## Abstract

The multivariate relationships between hourly surface wind and rainfall observations during typhoons affecting Taiwan have been investigated with maximum covariance analysis (MCA). Historical surface observations from 1987 to 2004 are used when typhoon centers were located inside the domain of 19°–28°N, 117°–127°E. The three leading MCA modes explain 70%, 20.6%, and 7.6% of the squared covariance fraction, and the correlation coefficients are 0.59, 0.48, and 0.49, respectively. The wind directions of the three leading positive modes are 1) northwesterly flow perpendicular to the Snow Mountain Range (SMR), 2) southwesterly flow toward the river valleys of the southwestern Central Mountain Range (CMR) and the southern SMR, and 3) easterly flow toward the northeastern SMR and the northern CMR. The rainfall patterns of the three principal modes reveal the contrast between the windward and the leeward sides of the mountain ranges. Based on the MCA singular vectors, historical typhoon surface wind patterns are categorized into major types. The results show that the three major wind types consist of 53% of the data, with 25%, 9%, and 19%, respectively, for these wind types. Furthermore, the analyses of the corresponding surface air temperatures, relative humidities, and air pressures also reveal contrasting patterns between the windward and leeward sides.

## 1. Introduction

Mountainous terrain with the highest elevation at around 4000 m, heavy orographic rainfall, and strong winds associated with typhoons usually induce severe hazards in Taiwan such as floods, landslides, and debris flows, especially on windward sides. A single typhoon event may cause millions of dollars in property losses; an example of such damage was seen following Typhoon Herb in 1996.

As a typhoon approaches Taiwan, its track and intensity are influenced by the topography of the Central Mountain Range (CMR; Wu and Kuo 1999; Wu et al. 2002). Wu et al. (2002) showed the impact of the CMR on the rainfall simulation of Typhoon Herb over Taiwan. The existence of the topography increases the rainfall amount significantly by lifting the moist air over the windward side of the mountains. The wind field is modulated by the topography and the rainfall pattern will adjust along with the wind pattern. Thus, most of the previously documented statistical models that infer typhoon rainfall utilize typhoon center coordinates and maximum wind speeds as predictors (Wang 1983; Lee et al. 2000; Lee et al. 2006). These methods implicitly assume phase-locked conditions among wind, rainfall, and topography. Given similar typhoon center locations and maximum wind speeds, the wind and rainfall patterns are alike.

However, the analysis of observational data shows that comparable typhoon center positions and maximum wind speeds may not imply the same flow regime, meaning that the rainfall deviation may be substantial. Hsieh et al. (1996) generalized four kinds of flow regimes during typhoons affecting Taiwan: 1) unblocked flow, 2) blocked flow, 3) parallel flow, and (4) combined flow. The combined flow regime utilizes at least two of the first three regimes. In both the unblocked and blocked flow regimes, the wind directions are nearly perpendicular to the longitudinal axis of the mountain range. The flow of the unblocked flow regime travels directly over the mountains; hence, heavy rainfall appears on the windward side and the foehn phenomenon can be seen on the leeward side. In contrast, the blocked flow regime has wind fields that are nearly stagnant on the windward side. Blocked flows are mainly around the ends of the mountain range, and the rainfall is relatively small. For the parallel flow regime, airflow is parallel to the configuration of the mountain range (i.e., not impinging on the mountains) and is accompanied by minimal rainfall. Lin et al. (2002) concluded that the rainfall occurring near the terrain was primarily orographically induced, rather than being an effect of the typhoon embedded mesoscale rainbands; heavy orographic rainfall may occur much earlier than typhoon landfall. Thus, the distance from a typhoon center to Taiwan (or the center position of the typhoon) is not a necessary condition for inducing heavy rainfall.

