typhoon generally decreases with radius except near the center. The standard deviations are

Figure 1. Locations of 371 rainfall stations in Taiwan (a) and hourly center positions of 58 typhoons that aﬀected Taiwan in 1989–2001 (b). The contours in (a) show the 1000 and 2000 m height. The star in (b) shows the location of Taipei station and the rectangles show two grid boxes used in the climatology model. OE O OEATN YHO RAINFALL TYPHOON FORECASTING FOR MODEL

Table III. Occurrence (in percentage) of hourly rainfall amount at diﬀerent ranges (R, in mm) and average hourly rainfall amount for stations at diﬀerent elevations (H, in m), located within 450 km from the typhoon center

R Hourly rainfall amount (mm) Averaged rainfall (mm) Standard deviation (mm) Number of stations/data Occurrence (%) 0–0.9 1–9.9 10–19.9 ‡20

H >2000 57.7 31.5 7.0 3.8 3.4 (8.0)* 7.7 (10.3)* 20/23869 1500–2000 61.6 28.2 6.6 3.7 3.3 (8.4) 7.8 (10.8) 19/19263 1000–1500 62.6 27.4 6.1 3.8 3.2 (8.3) 7.9 (11.1) 26/26946 700–1000 65.8 24.9 5.5 3.8 3.0 (8.8) 8.2 (12.1) 23/24744 400–700 62.7 27.3 5.5 4.5 3.3 (8.8) 8.4 (11.8) 25/23762 250–400 63.0 27.4 5.8 3.8 3.1 (8.2) 7.4 (10.2) 33/35187 150–250 68.4 24.2 4.6 2.9 2.5 (7.6) 6.7 (10.1) 37/40957 100–150 68.9 23.4 4.7 3.0 2.5 (7.9) 6.9 (10.4) 42/44603 50–100 71.9 21.7 3.9 2.5 2.1 (7.5) 6.6 (10.8) 49/52904 25–50 71.6 22.1 4.0 2.3 2.1 (7.4) 6.3 (10.1) 40/46047 0–25 72.0 21.9 3.8 2.4 2.1 (7.4) 7.6 (12.9) 52/61430

Numbers within parentheses (marked by *) are averaged rainfall amounts when only rainfall data ‡1 mm are considered. 91 () g yp p p

92 CHENG-SHANG LEE ET AL. always larger than the mean as rain is usually a log-normal distribution, rather than a normal one (Lonfat et al., 2004). In Figure 2, the averages of the rainfall measurements were taken for all stations, stations with elevation less than 100 m and five small island stations (shown in Figure 1a), respectively. Results show that the average rain rates are smaller for stations with lower elevation. In addition, for the island station, the average hourly rainfall was 6.9 mm at 0–25 km radius, but increased to 12.8 mm and 10.8 mm at 25–50 km and 50–75 km radial ranges, respectively. These rain rates are about the same as the mean rain rate (11.3 mm h)1) at the eyewall of Hurricane Allen (1980) analyzed by Marks (1985). These results indicate that some typhoons still had a well-defined eye structure before hitting Taiwan such that the hourly rainfall peaked at radius of 25–75 km instead of at 0–25 km as in the two other cases. On the other hand, Frank (1977) used rainfall data taken at 13 island stations in the western North Pacific to compute the rainfall associated with typhoons. His results showed that the averaged rain rates at 0–2 and 2–4 radius were 95 and

Figure 2. The variations of average hourly rainfall amount with radius. The averaging was taken for all stations (circle), the stations with elevation <100 m (*) and island stations (·). The dashed curve shows the standard deviation for the case of all stations. MODEL FOR FORECASTING TYPHOON RAINFALL 93

