Linking typhoon tracks and spatial rainfall ... - Wiley Online Library

WATER RESOURCES RESEARCH, VOL. 48, W09540, doi:10.1029/2011WR011508, 2012

Linking typhoon tracks and spatial rainfall patterns for improving flood lead time predictions over a mesoscale mountainous watershed Jr-Chuan Huang,1 Cheng-Ku Yu,2 Jun-Yi Lee,1 Lin-Wen Cheng,2 Tsung-Yu Lee,1 and Shuh-Ji Kao3,4 Received 13 October 2011; revised 8 May 2012; accepted 6 August 2012; published 22 September 2012.

[1] Typhoon rainfall characteristics over a mesoscale mountainous watershed (drainage area of 620 km2) located in eastern Taiwan were analyzed to fill the gaps in our knowledge concerning the linkage between typhoon track, rainfall patterns, and flood peak time. This study used spatially high-resolution radar-derived rainfall estimates from 38 storm events (2800 h) to investigate this linkage. The effect of spatial rainfall patterns on the timing of flood peak for the selected events was examined with the aid of a diffusive wave model. The results show that the typhoon rainfall was spatially aggregated and that the relative variations in the rainfall became smaller at higher rainfall rates. The maximum hourly rainfall was approximately twice the areal mean rainfall. Three major rainfall types were identified statistically, and different typhoon tracks appeared to have preferable rainfall types. This finding is presumably due to the interaction of the typhoon circulation and precipitation with the mountainous landscape. Flood lead times were derived for the different rainfall types, and it was found that differences in their lead times could be as large as 3 h over the studied mesoscale watershed. It is recommended that this empirical approach be incorporated into flood forecasting and warning systems. Citation: Huang, J.-C., C.-K. Yu, J.-Y. Lee, L.-W. Cheng, T.-Y. Lee, and S.-J. Kao (2012), Linking typhoon tracks and spatial rainfall patterns for improving flood lead time predictions over a mesoscale mountainous watershed, Water Resour. Res., 48, W09540, doi:10.1029/2011WR011508.

1. Introduction [2] Tropical cyclones (TCs), usually called hurricanes in the North Atlantic Ocean and typhoons in the western North Pacific Ocean, are one of the most devastating weather phenomena in the world. The intense winds and torrential precipitation associated with TCs usually have a wide variety of major effects on the Earth system and society [Rozanova et al., 2010]. For human societies, landslides, debris flows, and floods triggered by TCs can significantly threaten infrastructure, agriculture, and residents living nearby in downstream areas [Huang et al., 2009; Xiao and Xiao, 2010]. In fact, TC-induced disasters are ranked second by the World Meteorological Organization in terms of the loss of human life they cause [Bengtsson, 2007]. For Earth systems, TCs in the western North Pacific are the major forcing that disturb 1

Department of Geography, National Taiwan University, Taipei, Taiwan. Department of Atmospheric Sciences, Chinese Culture University, Taipei, Taiwan. 3 Research Center for Environmental Changes, Academia Sinica, Taipei, Taiwan. 4 State Key Laboratory of Marine Environmental Science, Xiamen University, Xiamen, China. 2

Corresponding author: C.-K. Yu, Department of Atmospheric Sciences, Chinese Culture University, 55, Hwa-Kang Road, Yang-Ming-Shan, Taipei 11114, Taiwan. ([email protected]) ©2012. American Geophysical Union. All Rights Reserved. 0043-1397/12/2011WR011508

forest ecosystems [Mabry et al., 1998; Lugo, 2008; Ito, 2010], induce landslides and debris flows [Montgomery and Dietrich, 1994; Wu and Kuo, 1999; Huang and Kao, 2006], and transport sediments and nutrients. For example, more than 80% of sediments in Taiwan are transported during the influences of TCs [Kao and Liu, 1996; Hilton et al., 2008; Kao et al., 2011]. [3] Taiwan is a well-known target for TCs originating over the northwestern Pacific Ocean. On average, losses associated with typhoons in Taiwan can reach 500 million US dollars per year [Kao et al., 2011]. For example, Typhoon Morakot (6–10 August 2009) brought 2500 mm of rainfall over 5 days in southwestern Taiwan and caused huge losses (673 people killed, 26 missing, and more than 600 million US dollars in damage). Thus, early TC warnings, effective hazard mitigation, and prompt recovery are crucial issues for TC-prone regions [Chang et al., 2007; Lin et al., 2010]. [4] Accurate forecasts of typhoon-induced rainfall amounts are essential for effective flood forecasting, operational warning systems, and decision-making processes [Chang et al., 2008; Huang et al., 2011]. Taiwan Island, located in the main path of typhoons in the northwestern Pacific Ocean, experiences three to four typhoons each year [e.g., Yu and Chen, 2011]. The island is located in the Pacific Orogenesis belt, where the elevated tectonic uplift rate shapes rugged, steep, and mountainous landscapes. Accurate rainfall forecasting, particularly on the mesoscale, is highly challenging in Taiwan because of the variable typhoon tracks and the

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HUANG ET AL.: RAINFALL PATTERNS AND FLOOD LEAD TIME

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Figure 1. (a) Schematic diagram showing the typhoon track categories (1–10) defined by the CWB and the percentage of occurrence for each track. (b) Radar-based rainfall for Typhoon Bilis over the study domain (inset box in Figure 1a). (c) Terrain height for the study area. In Figures 1b and 1c, the black dots represent locations of rain gauges, and the upstream (downstream) red triangle is the location of the Lushui discharge station (Jinwun Bridge). complicated interaction between the typhoon circulations and the diverse landscape. [5] Recent studies have indicated that typhoon characteristics (e.g., the maximum wind speed near the center, the central pressure, and typhoon movement) can be used as a model input to improve the long lead time flood forecasting [Lin et al., 2010]. However, the typhoon track characteristics linked to the spatial patterns of rainfall and runoff over a mesoscale watershed are still poorly understood. Although a trend in precipitation intensity and pattern has been linked to the typhoon track and the relative location of the typhoon circulation center to the topography in many previous investigations in Taiwan [e.g., Wang, 1989; Chang et al., 1993; Lee et al., 2006], these studies only focused on largerscale (the whole island) rainfall patterns determined with conventional rain gauge data. Because the rain gauge observations have a relatively coarse resolution, possible connections between the smaller-scale precipitation distributions and the typhoon tracks have been unexplored. [6] This study explores possible connections between typhoon tracks, statistical characteristics of rainfall, and the flood peak time by using spatially high-resolution radar observations. A total of 38 rainfall events (2800 radarbased hourly rainfall estimates) during 2000–2010 were analyzed over a mesoscale mountainous watershed (drainage area of 620 km2) located in eastern Taiwan. We used a comprehensive data set of radar-based rainfall estimates to