The analysis of flow regimes and corresponding rainfall patterns by Hsieh et al. (1996) is logically reasonable yet lack results from quantitative analysis. In this study we investigated the wind–rain relationships statistically and quantitatively by analyzing hourly rainfall and wind observations at surface stations as typhoons approach Taiwan. Maximum covariance analysis (MCA; Prohaska 1976; von Storch and Zwiers 1999), described in more detail later, was applied in this study. Unlike principal component analysis (PCA), which is mainly for single-field analysis, MCA is a statistical method for analyzing the relations between coupled fields. Prohaska (1976) first applied MCA to study the relationships between monthly mean surface temperature and sea level pressure patterns. Wallace et al. (1992) showed that MCA can explain more of the squared covariance between two fields than canonical correlation analysis (Preisendorfer 1988) can on leading modes (52% vs 24% for the first mode).

PCA and MCA are primarily for scalar-field analysis. Chang et al. (1993) applied PCA to identify the surface pressure modes of typhoons over Taiwan. These pressure modes were then linearly related with the other surface observations’ PCA modes, such as hourly air temperature, relative humidity, wind, and rainfall, to identify the corresponding surface patterns. Yeh (2002) investigated the modes of 6-h accumulated rainfall when typhoons were inside the study domain (18°–28°N, 116°–126°E). For vector data such as wind fields, Barnett (1977) divided wind vectors into *u* (zonal component) and *υ* (meridional component) scalar fields and used PCA to study the Pacific trade wind field separately. Hardy (1977) proposed a complex principal component analysis (CPCA) method to study vector fields. He treated horizontal wind as complex numbers *se ^{iθ}* (

*s*is wind speed;

*θ*is wind direction) and then performed PCA in the complex number domain. Webber et al. (1997) divided a three-dimensional flow field into

*u*,

*υ*, and

*w*components and took these components as a scalar field to perform a “combined PCA” (called real-vector PCA: RVPCA). The RVPCA-obtained eigenvectors can be plotted at original data locations to reconstruct the main features of the flow. Kaihatu et al. (1998) analyzed ocean surface currents by using CPCA and RVPCA methods. They summarized that RVPCA is better for recognizing the tides. Furthermore, they also noted that there seemed to be no way to extend the complex method, whereas the real-vector analysis can be applied to three-dimensional vector fields easily. Ludwig et al. (2004) recently applied RVPCA to identify surface wind patterns in mountain valleys during the Vertical Transport and Mixing Experiment (VTMX). The most dominant flow patterns classified by RVPCA were channeled or thermally driven.

In this study, surface wind vector observations are divided into zonal and meridional components similar to RVPCA, and MCA is applied to directly investigate the multivariate relationships between the vector wind and rainfall during historic typhoons. After the wind–rain MCA is carried out, a MCA-supervised categorization method is developed to categorize historical hourly typhoon surface wind patterns into major types according to the MCA singular vectors. In the following sections we will discuss typhoon tracks, surface observations, and the analysis procedures. MCA theory and the proposed wind-patterns categorization method are briefly described in section 3. In section 4, the analysis results are discussed, and the main conclusions are summarized in the last section.

## 2. Data and analysis procedures

### a. Typhoon tracks

The 6-hourly best-track data from 1987 to 2004 were obtained from the Joint Typhoon Warning Center (JTWC) and are linearly interpolated to get hourly positions. Figure 1 shows the hourly positions of typhoon centers inside the study domain, ranging from 19° to 28°N and from 117° to 127°E.

### b. Surface observations

The surface stations used by Chang et al. (1993) and Yeh (2002) are mainly located around the coasts and over the mountain ranges at the middle of Taiwan. Thus, the identified rainfall patterns lack information over the Snow Mountain Range (SMR). In this study, 17 surface weather stations with hourly rainfall *R*, wind speed WS, wind direction WD, air temperature *T _{x}*, and relative humidity RH records, and four automatic rainfall stations with hourly precipitation records, were chosen (Table 1, Fig. 2). These surface stations are installed and maintained by the Central Weather Bureau of Taiwan. Because heavy orographic rainfall events usually occur over the mountain ranges of northern Taiwan, the stations located over the SMR (i.e., M1–M4) were selected to present the characteristics of rainfall over the SMR. By using wind vector data, we are able to recognize the characteristics and variations of wind patterns rather than just using wind speed data. Table 1 shows the latitudes, longitudes, and altitudes of these stations. A total of 4955 h of historical typhoon positions with corresponding hourly observations at all selected stations are available. This dataset consists of 163 typhoons.