36 mm d)1, respectively. Our analysis gives similar results, or 114 and 35 mm d)1 at radius of 0–225 and 225–450 km for the all-station case. These numbers drop to 99 and 27 mm d)1 (92 and 24 mm d)1) for stations with elevation <100 m (island stations). These results indicate the terrain- slope lifting did enhance the rainfall within 2-radius. It should be noted that, although the rainfall would be enhanced on the windward side, it would be reduced on the lee-side. Recently, Lonfat et al. (2004) studied the rainfall distribution in tropical cyclone using the Tropical Rainfall Measuring Mission (TRMM) microwave imager rain estimates. They showed that the azimuthal mean rain rates varied with storm intensity. The maximum rain rate was about 12 mm h)1 for category 3–5 hurricane-strength systems (CAT35, winds >49 m s)1), but decreased to 7 mm h)1 for category 1–2 systems (CAT12, winds = 34–48 m s)1), and to 3 mm h)1 for tropical storms (winds <33 m s)1). Our results of all stations (Figure 2) are comparable with their values for CAT35 systems beyond 100 km radius. Within 100 km radius, our values are smaller than those of CAT35 systems but larger than those of CAT12 systems. However, the average storm intensity in this study is only 31.8 m s)1, even weaker than CAT12 systems. Such results also indicate the role of topographical lifting in enhancing the typhoon rainfall in Taiwan. In order to understand the effect of topography in increasing the rainfall associated with typhoons, the averaged hourly rainfall at different elevations was computed and shown in Table III. Here all the rainfall measurements (including no rain) were considered and the no-rain data accounted for 2.2–4.5% of the whole data sample at different elevations. Also shown in Table III were the occurrences (in percentage) of different hourly rainfall amounts (0–0.9, 1–9.9, 10–19.9 and ‡20 mm, respectively) for stations located at different elevations. Results showed that the averaged hourly rainfall increased from 2.1 mm at elevation of 0–25 m to 3.4 mm at elevation >2000 m, except a local maximum (3.3 mm) at 400–700 m. However, the standard deviation was always much larger than the mean value due to the large case variations, transient features and the variations of rainfall from windward side to lee-side. The occurrence of hourly rainfall at 1–9.9 and 10–19.9 mm also increased with station elevation except at 250–700 m. These results suggest that the heavier rainfall occurred more easily at elevation of 250–700 m where the level of free convection usually lies. If only hourly rainfall data P1 mm were averaged (shown in parentheses and marked by a star in Table III), the maximum average rainfall of 8.8 mm occurred at elevation of 400–700 m where the ) occurrence of stronger rainfall (‡20 mm h 1) was also higher (4.5%). The effect of Taiwan topography on typhoon rainfall was further high- lighted in Figure 3, which shows the average cumulative rainfall during 94 CHENG-SHANG LEE ET AL.

Figure 3. The average cumulative rainfall (in mm) during typhoon period (a) and the occurrence (per thousand) of hourly rainfall amount ‡50 mm (b). The characters show the locations of top 10 maximum cumulative rainfalls (a) and of top 10-hourly rainfalls (b) during individual typhoon period in alphabetical order. typhoon period and the occurrence (per thousand) of ‡50 mm hourly rainfall. Results showed that large average typhoon rainfall occurred generally over the mountain areas especially the northeast mountain area and the eastern slope of the CMR. This was likely due to the fact that two-thirds of typhoons that affected Taiwan approached the island from the east (Wang, 1992). Terrain-slope lifting of typhoon circulation could easily lead to intense torrential rain at the eastern slope of the CMR especially the northern half where flows were on-shore and up-slope. As shown in Fig- ure 3a, five of the top 10 maximum cumulative rainfalls of individual typhoons occurred in this region. It should be noted that only the station with maximum rainfall in a river basin during one typhoon period was considered when selecting these top 10 maximum rainfalls. Among these top 10 rainfalls, four (marked by the letters C, D, E and G) occurred during Typhoon Nari (2001), which moved from northeast toward southwest across the whole island and stayed over land for 51 h. When considering the occurrence of intense hourly rainfall, such as hourly rainfall ‡50 mm, the distribution pattern of higher percentage appeared to be more random as shown in Figure 3b. However, the effect of topography was still very important in producing the intense hourly MODEL FOR FORECASTING TYPHOON RAINFALL 95 rainfall. Besides the regions where large cumulative rainfall often occurred as mentioned before, intense hourly rainfall also often occurred around Ah-Li Mountain (marked by the letter A in Figure 3a and J in Figure 3b) where the station elevation is 2415 m. Figure 3b also shows that the locations of the top 10 maximum hourly rainfalls spread over the whole island. Most of them (except F and D) were located in mountainous areas. These results suggest that although the terrain slope lifting could easily lead to intense torrential rain, the convective features associated with individual typhoon could also result in local intense hourly rainfall. Results also show that three (marked by the letters E, I and J) of the top 10-hourly rainfalls occurred around the central-eastern Taiwan during the passage of Typhoon Toraji (2001). Toraji was a compact but intense system and produced intense hourly rainfall along its path, leading to severe debris flows around the central mountain area. Two-hundred and fourteen people lost their life during the typhoon period of Toraji (Table I).