investigate the spatial variability of rainfall over the watershed. Using statistical methods, we identified major rainfall types based on the similarity of spatial patterns in the rainfall estimates. We also estimated the flood peak times associated with each event using a diffusive wave model. Finally, we linked flood peak times to the rainfall types and typhoon tracks. As we will show, these sequential features can provide helpful information for designing real-time flood warning strategies.

2. Data and Methodology 2.1. Study Area [7] Because TCs generally move westward in the northwestern Pacific Ocean, the eastern portion of Taiwan is most directly impacted by approaching typhoons. In distinct contrast to the western coast of Taiwan, the topography along eastern Taiwan is rather steep, with terrain rising abruptly to more than 1500 m above mean sea level (MSL) within 10–20 km of the shore [Yu and Lin, 2008]. The wellknown Taroko marble gorge is located in this region, attracting more than 6 million tourist visits per year. However, the rockfall and quick surges in water levels caused by heavy rainfall due to the interaction of TCs with steep mountainous landscapes frequently cause injuries, deaths, and road damage. Predicting such TC-related hazards is one of the most challenging tasks for the Taroko National Park

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Figure 2. Scatterplot of radar-based rainfall estimates versus rain gauge measurements over the study domain for all of the events. Results (a) with and (b) without the rainfall adjustment procedure (see text for details). The black thick line is the least squares fitting curve. Authority, especially because of the lack of adequate meteorological observations (e.g., rain gauge measurements) over this mountainous area. Access to accurate flood forecasts in advance of these events is crucial for the prevention of the aforementioned hazards. [8] In the Taroko marble gorge, the Li-Wu River is the main stream; it originates from Mount Qi-Lai (3500 m MSL) and flows 58.4 km into the western Pacific (Figure 1c). Due to the policy of protecting national park land, undisturbed forest remains the main land cover in this catchment. To determine flood peak time, we used the Lushui discharge station (Figure 1b), located 1.5 km upstream of the entrance to the Taroko marble gorge, and having a drainage area of 430 km2, in this study. Lushui, the only discharge station along the Li-Wu River, is a good reference for discharge estimation at the downstream site, Jinwun Bridge (Figure 1b), the downstream exit of the Taroko gorge. The mean daily discharge during 1998–2009 at the Lushui station was 26 m3s1; the discharge during the wet season (May to October) accounts for 66% of the annual discharge. TC-induced rainfall is the major contributor to rainfall in the wet season. The hourly discharge rate during TC events can reach 2000 m3s1, which can raise the water level by more than 10 m and inundate bridges. According to the rain gauges surrounding the watershed, the mean annual rainfall (for 1998–2009) was 2595 mm. The rainfall totals in the upstream and northern portions of the watershed are generally higher than those in the downstream and southern portions. The mean annual runoff depth is 1921 mm. The runoff coefficient, defined as the ratio of the annual discharge and the annual rainfall, is 0.75, which is similar to other rivers in Taiwan (0.8). 2.2. Typhoon Track Characteristics and Radar-Based Rainfall Estimates [9] A mature typhoon is typically characterized by a welldefined sea level pressure minimum and circulation center,

intense winds, and considerable precipitation. Precipitation is not distributed uniformly within a typhoon but occurs in localized areas with organized, banded features called “rainbands.” In addition to the eye and the surrounding eye wall, typhoon rainbands are the most striking and persistent features of tropical cyclones as seen from meteorological radar and satellite images. These rainbands often contain the regions of heaviest precipitation in the storm [e.g., Jorgensen, 1984; Yu and Tsai, 2010]. Torrential rainfall frequently occurs over Taiwan as typhoon circulations and their associated rainbands interact with the topography. [10] The Central Weather Bureau (CWB) of Taiwan, in an effort to improve forecasts of typhoon rainfall, has classified typhoon tracks into 10 categories (Figure 1a) using an extensive database of historical typhoons from the past 100 years. For typhoons affecting Taiwan, nearly all of their tracks could be classified except for a very small fraction (2%) that possessed special paths (i.e., track category 10 in Figure 1a). Track categories (hereafter denoted as “tracks”) 1 to 5 belong to the so-called “westward movement of typhoons,” and tracks 6 to 9 belong to the so-called “northward movement of typhoons.” The primary difference between these tracks is the location of the track with respect to Taiwan, a critical factor controlling the island-scale precipitation pattern. As will be shown later, this track-precipitation relationship is, to some extent, still valid when trying to explain the smaller-scale rainfall distributions over the mountainous watershed considered in this study. [11] An island-wide Doppler radar network was established in Taiwan by the CWB in 2000 [e.g., Yu and Chen, 2011] to help improve the real-time flood warning system and mitigate typhoon-induced hazards. Previous studies have documented that radar-based and gauge-based rainfall estimates are generally consistent, particularly for intense rainfall [Krajewski and Smith, 2002; Yu and Cheng, 2008; Huang et al., 2011]. In this study, we used the spatially highresolution reflectivity measurements from the operational

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Table 1. Basic Information for the 38 Analyzed Rainfall Events Event

Date (yyyy/mm/dd)

Total Rainfall (mm)

Duration (h)

Minimum Pressure (hPa)

Maximum Wind Speed (m/s)

Radius of 15 m/s (km)