### c. Analysis procedures

The analysis procedures are conducted in the following order. First, following the researches of real-vector PCA (Kaihatu et al. 1998; Ludwig et al. 2004), wind vector data are divided into zonal and meridional components to be transformed into a combined scalar field. Thus, the left field of MCA is a combination of *u* and *υ* components at 17 stations (i.e., 34 scalars), and the right field is hourly rainfall at 21 surface stations (21 scalars). After the wind–rain MCA was carried out, we developed an MCA-supervised categorization method to classify historical hourly typhoon records into major wind pattern types according to the MCA–wind singular vectors. Last, the corresponding surface climatic conditions of these major wind types are discussed.

## 3. Method

### a. Maximum covariance analysis

Maximum covariance analysis, also known as singular vector analysis (Prohaska 1976; Bretherton et al. 1992; Wallace et al.1992; Lau and Weng 2001; Chiang and Vimont 2004), is a method for analyzing the relations between coupled fields. Considering two datasets, the left field is *X _{i}*(

*t*) (i.e., wind field) and the right field is

*Y*(

_{j}*t*) (i.e., rainfall), for

*i*= 1, … ,

*m*stations,

*j*= 1, … ,

*n*stations, and

*t*= 1, … ,

*T*times. MCA performs axes rotations on both fields, and the projections of

**X**and

**Y**onto new axes,

**a**

*and*

^{k}**b**

*, are expressed as below:*

^{k}where *E*[*X _{i}*(

*t*)] =

*E*[

*Y*(

_{j}*t*)] = 0, ∀

*i*, ∀

*j*, and

**a**

*and*

^{k}**b**

*are unit vectors that maximize the cov*

^{k}^{2}(

*Z*,

_{x}^{k}*Z*). Thus, the objective function

_{y}^{k}*J*is

Subject to cov(*Z _{x}^{i}*,

*Z*) = 0 for

_{y}^{j}*i*≠

*j*, the solutions of Eq. (3) are equivalent to the singular value decomposition of the cross-covariance matrix between

**X**and

**Y**[i.e., cov(

**X**,

**Y**)]. Arranging the squared singular values

*λ*

^{2}of cov(

**X**,

**Y**) in descending order,

where *p* = rank[cov(**X**, **Y**)] ≤ min(*m*, *n*); *λ*_{1}^{2} denotes the maximum squared cross covariance, and the accompanying singular vectors **a**^{1} and **b**^{1} are the optimal solutions of MCA mode 1 that project **X** and **Y** onto the *Z _{x}*

^{1}and

*Z*

_{y}^{1}fields. The singular values

*λ*

_{2}–

*λ*and the singular vectors

_{p}**a**

^{2}–

**a**

*,*

^{p}**b**

^{2}–

**b**

*are the solutions of succeeding MCA mode 2 to mode*

^{p}*p*.

Squared covariance fraction (SCF* _{k}*), the percentage of squared cross covariance explained by a specific mode

*k*, is

and the cumulative squared covariance fraction (CSCF* _{k}*) for mode 1 to mode

*k*is

### b. MCA-supervised wind pattern categorization method

To classify historical typhoons into major wind pattern types, a categorization algorithm based on the singular vectors of MCA wind modes was developed. First, the wind observations at time *t*, **W*** _{t}* {=[(

*u*

_{1t},

*υ*

_{1t})], … , [(

*u*,

_{mt}*υ*)],

_{mt}*m*= the number of stations}, are preprocessed according to the following two steps. 1) The averages of

*u*and

_{i}*υ*at station

_{i}*i*are subtracted from the original wind observations to obtain the wind anomaly,

where *u*′* _{it}* =

*u*−

_{it}*u*,

_{i}*υ*′

*=*

_{it}*υ*−

_{it}*, and*

_{i}*u*and

_{i}*are the averages of*

_{i}*u*and

_{i}*υ*at station

_{i}*i*, for

*i*= 1, … ,

*m*. Then, 2)