3. The Development of the Climatology Model for Typhoon Rainfall The basic consideration in developing the climatology model was that the terrain slope lifting of the typhoon circulation played one major role in determining the rainfall amount besides the rainfall variations with radius. The model comprises of a set of rainfall climatology maps, one for each rainfall station. To construct the rainfall climatology map for a rainfall station, such as Taipei (marked by the star in Figure 1b), all the hourly rainfall data (including no rain) at Taipei station when typhoon centers were within one 0.5 latitude · 0.5 longitude grid box (shown by the rect- angle in Figure 1b) were averaged and shown at that grid box. Therefore, the average value at one grid box represents the rainfall climatology at Taipei station when the typhoon center is located at that grid box. Similar analysis with 2·2 grid box had been done by Chang et al. (1993) for 22 surface stations. The domain considered was 19–27 N, 118–126 E, with 256 grid boxes (Figure 1b). However, there might be some grid boxes with- out data due to the limited typhoon cases and the variations in typhoon tracks. Such results seriously limited the applicability of this model in real- time operation. Therefore, we applied the interpolation scheme developed by Barnes (1973) to ﬁll in the blank grid box and to increase the grid reso- lution from 0.5·0.5 to 0.1·0.1 (around 11 km). After the rainfall climatology map for a station had been developed, the hourly rainfall amount at that station could be estimated for a given typhoon center. During the typhoon period, the hourly rainfall at the station can be computed for every hourly center position along the forecasted typhoon track. The cumulative rainfall at each station, especially where it 96 CHENG-SHANG LEE ET AL. is vulnerable to debris ﬂow, during the whole typhoon period can then be computed. The distribution of cumulative rainfall around the whole island during typhoon period (similar to that of Figure 3a) thus can be produced from computed data at the 371 rainfall stations. Besides the 371 rainfall stations, the rainfall climatology maps for 32 river basins as shown in Figure 4 were also developed. For simplicity, we took the averaged rainfall of all stations (including no rain) within a river basin to represent the rainfall of that river basin. On the other hand, the hourly rainfall of a river basin can also be obtained by averaging the model-estimated hourly rainfall amounts at all stations located at that river basin. However, we found that the river basin rainfall climatology map was easier for real-time application that is very time sensitive. In this paper, the results of Dan-Shui River Basin (DSH) and Kao-Ping River Basin (KPS) are discussed in more detail to highlight the characteristics of the climatology model. DSH and KPS, located at the north and south of Tai- wan, contain the largest numbers of rainfall stations, or 53 and 29 stations respectively (Figure 4). However, the available data at KPS started from 1992, so the data time period was only 10 years instead of 13 years for DSH. Figure 5 shows the rainfall climatology maps for DSH and KPS. Results indicate that the Dan-Shui River Basin had larger precipitation (>6 mm h)1) when typhoon center was located to the east of Taiwan and the regions to the north and east of Taipei. In addition, the hourly rainfall at DSH also exceeded 15 mm when the typhoon center was located south

Figure 4. The distribution of 32 river basins in Taiwan (middle) and the locations of rainfall stations (marked by the circled cross) for Dan-Shui River Basin (right) and Kao-Ping River Basin (left). MODEL FOR FORECASTING TYPHOON RAINFALL 97

Figure 5. Typhoon rainfall climatology map for Dan-Shui River Basin (a) and Kao- Ping River Basin (b). The contour intervals are 3 mm h)1. The gray areas are rainfall ) ‡6mmh 1. of Taiwan at the area around 21.8N, 120.8E. Due to the eﬀect of Taiwan topography, the rainfall amounts at DSH and KPS could be quite diﬀerent for a given typhoon center. For example, when the typhoon center was located around 24.3 N, 123.3 E, the hourly rainfall at DSH exceeded 18 mm, but was <3 mm at KPS. Similar features were also discussed by Yeh (2002). Our analysis can also give the probability (based on climatology) that the heavy rainfall (hourly rainfall >15 mm) would occur when the typhoon center is located at a certain grid box. For example, during the time period of 1989–2001, there were 17-hourly typhoon center positions located within grid box A of Figure 1 (25–25.5 N, 122.5–123 E) and 29% of all hourly rainfall measurements at individual stations of DSH exceeded 15 mm. However, there were also 17-hourly typhoon center positions located within grid box B (25–25.5 N, 120–120.5 E) but none of the rainfall stations of DSH measured rainfall ‡15 mm. Such information is very useful in decision making during the real-time typhoon forecast and hazard mitigation operation. Finally, due to the availability of data, these rainfall climatology maps have yet to be updated in the future to provide more stable results. In addition, the rainfall variations with storm intensity or size have to be examined if the data sample allows.