Track Category

Kai-tak Bilis Chebi Utor Toraji Nari Lekima storm Nakri Morakot Dujuan Mindulle Aere Nock-ten Nanmadol storm Haitang Matsa Sanvu Talim Damrey Longwang Chanchu storm storm Bilis Kaemi Saomai storm Pabuk Sepat Kalmaegi Fung-wong Sinlaku Fanapi Molave Morakot Parma

2000/07/08 2000/08/22 2001/06/23 2001/07/04 2001/07/29 2001/09/16 2001/09/25 2001/12/08 2002/07/08 2003/08/03 2003/09/01 2004/07/01 2004/08/24 2004/10/24 2004/12/03 2005/05/12 2005/07/17 2005/08/04 2005/08/12 2005/08/31 2005/09/22 2005/10/01 2006/05/17 2006/05/28 2006/06/08 2006/07/13 2006/07/24 2006/08/08 2007/06/06 2007/08/07 2007/08/17 2008/07/17 2008/07/27 2008/09/13 2010/09/18 2009/07/17 2009/08/07 2009/10/05

197.3 801.2 98.0 290.5 369.7 320.9 382.1 116.0 185.5 125.8 346.1 553.8 181.8 142.2 548.5 177.9 756.0 185.6 408.0 449.7 291.4 472.2 202.3 174.7 434.2 239.2 308.4 186.4 228.9 328.7 689.8 235.9 545.5 422.6 347.6 101.5 493.2 398.9

56 68 37 62 57 138 48 48 80 72 82 144 63 34 71 96 96 71 82 63 72 54 59 120 123 96 54 35 96 61 61 61 81 65 48 62 128 56

965 930 965 960 962 960 965 987 990 950 942 960 945 940 912 955 985 920 955 925 943 978 960 935 980 920 970 948 925 940 980 955 945

35 53 35 38 38 40 35 18 23 43 45 38 43 38 55 40 25 53 25 51 45 25 38 48 28 53 33 43 51 45 28 40 43

150 300 200 350 250 150 180 80 100 250 250 200 250 250 280 250 200 250 200 200 300 300 200 180 150 250 120 220 250 200 100 250 250

6 3 7 5 3 10 4 0 9 4 5 6 1 6 9 0 3 1 5 3 5 3 9 0 0 2 3 1 0 4 3 2 3 2 4 5 3 10

S band (10 cm) Doppler radar (WSR-88D) at Wu-Fen-San (WFS) to estimate rainfall intensities. Details about the radar characteristics have been given by Yu and Cheng [2008]. The WFS radar is located in northern Taiwan (Figure 1a) and has an elevation of 766 m MSL. The horizontal distance from the radar site to the studied watershed is roughly 100 km. The higher elevation of this site provides better data coverage and less topographic blocking over the study domain than other radar sites in Taiwan. The reflectivity measurements had a spatial (temporal) resolution of 1 km (6 min) and were converted to hourly rainfall rates by applying the well-known power law relationship: Z ¼ aRb

ð1Þ

where Z is the reflectivity factor (mm6 m3), R is the rainfall rate (mm h1), and a and b are coefficients that are determined experimentally. The coefficients in (1) are varied with space and time [Smith et al., 1996]; theoretically, they depend on drop size distributions within precipitation systems [Battan, 1973]. However, drop size distributions commonly change from storm to storm and even differ within the same storm [Steiner et al., 1999]. On the basis of an empirical Z–R relationship proposed by Xin et al. [1997], we have chosen the coefficients a and b to be constant

values of 32.5 and 1.65, respectively. These values are most applicable for the convective precipitation that is expected to frequently occur in the regions of intense rainfall associated with typhoons. [12] In addition to the uncertainty associated with the Z–R relationship, another important source of errors in radarestimated rainfall is that radar systems cannot capture precipitation information very close to the ground because of inherent limitations of its scanning strategies. Any difference in reflectivity values between the ground and elevated locations (where the radar can retrieve data) can contribute to additional errors of the rainfall estimates in (1). For example, the radar beams from the low-level plan position indicator scans of the WFS radar can reach a height of 0.5– 4 km above the ground over the study domain. [13] To reduce the potential uncertainties for the radarderived rainfall described above, we also used surface rain gauge data, which we considered as ground truth for rainfall, to adjust the rainfall intensity estimated from (1). In this procedure, the differences in the rainfall intensity between the rain gauges and the radar estimates at a given station location were calculated and distributed over the study domain by the Cressman weighting function [Cressman, 1959]. A new radar-based rainfall estimate at given Cartesian grids (1 km grid spacing) and time periods was then

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Figure 3. Scatterplot of total rainfall versus (a) minimum pressure and (b) maximum wind speed. (c) Rv versus total rainfall. (d) Aggregation index versus total rainfall. Symbols represent the typhoon tracks. obtained by adding these calculated differences to the original radar-derived rainfall estimates. Comparisons between the radar-based rainfall estimates and rain gauge measurements with and without this rainfall adjustment are shown in Figure 2. Figure 2a shows that without the rainfall adjustment, the radar-based rainfall estimates were generally in good correlation with the ground truth, but they tended to underestimate the rainfall rates. As determined empirically, this underestimation for radar-derived rainfall occurs much more commonly over mountainous regions than in relatively flat areas because orographic enhancement of precipitation is typically confined to a shallow layer close to the ground where the radar does not receive information [e.g., Smith et al., 2009]. This problem was mitigated by the adjustment procedure described above. As shown in Figure 2b, the adjusted radar-derived rainfall estimates were in better agreement with the rain gauges. A sample plot showing a detailed distribution of radar-derived rainfall for Typhoon Bilis (2000) over the study domain is shown in Figure 1b. 2.3. Rainfall Spectrum and Spatial Pattern [14] To characterize the rainfall spectrum and spatial pattern associated with typhoons, we introduce two statistical indices: rainfall variability (Rv) and rainfall aggregation (Ra). For Rv, the coefficient of variation (CV) for each hourly rainfall estimate is defined as the ratio of the standard deviation and the areal mean value calculated over the study domain. The rainfall variability (Rv) for a given rainfall

event is assessed by the mean CV averaged over the duration of the event and can be expressed as Rv ¼