**W**′

*is normalized to transform it into a unit vector:*

_{t}where ||**W**′* _{t}*|| is the vector norm of

**W**′

*. The distance between the singular vector of MCA mode-*

_{t}*k*wind (

**a**

*) and normalized observation*

^{k}**W**″

*was defined as (Kaufmann and Whiteman 1999)*

_{t}If the amount of major wind types derived by MCA is *P*, the MCA-supervised categorization algorithm searches the minimum distance among *d*_{t,1}–*d*_{t,P}. The type of wind pattern **W*** _{t}* can be determined by

where *d*_{k,threshold} is a radius distance threshold to be determined. If *d*_{t,1}, … , *d*_{t,P} are larger than their corresponding *d*_{threshold}, the wind observation **W*** _{t}* is categorized as type (

*P*+ 1). The diagram of the proposed method is shown in Fig. 3. For example, for observation A,

*d*

_{1}is the shortest distance among

*d*

_{1},

*d*

_{2}, and

*d*

_{3}. Also,

*d*

_{1}is smaller than

*d*

_{1,threshold}. Thus, observation A is categorized as type 1. Observation B is grouped as type 4 because it is outside the three defined cluster domains.

## 4. Results and discussions

### a. Wind–rain MCA results

The CSCF and correlation coefficients between MCA wind and rain modes are shown in Fig. 4. The three leading modes explain about 98.2% of the squared covariance, and the SCFs are 70%, 20.6%, and 7.6%, respectively. The correlation coefficients are 0.59, 0.48, and 0.49. The rest of the MCA modes only explain approximately 1.8% of the squared covariance. The three leading modes are apparently the major representatives of the wind and rainfall characteristics in Taiwan; therefore, our study will mainly focus on these modes.

By assigning the dimensionless singular vectors **a*** ^{k}* and

**b**

*to the corresponding coordinates of the weather stations, wind–rain MCA patterns can be analyzed in a geographic manner. Figure 4 shows the patterns of the three leading modes at positive phase. The definition of the positive phase for mode 1 and mode 2 is defined as positive anomalies of rainfall pattern are over the windward side of western Taiwan. For mode 3, the positive mode is defined when major parts of positive anomalies are over eastern Taiwan.*

^{k}The wind directions of the first positive mode (Fig. 5a) are northwesterly and perpendicular to the SMR, and the wind speeds on the leeward sides are small. The corresponding rainfall pattern is bipolar (Fig. 5d), with the positives occurring on the windward sides (i.e., SMR area, stations N2 and S2) and the negatives occurring on the leeward sides of the mountain ranges.

For the second mode (Figs. 5b and 5e), the wind directions are southwesterly toward the river valleys of the southwestern CMR and the southern SMR. In southeastern and northwestern Taiwan, wind directions are parallel to the mountains. The corresponding rainfall also has an out-of-phase pattern. The maximum rainfall is centered at Alishan Station and extends northward to the southern part of the SMR. The wind directions of mode 3 are easterly over northeastern Taiwan and parallel to the mountains over the northwestern part. Rainfall shows a contrasting pattern among southern SMR and other areas.

The variance of rainfall is larger than that of the surface wind; thus, the objective function [Eq. (3)] is dominated primarily by the rainfall modes *Z _{y}*. The patterns in Fig. 5 represent the rainfall over the major mountain areas and watersheds where dense population and several important reservoirs are located. Therefore, the positive phase of the three leading modes will be emphasized in the following.

Because heavy-rainfall events are the key factors for inducing severe hazards during typhoons affecting Taiwan, the covariance matrix is used in the wind–rain MCA analysis. However, we have standardized the dataset and performed wind–rain MCA. We found that coupled wind–rain patterns are not discernibly different because the variation of the rainfall observations is larger than that of the wind. Thus, we still use the original dataset to preserve the original unit.