4. The Evaluation of the Typhoon Rainfall Climatology Model Since the rainfall climatology could represent only the average condition during the time period of available data, it was highly desirable to 98 CHENG-SHANG LEE ET AL. understand how the climatology could explain the variations in individual cases. Therefore, the scatterplots of observed versus model-estimated cumulative rainfall using the observed typhoon tracks are shown in Fig- ures 6a and 6b for DSH and KPS. In this section, the model-estimated rainfall of DSH or KPS was computed using the river basin climatology. On the other hand, the observed cumulative rainfall of DSH or KPS was the sum of hourly rainfall which was the average of all stations in the river basin. (The climatology map of DSH or KPS was derived from the river basin-averaged hourly rainfall.) In these two ﬁgures, each value represents a pair for every typhoon. Results show that the model tends to underestimate the larger rainfall (also discussed by Yeh, 2002) and overestimate the

Figure 6. Scatter plots showing the observed versus the model estimated cumulative rainfall (mm) for river basin (a, b) and individual stations (c, d) of Dan-Shui River Basin (left) and Kao-Ping River Basin (right). Diagrams (e) and (f) are similar to (a) and (b), except for 3-hourly rainfall. ( ) yp ( g )

MODEL FOR FORECASTING TYPHOON RAINFALL 99 light rainfall (or no rain). The slope thus was less than one in both cases. However, the bias, defined as the ratio of the total model estimated rainfall to the total observed rainfall (Charba et al. 2003), was 1.03 for both river basins and the squared correlation (R2) values reached 0.70 and 0.81 for DSH and KPS, respectively. These results indicate that the climatology model gives reasonable estimate of cumulative rainfall for most typhoons if an accurate typhoon track forecast is provided. The R2 values decreased from 0.70 and 0.81 to 0.69 and 0.73 if individual stations were considered as shown in diagrams c and d of Figure 6. The decreases in R2 values were even more pronounced (from 0.70 and 0.81 to 0.41 and 0.51) if 3-hourly time period (instead of the whole typhoon period) was considered (Figures 6e and f). The decrease in R2 value was evident if shorter time period was considered due to the transient convective features embedded in a typhoon system discussed by many studies (e.g. Gray, 1981; Burpee and Black, 1989). Results also indicate that the R2 values for KPS were generally larger than those for DSH especially when the river basin was considered (0.81 and 0.51 versus 0.7 and 0.41). However, the difference in R2 values between KPS and DSH decreased significantly if individual stations were considered, or 0.73 versus 0.69 for cumulative rainfall and 0.41 versus 0.41 for 3-hourly rainfall (not shown). This might be due to the difference in the topography of these two river basins. For KPS, the terrain generally increases toward north-northeast which provided a more uniform terrain slope lifting for a given prevailing wind direction (for example, southwest flow could produce heavier rainfall). The average rainfall thus represents better the rainfall of the whole river basin and the R2 values were higher. For the DSH, topography is more complicated and thus rainfall variations within the river basin were larger for any given prevailing wind direction. However, if individual stations were considered, the transient convective features tended to decrease the R2 value for KPS (0.81–0.73 and 0.51– 0.41), but not for DSH (0.70–0.69 and 0.40–0.41). From the hazard mitigation point of view, the early warning of torrential rain, especially at areas vulnerable to inundation or debris flow is highly desirable (Fread et al., 1995). In real-time practice, the flood warning is issued based on the inundation maps which were constructed for different rainfall amounts. To evaluate the capability of this climatology model in estimating the torrential rain during the typhoon period, the threat score (TS) for the model to give a correct estimate of the observed cumulative rainfall at DSH and KPS over a certain threshold was computed. The threat score was defined as TS = C/(A+B+C), where A(B) is the number of cases when the observed (model estimated) rainfall amount exceeded the assigned threshold, and C the number of cases when both the observed and the estimated rainfall exceeded the assigned threshold. In our study, 100 CHENG-SHANG LEE ET AL.