∑nt¼1 Rcv;t n

ð2Þ

where Rcv,t is the rainfall CV at a specific hour. As the Rv value becomes larger, the rainfall event can be considered more variable, while a lower Rv means that the spatial variability of the rainfall event is relatively insignificant and has a narrower spectrum width. [15] Rainfall aggregation (Ra) is defined as the weighted Moran’s I coefficient over the duration of an event. The Moran’s I coefficient (Rsa,t) is widely used and represents spatial autocorrelation [Paradis, 2006]. Rsa,t can be calculated within a pixel array of dimension r c for a given hourly rainfall pattern: Rsa;t

rc rc N ∑j¼1 ∑i¼1 dij Ri;t Rt Rj;t Rt ¼ 2 S0 ∑rc Ri;t Rt

ð3Þ

i¼1

Ra ¼

Rt n ∑t¼1 Rt

Rsa;t

ð4Þ

is the where Ri is the rainfall rate at a certain pixel and R areal mean rainfall for 1 h; d ij = 1 if pixels i and j are adjacent and dij = 0 otherwise. S0 = SSdij is the number of contiguous pairs, and N is the total number of pixels. Rsa values range

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Table 2. Statistical Characteristics of the Rainfall Variability and Aggregation for the Analyzed Rainfall Eventsa Track

Total Rainfall (mm)

Maximum Rainfall (mm)

Rainfall Variability, Rv

Rainfall Aggregation, Ra

-

116.0 177.9 174.7 434.2 228.9

291.4 516.3 461.3 1038.3 581.6

1.16 1.09 0.96 0.88 0.92

0.936 0.944 0.943 0.934 0.908

Aere (2004) Matsa (2005) Saomai (2006)

1 1 1

181.8 185.6 186.4

420.1 446.3 354.2

1.08 1.24 1.02

0.904 0.937 0.957

Bilis (2006) Kalmaegi (2008) Sinlaku (2008)

2 2 2

239.2 235.9 422.6

358.4 339.8 836.3

1.17 0.90 0.73

0.891 0.900 0.908

Bilis (2000) Toraji (2001) Haitang (2005) Talim (2005) Longwang (2005) Kaemi (2006) Sepat (2007) Fungwong (2008) Morakot (2009)

3 3 3 3 3 3 3 3 3

801.2 369.7 756.0 449.7 472.2 308.4 689.8 545.5 493.2

1513.3 526.3 1081.9 878.6 821.6 594.4 1191.3 920.7 195.6

0.84 1.62 0.96 1.20 1.69 0.87 0.69 0.97 0.93

0.955 0.953 0.926 0.940 0.963 0.957 0.953 0.942 0.963

Lekima (2001) Morakot (2003) Pabuk (2007) Fanapi (2010)

4 4 4 4

382.1 125.8 328.7 347.6

647.7 217.2 524.9 1087.7

0.59 1.64 0.69 1.17

0.919 0.932 0.936 0.951

Utor (2001) Dujuan (2003) Sanvu (2005) Damrey (2005) Molave (2009)

5 5 5 5 5

290.5 346.1 408.0 291.4 101.5

510.6 591.3 760.6 521.8 712.2

0.83 1.64 1.23 1.26 1.10

0.956 0.948 0.959 0.938 0.944

Kai-tak (2000) Mindulle (2004) Nock-ten (2004)

6 6 6

197.3 553.8 142.2

292.4 1097.6 310.8

1.15 1.32 0.95

0.930 0.930 0.919

Chebi (2001) Nakri (2002) Nanmadol (2004) Chanchu (2006)

7 9 9 9

98.0 185.5 548.5 202.3

190.5 272.7 1051.1 380.7

1.27 1.11 1.36 1.06

0.956 0.906 0.966 0.954

Nari (2001) Parma (2009)

10 10

320.9 398.9

872.0 1020.0

1.33 0.94

0.917 0.925

Event Storm Storm Storm Storm Storm

(2001) (2005) (2006.05) (2006.06) (2007)

a

The typhoon track, total rainfall, and maximum accumulated rainfall are also shown.

from 1 to +1, indicating a negative and positive autocorrelation, respectively. Positive autocorrelation means that the rainfall distribution is aggregated in space, and a zero value of Rsa indicates a random spatial pattern. The summation of the weighted Rsa values obtained from different hourly periods (Ra) gives a measure of rainfall aggregation for a particular event. The fundamental characteristics of the spatial variation of precipitation can be quantitatively revealed with the two statistical indices, Rv and Ra. [16] To further evaluate the degree of similarity for spatial rainfall patterns in a quantitative and objective manner and generate possible representative rainfall patterns, we applied the Kappa method and cluster analysis to group the spatial rainfall patterns. Because it is not practical to determine the similarity for a spatially continuous data set, we classified the hourly rainfall rates into five different bins of intensity that each contains an equal number of grid points (i.e., 20% of domain coverage for each rainfall bin). We then applied

the Kappa method for the similarity comparison. The Kappa value is a precise, statistical index widely used in image analysis; it provides a quantitative measure for the degree of agreement among interobservers [e.g., Viera and Garrett, 2005]. Kappa can be expressed mathematically as Kappa ¼

Ka Ke 1 Ke

ð5Þ

where Ka and Ke are the actual and expected agreement, respectively. The actual agreement is the total probability of all bins for which the two rainfall images agree in comparison. The expected agreement is the summation of probabilities that are the products of the specific bin probabilities of the interobservers. The concept of Kappa is based on the difference between how much agreement is actually present (i.e., actual agreement) and how much agreement would be expected by chance alone (i.e., expected agreement). This index becomes positive only when the actual agreement is

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Figure 4. Locations of the rainfall maxima observed in each studied event. Symbols represent the typhoon tracks.