### b. Historical typhoon surface wind patterns categorization

The principal wind–rain patterns can be identified by MCA; therefore, the surface wind observations are categorized based on the MCA results. To perform the MCA-supervised categorization method, the thresholds of radius distance [*d*_{threshold}; Eq.(10) and Fig. 3] have to be determined in advance.

The positive modes of the wind–rain MCA are investigated. The correlations between wind and rain modes (*Z _{x}^{k}* and

*Z*) at different radius thresholds (Fig. 3) show that the correlations

_{y}^{k}*ρ*are decreasing if the distance threshold values are larger. For instance,

*ρ*is 0.59 for mode 1 at

*d*

_{1,threshold}= 0.4, and

*ρ*is 0.82 for

*d*

_{1,threshold}= 0.12. This means that the correlations between wind and rain modes increased as the variations of the wind patterns decreased.

Moreover, if the portions of overlapping area for the chosen types are large, the discrimination results may be ambiguous. For type 1 as an example, the overlapping condition for the data is shown in Fig. 6b. If *d*_{1,threshold} = 0.24, the data number for the distance of a normalized observation to mode 1’s singular vector [i.e., *d*_{t,1}; Eq. (9)] within this range is about 1300 h of data. Meanwhile, the data number for *d*_{t,2} (or *d*_{t,3}) ≤ 0.24 is trivial. If the *d*_{1,threshold} increases, the overlapping portion is more significant and the performance of the categorization will be low. Therefore, the *d*_{k,threshold} should be chosen adequately.

To have highly correlated wind–rain modes and to ensure that the overlapping portions of the clusters are appropriate, the thresholds for three modes were chosen:

An hourly wind observation that does not belong to these three types is grouped as type 4. The three major wind types consist of 25%, 9%, and 19% of the data, respectively. The scatterplots of wind–rain MCA modes (i.e., *Z _{x}^{k}* and

*Z*) for these three types after performing the categorization method (Fig. 7) show that the correlation coefficients are raised to 0.69, 0.66, and 0.58. The classification result inside the study domain is shown in Fig. 8. The cases of type 1 are generally located in the northeast of Taiwan with the centroid coordinates at 24.5°N, 124.3°E. Type-2 cases are on the northwest, and the centroid coordinates are 25.1°N, 120.5°E. The centroid coordinates of type 3 cases are 21.5°N, 121.3°E. These cases are generally south of Taiwan.

_{y}^{k}The mean patterns of three major wind types and their corresponding rainfall features (Fig. 9) resemble the MCA singular vectors (Fig. 5). Furthermore, the scatterplots of wind and rainfall averages at all selected surface stations (figures not shown) reveal that the wind–rain linear relationships are well correlated. The correlation coefficients are 0.70, 0.75, and 0.61. These results indicate that the wind pattern classification is appropriate and also affirm the highly correlated relationships between wind and rainfall observations.

The seasonal variation for the four types is also investigated. The monthly frequency of type-2 cases is reduced significantly after August when comparing with other types (figure not shown). According to previous studies (Chen et al. 1999; Yen and Chen 2000), the result should reflect the typhoon tracks and the weakening of the southwesterlies.

### c. Corresponding surface climatic patterns

The horizontal scale of the CMR is analogous to the typhoon’s radius. The dominant topography induces significant distortions to the circulation of a typhoon and Taiwan’s surface structure (Chang et al. 1993; Wu and Kuo 1999). Chang et al. (1993) analyzed the relationships between the PCA modes of surface pressure and other surface climatic factors to identify the corresponding surface patterns. In our study, surface climatic patterns can be investigated directly on the basis of wind-pattern classification results. The patterns of the corresponding surface air temperature *T _{x}*, relative humidity RH, and air pressure

*P*anomalies for the three major wind types are examined. The anomaly of a variable is obtained by subtracting the mean of the whole dataset from the average for a specific wind type

_{a}*N*:

where *O* denotes the specific surface observation mentioned above and the overbar denotes the average.