Table IV. The threat score (TS) of the climatology model to estimate correctly the heavy rainfall event (cumulative rainfall ‡ 75, ‡ 130, ‡ 200 and ‡ 300 mm, respectively) at the Dan-Shui and Kao-Ping River Basins in 1989–2001

Rainfall Dan-Shui River Basin (58) Kao-Ping River Basin (40)

‡75 ‡130 ‡200 ‡300 ‡75 ‡130 ‡200 ‡300

TS 0.66 0.50 0.67 0.45 0.90 0.67 0.45 1.0 PF 0.93 0.73 0.75 0.50 1.0 0.85 0.50 1.0 PA 0.69 0.62 0.86 0.83 0.90 0.77 0.83 1.0 A 292216101812104 B 3926146201364 C 2716125181054

The numbers within parentheses show the number of typhoons for each river basin. A (B)is the number of event observed (estimated) and C, the number of event estimated correctly. PF is the pre-figurance = C/A and PA, post-agreement = C/B.TS=C/(A+B+C). the thresholds of cumulative rainfall at 75 mm (3 in.), 130 mm (5 in.), 200 mm and 300 mm are used. As shown in Table IV, the case number decreases for larger threshold value. For KPS 18 cases (out of 40 cases) had the observed rainfall ‡75 mm, but only four cases had rainfall ‡ 300 mm. The limited number of available cases for threshold ‡300 mm at KPS makes this result less significant. The threat score generally decreases with increasing threshold value except the 200 mm of DSH and the 300 mm of KPS (Table IV). Results also show that the pre-figurance (PF, defined as C/A, second row in Table IV) was often greater than the post-agreement (PA, defined as C/B, third row in Table IV) for thresholds of 75 mm and 130 mm, indicating that the model tends to overestimate for light to moderate torrential rain. However, the post-agreement was generally greater than the pre-figurance for thresholds of 200 and 300 mm (except 300 mm of KPS). For DSH, the pre-figurance dropped from 0.75 for 200 mm to 0.5 for 300 mm, indicating that the climatology model missed half of the very intense torrential rain events. That the pre-figurance values for the model to estimate correctly the intense torrential rain were relatively lower is a common drawback of the climatology model (similar results in Figure 6). On the other hand, the very high values of the post-agreement (ranging from 0.83 to 1.0) assures that the intense torrential rain (‡ 200 mm) event would likely occur if the model indicates so. The previous evaluation was based on the dependent data set (1989– 2001). To understand how the climatology model performed for the independent data set, three typhoons, namely Rammasun, Nakri and Sin- laku affecting Taiwan in 2002 were considered. Figure 7 shows the 3-hourly positions of these typhoons as well as the observed and the MODEL FOR FORECASTING TYPHOON RAINFALL 101

Figure 7. The tracks of typhoons affecting Taiwan in 2002. Center positions are circled every 3 h and numbers show date and hour (UTC). Numbers to the right of dia- gram show the observed (O) and model (M) estimated cumulative rainfall (in mm) for the Dan-Shui (DSH) and Kao-Ping (KPS) River Basins. model-estimated cumulative rainfall amounts. Results show that the model underestimates the rainfall for Rammasun and overestimates that of Nakri. For Sinlaku, the model-estimated rainfall (100 mm) for DSH is about the same as the observation (103 mm). However, it should be noted that although the model gives reasonable estimate for the cumulative rainfall, the difference between observation and model estimate might be large for hourly rainfall (Figure 8a). The temporal variations of model-estimated hourly rainfall are generally smooth. However, the observed heavier hourly rainfall around 2200UTC 06 Sep.–0100UTC 07 Sep. occurred more ran- domly due to the effects of rainbands and convective cells embedded in typhoon system. For Rammasun, the observed cumulative rainfall at DSH was 122 mm while the model estimate is only 28 mm. The outer rainbands associated with Rammasun were relatively active, such that the rainfall at DSH was still significant when the typhoon center was about 400 km away, leading to the underestimate of the climatology model. For Nakri (Figure 8b), the model estimated cumulative rainfall at DSH was still quite reasonable for the first 24 h, or 85 mm (model estimate) versus 76 mm (observed). The difference between the model estimate and observation increased at later time period when Nakri made landfall on Taiwan and weakened. Accord- ing to the JTWC best track data, Nakri only maintained mostly as a minimal tropical storm (maximum wind at 35 knots) during this time period and weakened to a tropical depression during landfall. The size of 102 CHENG-SHANG LEE ET AL.