higher than expected, similar to the Nash efficiency coefficient [Nash and Sutcliffe, 1970]. For image analyses, a Kappa value larger than 0.4 suggests a moderate agreement between two images. Perfect congruence is present if the Kappa value is exactly equal to 1.0 [Huang and Kao, 2006]. [17] To obtain typical hourly rainfall patterns, the calculated Kappa values were taken as variables into the k-means cluster analysis. The k-means cluster analysis is used to group similar objects and patterns in underlying data [Halkidi et al., 2001; Muñoz-Díaz and Rodrigo, 2004]. In this statistical analysis, the Euclidean distance between the new cluster and another cluster can be expressed as

djm

nj þ nk djk þ nj þ nl djl nj dkl ¼ nj þ nm

ð6Þ

where nj, nk, nl, and nm are the number of objects in clusters j, k, l, and m, respectively. The variables djk, djl, and dkl represent the squared Euclidean distances between the observations in clusters j and k, j and l, and k and l, respectively. Combining the Kappa method and cluster analysis can help classify the observed spatial rainfall patterns into representative rainfall types. 2.4. Travel Time Estimation [18] To evaluate the time required for a raindrop or surface flow to reach an outlet (i.e., Jinwun Bridge in this study), it is necessary to estimate the travel time. Liu et al. [2003] integrated the diffusive wave model into the flow path unit response function to estimate the travel time at any location within the watershed. In this study, we used Manning’s equation and energy dissipation theory [Molnar and Ramirez, 1998] to approach diffusion wave solutions. The approximate solution can be written as " # 1 ðt t 0 Þ2 U ðt Þ ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffi exp 2p⋅t=t0 2p⋅t 3=3 t 0

ð7Þ

and the outlet discharge can be expressed mathematically as Z Z Q s ðt Þ ¼

t

qðt Þ⋅U ðt t ÞdtdA

ð8Þ

A 0

where U(t) is the flow path unit response function, q(t) is the effective rainfall, t0 is the average travel time from a certain location to an outlet along the flow path and s is the standard deviation of the travel time. Both parameters t0 and s can be estimated from Digital Elevation Models (100 m resolution in this study) to mimic the spatial distribution [Liu et al., 2003]. Note that the hydraulic radius, slope gradient, and surface roughness are used to estimate the surface flow velocity and the travel time. The hydraulic radius is derived from the specific contributing area [Huang et al., 2009]. In other words, each flow path has its own parameters that depend on the length of the flow path and the physical characteristics of the flow path elements. The total discharge at an outlet is obtained by the convolution integral of the flow response from all locations. Therefore, the contribution of rainfall at any location to the discharge or flood peak time can be analyzed.

3. Rainfall Characteristics for the Studied Events [19] In this study, the 33 typhoon events that caused significant surges in water levels during the study period were selected for analyses. The database of the selected typhoons is about 45% of the total number of typhoons affecting Taiwan during the study period. For comparison, the five convective rainstorms, which also caused noticeable surges in water levels, were analyzed. The basic attributes for the total 38 chosen rainfall events are shown in Table 1. The total rainfall (i.e., accumulation of areal mean rainfall over the duration of an event) for the selected cases ranged from 98 to 801 mm with an average of 335 mm. The duration of the rainstorms varied from 34 to 144 h with an average of 71 h. Typhoon rainfall usually persisted 3 days and produced a mean daily rainfall of 113 mm. According to

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Figure 5. Scatterplots of (a) the maximum hourly rainfall versus the mean hourly rainfall, (b) the CV versus the mean hourly rainfall, and (c) the aggregation index versus the mean hourly rainfall over the study domain. historical records, the hazards in Taiwan are triggered when daily rainfall exceeds 150 mm d1 [Huang et al., 2007]. Rainfall amounts associated with typhoons were generally higher than in convective rainstorms. The average magnitudes of the central pressure, the maximum wind speed, and the radius of 15 m s1 wind speed associated with the typhoon events were 953 hPa, 39 m s1, and 215 km, respectively. The number of typhoons in track 3 is slightly larger than for the other tracks. [20] The relationship between the total rainfall and minimum pressure (maximum wind speed) is illustrated in Figures 3a and 3b. Figure 3a shows that the total rainfall

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generally increased with a decrease of central pressure in typhoons, suggesting that stronger typhoons usually produce heavier rainfall over the study domain. In addition, the total rainfall tended to increase with the observed maximum wind speed (Figure 3b). Interestingly, the typhoons that followed tracks 2 and 3 (i.e., hit central Taiwan directly) frequently had the lowest pressure, strongest wind speeds, and heaviest rainfall. In contrast, the typhoons that followed track 1 (i.e., moved over regions immediately north of Taiwan) often brought less rain, which is consistent with the generally leeside location of the study domain relative to the typhoon circulation for this track. Note that a typhoon is an approximately circular, intense, cyclonic vortex, and as it approaches the eastern coast of Taiwan (particularly via tracks 3, 4, and 5), the study domain can experience increased onshore flow and orographic lift (Figure 1a). This idea is partially supported by a generally positive correlation between the wind speed and rainfall as shown in Figure 3b. [21] The rainfall variability (Rv), maximum accumulated rainfall, and rainfall aggregation (Ra) calculated from each of the studied events are summarized in Table 2. The value of Rv varied from 0.59 to 1.69 and had a mean magnitude of 1. In Figure 3c, the Rv appears to decrease slightly with the total rainfall, but there is no obvious dependence of Rv on the typhoon track. The maximum accumulated rainfall over the study domain was roughly two times the total rainfall. The aggregation indices were calculated to be 1.0, suggesting that the spatial rainfall patterns for the selected events were strongly aggregated (Figure 3d and Table 2). However, there was no obvious relationship between the aggregation index and total rainfall. [22] Because the spatial patterns of rainfall events tend to have an aggregated characteristic, as described above, the locations of heaviest rainfall (or hot spots) can be analyzed to provide further insight into the nature of the precipitation over the mountainous watershed. The location of maximum accumulated rainfall associated with each of the studied events is shown in Figure 4. The heaviest precipitation was concentrated in three main areas in the study domain. The first area was near the middle southern divides. This precipitation maximum occurred in association with typhoon tracks 3, 4, 5, and 9. The second concentration area, with more than 50% of the studied events, was located in the northeastern divides. Nearly half of the precipitation maxima in this region was associated with typhoons following track 3. Because typhoons rotate counterclockwise in the northern hemisphere, the prevailing winds over the study domain are most often easterlies (i.e., onshore flow) for the aforementioned typhoon tracks, and the northeastern and middle southern divides can be considered to be on the forefront of the mountain barriers. One can reasonably expect significant lifting of the moist boundary layer flow by topography can in these regions, and this is indeed consistent with the locations of heaviest rainfall in Figure 4. [23] The third area of concentrated rainfall maxima was located in the vicinity of the western highest divides and was primarily characterized by ordinary rainstorms and a few isolated typhoon events with relatively diverse tracks. Inspection of larger-scale precipitation patterns for these events (not shown) indicates that intense rain over Taiwan was primarily confined to its western and northwestern sides. Moreover, the rainfall maxima found along the western edge of the study domain (Figure 4) were generally the

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Figure 6. (a-c) Spatial patterns of the classified rainfall types A, B, and C, respectively. (Figures 6d–6i) Two selected hourly rainfall distributions with different Kappa values for each rainfall type are shown to illustrate the similarity of the rainfall patterns. Shading key at bottom denotes the five rainfall bins. eastern extension of enhanced precipitation over the western slopes of Taiwan. In addition to the upslope enhancement of precipitation, the complicated interaction between background typhoon precipitation (i.e., typhoon rainbands or hydrometeors inherently associated with typhoon circulations) and orographically forced precipitation may also play a role in these rainfall events [e.g., Yu and Cheng, 2008; Smith et al., 2009]. Despite this complexity, the rainfall maxima, as seen in Figure 4, were closely correlated with the particular configurations of the mountainous landscape, which suggests that for the selected rainfall events, the local terrain forcing and its interaction with typhoon circulations were important for the generation of heavy rainfall.

rain gauge locations. For example, if rain gauges were deployed only in regions near the location of the observed rainfall maximum, they would be expected to significantly overestimate the areal rainfall, and vice versa. Thus, it appears that a diverse location of rain gauges distributed over the mesoscale watershed is required for a more representative estimate of the areal rainfall. Table 3. Mean and Standard Deviation of the Normalized Rainfall Calculated From Different Intervals of Percentiles for Each Classified Rainfall Type Pattern Type Type A

4. Spatial Patterns and Classification of Hourly Rainfall [24] The maximum, CV, and aggregation index of the hourly rainfall as a function of hourly areal mean rainfall were also analyzed to investigate rainfall characteristics over the study domain (Figure 5). The maximum hourly rainfall was observed to be approximately two times the mean rainfall over the mesoscale watershed (Figure 5a). This relationship was statistically significant (R2 = 0.91 with P < 0.01). This finding raises an interesting issue about the connection between the areal rainfall estimates and the deployment of

Type B

Type C

Percentile

Mean

SD

Mean

SD

Mean

SD

0–10 10–20 20–30 30–40 40–50 50–60 60–70 70–80 80–90 90–100

0.16 0.38 0.52 0.68 0.84 1.01 1.20 1.41 1.67 2.10

0.12 0.13 0.12 0.12 0.10 0.09 0.09 0.11 0.16 0.34

0.17 0.37 0.50 0.62 0.75 0.91 1.10 1.36 1.73 2.40

0.15 0.18 0.21 0.21 0.20 0.20 0.17 0.18 0.32 0.70

0.10 0.30 0.45 0.62 0.78 0.94 1.12 1.36 1.71 2.48

0.13 0.20 0.20 0.19 0.16 0.14 0.12 0.16 0.24 0.59

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Figure 7. The frequency distribution of the three classified rainfall types calculated for each typhoon track. [25] The hourly rainfall CV had a clear inverse relationship with the mean rainfall (Figure 5b). Smaller CV values (i.e., 10.0 mm h1), nearly all aggregation indices were greater than 0.9 (i.e., were highly aggregated in space). One of the reasons that explain the rainfall characteristics above is probably related to the frequent influence of enhanced

stratiform rain (i.e., relatively weak horizontal variations of precipitation) over the study domain. Convective precipitation is typically characterized by stronger horizontal variations and higher rainfall rates, but stratiform precipitation embedded within tropical convection or tropical cyclones has been shown to have a wide range of rainfall rates in nature [Burpee and Black, 1989; Tokay et al., 1999; Ulbrich and Atlas, 2002; Matyas, 2009]. Determination of rainfall variability and aggregation indices could be the rule of thumb when designing the so-called “rainfall generator” as discussed by Gabellani et al. [2007]. Because the locations of heavy

Figure 8. (a) The spatial pattern of the travel time for the Li-Wu watershed and (b) the frequency distribution of the travel time. 10 of 15

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Figure 9. The simulated discharge for Typhoon Morakot (2003). The black solid line is the total discharge. The black dot is the peak flow and the yellow line segment shows the flow over 95% of the peak flow, respectively. The subhydrographs were generated by the corresponding hourly rainfall. The range marked by the two vertical dashed lines indicates the hour that the peak flow occurred; the gray shading indicates the area within 30 min of the occurrence of peak flow. Red, blue, and green represent types A, B, and C, respectively. rainfall were spatially aggregated, the classification of hourly rainfall distributions into specific patterns should be applicable to the studied events. [26] The hourly rainfall distributions over the study domain were further classified by using the Kappa method and k-means cluster analysis as described in section 2. Determining the cluster number is always difficult and somewhat arbitrary. In this study, we chose three clusters for the analysis because the number of instances of each cluster member was similar and the differences among clusters were relatively large after examining cluster numbers from 3 to 6. Three types of rainfall patterns (i.e., types A, B, and C) were identified in this study and are illustrated in Figure 6. The major rainfall pattern for type A represents an approximately north–northeast–south–southwest-oriented rainfall belt across the watershed. Type B was primarily characterized by a region of heavy rain in the northeastern part of the watershed. Unlike types A and B, type C had a distinct rainfall zone located over the western high divides. Two selected hourly rainfall distributions with different Kappa values for each type are illustrated in Figures 6d–6i to show the similarity between the hourly snapshots and the classified types. Based on Figure 6, Kappa values higher than 0.2 may suggest a visually acceptable agreement. [27] In addition to the comparison of spatial patterns, the mean and standard deviation of the normalized rainfall (the normalized rainfall is defined as the rainfall value at each grid point divided by the areal mean rainfall) for each rainfall type over varying percentile intervals of the data were