Figure 8. Observed (dark gray) and model estimated (light gray) hourly rainfall and cumulative rainfall (curves) at Dan-Shui River Basin (DSH) for Typhoon Sinlaku (left) and Typhoon Nakri (right) in 2002. convective clouds associated with Nakri was also relatively small due to the terrain eﬀect. Therefore, the model tended to overestimate rainfall especially during the later stage. These results reveal the important eﬀects of storm intensity or size on rainfall as have been shown by Lonfat et al. (2004) and needs to be investigated in the future.

5. Discussions and Conclusions Quantitative precipitation forecast (QPF) is one of the most important issues for the meteorological community. Many efforts had been spent to analyze the capability of numerical model in providing QPF. For example, Mao et al. (2000) evaluated the performance of the Regional Spectral Model (RSM) developed at the National Centers for Environmental Pre- diction (NCEP) in providing quantitative precipitation forecasts for the Tennessee and Cumberland River Watersheds, USA. They found that the model’s performance was more accurate than the traditional forecasts. However, the QPF performance of RSM for Hurricane Fran (1996) was relatively unsatisfactory. In Taiwan, QPF is also an important issue especially during the typhoon period. The major focus of the Meteorological Group, National S&T Center for Disaster Reduction of Taiwan thus has been placed on the development of the quantitative precipitation estimate (QPE) and QPF schemes during a typhoon period. Besides the typhoon rainfall climatology model, the Z–R relationships (Rosenfeld et al., 1994) for the areas vulnerable to debris flow are also under development. It is hoped that the MODEL FOR FORECASTING TYPHOON RAINFALL 103 damages caused by typhoons in Taiwan can be reduced significantly provided that better knowledge of current and future rainfall information be- comes available. Although it is more desirable to forecast typhoon rainfall based on the numerical model outputs, the rainfall climatology always exhibits some useful information (such as Chang et al., 1993, Charba et al., 1998, Lonfat et al., 2004). The statistical method developed by Yeh et al. (1999) and Yeh (2002) is more sophisticated and can probably give better results for the limited stations they analyzed. The climatology model that we developed, however, can provide reasonable cumulative rainfall estimate for each river basin and around the whole island. The emergency management personnel can use this information in hazard mitigation (Fread et al., 1995) before a typhoon hits the island. However, the climatology model requires a well forecasted typhoon track. On the average, the 24 h track error of the CWB was about 150 km. Such errors might cause some errors in model-estimated rainfall. In 2002, using the forecasted tracks instead of the observed tracks would reduce the rainfall estimate error for Rammasun and Nakri, but increase the error for Sinlaku. It must be noted that the climatology model can only give the average condition, thus any deviations from the average condition inherent in the individual cases would appear as error when applying the climatology model during real-time operation. For example, a system with active outer rainbands such as Rammasun would result in a significant error in rainfall amount around the area 200–500 km from the system center. On the other hand, the rainfall amount associated with a weakening or smaller system, such as Nakri would be much smaller than the average. These situations should be noted when applying the climatology model. Fortunately, the strong dependence of typhoon rainfall on radius and the strong topographical lifting made the current climatology model a useful tool in estimating the cumulative rainfall during typhoon period. As shown in Section 4, the R2 value between the observation and the model estimate reached 0.70 and 0.81 for the cumulative rainfall at Dan-Shui and Kao-Ping River Basins, respectively. These R2 values imply that the correlation coefficients of 0.84 and 0.90, which appear to be higher than those (about 0.62–0.74) obtained by Mao et al. (2000). Although this climatology model gives reasonable estimates of cumulative rainfall for DSH and KPS, the errors increase if individual stations or shorter time periods (e.g. 3 h) are considered. However, debris flows occur over very small areas and are strongly related to short period of heavy rainfall. Thus, to help the real-time debris flow warning, a Climatology and Persistence (CLIPER) scheme (Knaff et al., 2003) is under development in order to provide 3-hour or 6-hour quantitative precipitation forecasts for individual station. Finally, due to the limitation of available data 104 CHENG-SHANG LEE ET AL. in the current model, the typhoon rainfall climatology map will be updated (and variations with storm intensity or size be considered if possible) in the near future to provide better and more stable rainfall estimate.

Acknowledgments The authors would like to thank Dr K. Cheung, Dr L.-Y. Lin, Mr C.-T. Weng, Mr A.-X. Wang and Miss W-Y Huang for their help in data analysis and manuscript preparation. Careful reviews and numerous valuable comments made by two anonymous reviewers are highly appreciated. This research was supported by the National Science Council of the Republic of China (NSC 92-2625-Z-002-011, NSC 92-2625-Z-002-037 and NSC 92-3113-Z-002-001).

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