also calculated to understand the relative rainfall intensity of different rainfall types (Table 3). It appears that the mean values of the normalized rainfall at different percentiles for each rainfall type were very similar. The maximum of the mean values for type A was only a little less than for the other two types. This result indicates that the grouping we applied provides a feasible method for classifying the spatial patterns of the rainfall in a statistical manner and that the determined accumulated frequencies of rainfall intensity can also aid in studying rainfall-generating processes. [28] The frequency of occurrence of each rainfall type for different typhoon tracks is shown in Figure 7. The rainstorm, track 1 and track 2, categories were composed mostly of rainfall pattern type C. Type B was the main pattern for track 10. Tracks 4 and 5 were dominated by the rainfall pattern type A. Types A and B were also the two major patterns for tracks 3 and 9. In contrast, track 6 was not dominated by a specific rainfall type. Apparently, most of the typhoon tracks tended to have preferable rainfall types (i.e., one rainfall type occurs at a frequency of more than 50%). Because of the limitation of observations and the complicated processes involved with the generation of orographic precipitation in the typhoon environment [e.g., Yu and Cheng, 2008; Houze, 2012], a complete interpretation of the observed relationships between typhoon tracks and rainfall types is beyond the scope of this study. However, as suggested in section 3, the favorable regions for the heaviest precipitation within the study domain appear to be largely controlled by the spatial disposition of typhoon circulations in relation to the local

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Table 4. Sequential Changes in the Rainfall Type Within the 6 h Prior to the Flood Peak Time for Each Selected Eventa Rainfall Type Event

6h

5h

4h

3h

2h

1h

0h

Accuracy for Peakb

Accuracy for 95% Peakc

Storm (2001) Storm (2005) Storm (2006.5) Storm (2007) Aere (2004) Matsa (2005) Saomai (2006) Bilis (2006) Kalmaegi (2008) Sinlaku (2008) Bilis (2000) Toraji (2001) Haitang (2005) Talim (2005) Longwang (2005) Kaemi (2006) Sepat (2007) Fung-wong (2008) Morakot (2009) Morakot (2003) Pabuk (2007) Fanapi (2010) Utor (2001) Dujuan (2003) Sanvu (2005) Damrey (2005) Molave (2009) Kai-tak (2000) Mindulle (2004) Nock-ten (2004) Chebi (2001) Nakri (2002) Nanmadol (2004) Chanchu (2006) Nari (2001) Parma (2009)

B C C C C C A C C C B A B B B A A B C A C A A A A A A A C C A C A A B B

B C B C C C B B B C B B B B B A A B B A A A A B C A A A C B A B A A C B

B A C A C C B B A C A A C B B B B A C A A A A A A A A A C B A A A C C A

B C C A C C A C B C B A B B B A B A B B B C A B A A A A C B B A A C B B

B C C A C C A A C C A A C B A A A A B B A A B A A A A A C B A B A A B B

B C C A C C B A C C A A B A A B A A A A A A A C A A A B C B B B A B B C

B C C A C C A C C C A B C A B A A B B C B A A A A A B C C B B B A B B B

A P A F P A P P F P F P P F A A F A F F A F A F A P F A F A A A A P P A

P P A A P P A P A P A P P F P A A A A A A A A A A A A A A A P A P P P A

a The accuracy of the estimated flood peak time is also indicated. The discharge over 95% of the flood peak is also considered as a reference for evaluation of accuracy. P (precise) means that the estimated peak time fell within the hour of the recorded peak. A (acceptable) indicates that the estimated peak fell within 30 min of the recorded hour. F (failure) means the estimated time was beyond the accepted range. b Accuracy of (P) is 0.28 and accuracy of (P + A) is 0.36. c Accuracy of (P) is 0.69 and accuracy of (P + A) is 0.97.

topographic features. The results shown in Figure 7 further support this argument. Additional detailed meteorological observations within and nearby the studied watershed will be required to provide a more comprehensive investigation of the precipitation processes implicit in these relationships.

5. Effects of Spatial Rainfall Patterns on Flood Lead Time [29] The travel time to the outlet of the studied watershed for any location was estimated by the diffusive wave approach illustrated in Figure 8. The calibrated value of surface roughness was set to 0.46, which is comparable to other forestry watersheds in Taiwan [Huang et al., 2009, 2011]. In Figure 8, the travel time spectrum ranges from 0 to 9.3 h, mainly depending on the distance to outlet, with a mean travel time of 6–7 h. The travel time frequency can be regarded as the uniform-rainfall-induced unit hydrograph. One would expect that the hydrograph would be amplified or reduced at any time when the rainfall becomes heterogeneous in space. For example, if the three times rainfall falls within the travel time zone of 3–4 h, the hydrograph shape could be amplified 3 times and might exhibit a different

flood peak time. However, even if the 10 times rainfall occurs within the time zone of 0–1 h, the peak time would remain unchanged due to the small area of this time zone. Many previous studies have demonstrated the effect of rainfall variability on the hydrograph simulations [e.g., Sangati et al., 2009]. The significance of such amplification or reduction of the hydrograph depends closely on the rainfall variation, travel time zonation, and the time step. For flood warnings, the modulation of the hydrograph by natural rainfall variability prominently affects the flood peak time, which must be considered for mitigating hazards. [30] To derive the flood peak time, we applied this travel time analysis to the previously described rainfall events (only 36 events were analyzed; discharge data for two of the events were missing). A sample illustration from Typhoon Morakot (2003), which consisted of three rainfall types, is shown in Figure 9. The analysis indicated a lag time of 2 h from rainfall maximum to runoff peak. In addition, the peaks of the subhydrographs that responded to the type C rainfall pattern were slower than those derived for the other two types. The sequential change in the rainfall type within the 6 h prior to the flood peak for all studied events is shown in Table 4. The rainfall types remained unchanged in

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Figure 10. The estimated overall hydrograph (solid black line) and peak times (red triangles) for the three classified rainfall types. (a–c) Simulated results corresponding to types A, B, and C, respectively, with the assumption that the rainfall rate is uniform for each rainfall type. (d–f) Simulated hydrographs for types A, B, and C, respectively, when considering variations of rainfall rate for each rainfall type. The subhydrographs indicated by the dark green, green, cyan, blue, and dark blue curves are the results derived from the five rainfall bins for each rainfall type shown in Figure 6. most cases. The probabilities of occurrence for A to A, B to B, and C to C were relatively higher than for other sequences of changes in the rainfall type. As elaborated in section 4, this feature is implicitly consistent with Figure 7 and implies that each typhoon tended to be characterized by preferable rainfall types. [31] As for the accuracy of simulated flood peak times, in roughly 28% of the analyzed events the observed flood peak time took place within the hour of the estimated flood peak. The accuracy of the simulated flood peak time can be improved to 70% by considering 30 min as the error tolerance (Table 4). However, focusing on only the highest discharge might be misleading for flood warnings because the peak estimate itself may include some uncertainties. Instead of the highest discharge and its timing, the hazard managers are most concerned with the warning threshold or the absolute quantity. Therefore, if we take 95% of the flood peak as the “warning level” to evaluate the accuracy, 36% (97%) of the events reach a precise (acceptable) estimate, as shown in Table 4. [32] The travel time analysis was further applied to investigate the possible impacts of the three rainfall types on the flood peak time for the downstream site, Jinwun Bridge. The relevant results are summarized in Figure 10. The simulations were initially conducted with the assumption of a uniform rainfall rate to generate the overall hydrograph for each rainfall type, as shown in Figures 10a, 10b, and 10c. In these simulations, we only considered the different rainfall

areas covered by each rainfall bin (cf. Figure 6) and transformed them to the hydrograph. The overall hydrographs for the three rainfall types were exactly identical, with flood peak at 406 min. However, the behavior of their associated subhydrographs derived from the different rainfall bins was quite different. For example, for type C, the blue subhydrograph in Figure 10c responded more slowly because the stronger rainfall mainly occurred near the western divides (Figure 6c). [33] When the spatial variation of the rainfall rate (according to Table 3) was considered in our simulations, the shapes of the hydrographs were altered significantly, particularly for the flood peak time (Figures 10d–10f). This result supports the idea that the spatial variability of precipitation can indeed contribute a detectable impact to the properties of the hydrographs [Pokhrel and Gupta, 2011]. When the difference in weight (i.e., rainfall intensity) or area is large enough, the subsequent hydrograph can be modified substantially, as shown in Figure 10. For type A, the flood peak time took place much earlier, at 304 min, than that shown in Figure 10a. The time of warning threshold (e.g., 95% of the flood peak) occurred at 244 min. Type B also advanced 8 min and 115 min for the flood peak and warning threshold, respectively (Figure 10e). In contrast, the flood peak time derived from type C was only slightly postponed at 10 min, due to the relatively longer travel time (Figure 10f). Because flood peaks of types A and B tend to possess earlier, the warning system should work in advance

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for typhoons with tracks 3, 4, and 5 (Figure 7). For rainstorm, track 1 and track 2, the flood lead time was similar to the mean travel time. These results clearly demonstrate the linkage between the typhoon track, rainfall type, and subsequent flood peak time. A thorough understanding of this linkage may have a high potential to enhance the capability of a real-time flood warning system in the future. [34] It is noteworthy that the empirical approach described above may also benefit from the fact that the track prediction skill has been improved significantly due to advances in numerical weather prediction and data assimilation techniques. However, because only “track categories” was considered in the present study, for future application the linkage from the track type to flood peak time should not be very sensitive to the presence of errors, if any, in the predicted tracks. In the future, it is possible to explore this linkage over a mesoscale mountainous watershed by considering more detailed track information (e.g., the specific location of typhoon track).

6. Conclusions [35] The typhoon rainfall characteristics of rainfall variability and spatial aggregation over a mesoscale mountainous watershed located in eastern Taiwan were analyzed to improve the understanding of the linkage between typhoon tracks, rainfall patterns, and the flood peak time. Our analyses show that typhoon rainfall was highly aggregated in space and the relative variations were observed to be much less prominent at higher rainfall rates. The maximum hourly rainfall was found to have a strong relationship with the areal mean rainfall by a factor of 2. In addition, the selected rainfall events were classified into three major rainfall types (A, B, and C) over the studied watershed through the Kappa method and k-means cluster analysis. Different typhoon tracks appeared to have preferable rainfall types, presumably the result of the interaction of typhoon circulations and precipitation with the mountainous landscape. [36] The flood peak time, also evaluated with the aid of a diffusive wave model, was found to depend strongly on the rainfall types over the watershed. In particular, rainfall type A, with an approximately north–northeast–south– southwest-oriented rainfall belt across the downstream area of the watershed, advanced the flood peak time 3 h compared to the mean flood peak time. This result suggests that the flood warning system for typhoons with tracks 4 and 5 should be initiated much earlier because of the prevalence of type A rainfall for these two typhoon tracks (e.g., Figure 7). In contrast, for type C rainfall, whose major precipitation was primarily confined to regions of high mountains upstream of the watershed, flood peak time was slightly only postponed due to the relatively longer travel time. The connection between the typhoon tracks, rainfall types, and their sequential flood peak time, as depicted in this study, could provide important information for designing flood warning strategies and incorporating this empirical approach into flood forecasting is recommended. [37] Acknowledgments. The authors sincerely appreciate the Taiwan Central Weather Bureau and the Taiwan Power Company for providing rainfall, Doppler radar, and discharge data. We also thank four anonymous reviewers for providing helpful comments that improved the manuscript. This study was supported by Taroko National Park and the National Science Council of Taiwan under grants NSC-100-2116-M-002-016, NSC-100-

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2621-M-018-001, NSC-99-2111-M-034-002-MY3, and NSC-100-2628M034-001-MY3.

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