However, when a typhoon is approaching (departing) Taiwan, Chang et al. (1993) identified a pressure decrease (increase) occurring concurrently at all surface stations. To emphasize the surface pressure contrasts, the pressure observations are preprocessed following the procedure proposed by Chang et al. (1993):

Then, the anomaly of the corresponding surface air pressure for type *N* can be obtained by

Figures 10 and 11 reveal that *T _{x}* is increased (decreased) and RH is decreased (increased) on leeward (windward) sides. The results are mainly due to the CMR’s topographic effects. The moist air goes over the windward sides of mountain ranges, and dry downslope wind occurs on the leeward sides. Because of the aspect ratio of the CMR, the contrast between the surface

*T*and RH observations for the windward and leeward sides for types 1 and 3 is larger than that of type 2. Moreover, the anomaly patterns of surface pressure (Fig. 12) also show the contrast between the windward and leeward sides. The

_{x}*P*contrast pattern of type-1 cases is analogous to mode 3 in Chang et al. (1993), and type 2’s

_{a}*P*contrast pattern corresponds to mode 2 identified by Chang et al. (1993).

_{a}### d. The relationship between flow regimes and foehn phenomena

For a multivariate wind–rainfall component to be major in MCA, not only do the norms of both the wind and rainfall vectors have to be large, but they also have to be highly correlated. Among the main flow regimes defined by Hsieh et al. (1996), only the wind and rainfall data of the “unblocked flow regime” or even the “blocked flow regime” can conform to these standards. Thus, the data of the three leading cluster types apparently consist of the unblocked and blocked flow regimes.

Unblocked and blocked flow regimes can be discriminated by whether the foehn phenomenon can be observed on the leeward sides. Type-1 cases are taken as examples to investigate the differences between unblocked and blocked flow regimes. To analyze the foehn phenomenon, the relative humidity and dewpoint temperature observations at the leeward surface stations (i.e., E3, E4, and E5) are used. Hsieh et al. (1996) defined two criteria to identify the foehn phenomenon during typhoon days:

where *T _{d}* is dewpoint temperature.

Among the type-1 cases, an hourly observation is denoted as an unblocked flow regime case when any of the E3–E5 stations meet the above conditions. However, the surface stations in Taiwan are subject to a simultaneous pressure increase before typhoons reach Taiwan (Chang et al. 1993). The subsidence flows of high pressure areas may cause high air temperatures over all of Taiwan. To avoid the faults in the foehn identifications based on Eqs. (15) and (16), the air temperature contrast between the windward and leeward sides is considered as follows. First, the mean air temperature at each station (*i* = 1, … , *m*) is removed:

Second, the coinstantaneous mean of the air temperature at all stations is removed:

Third, the air temperature contrast between the east and west coasts is considered in two ways: i) a check is done of whether the pattern of air temperature is out of phase between the eastern stations (labeled with E) and western stations (labeled with W) of Taiwan, that is, whether

and ii) a check is done of whether the air temperature anomaly in eastern Taiwan is higher than that in the western region, that is, whether

where the overbar denotes the average amount over the selected stations. Stations E3–E5 are chosen as the eastern stations, and the western stations are W1, W2, and N4. If an observation meets the criteria in Eqs. (15), (16), (19), and (20), it is assumed that a foehn is observed on the leeward side.

Figures 13a and 13b show the average patterns of wind and rainfall under different flow regimes. It is observed that heavy rainfall appears on the windward side, and wind directions are more perpendicular to the SMR if a foehn can be observed on the leeward side. The contrasts are more significant when the criteria in Eqs. (15) and (16) are altered as 1) *T _{x}* ≥ 30°C and 2)

*T*−

_{x}*T*≥ 10°C. The result is shown in Fig. 13c. The windward rainfall is substantial; the maximum for the rainfall average is 28 mm h

_{d}^{−1}. The wind pattern has a coherent northwesterly direction on the windward side. Furthermore, the analysis of the wind speed average on the leeward side shows that when no foehn was observed on the leeward side the wind speed averages were 1.45, 2.52, and 1.62 m s

^{−1}at E3, E4, and E5, respectively. When a foehn was observed at any of the E3–E5 stations, the wind speed averages rose to 2.33 (+61%), 3.06 (+21%), and 2.43 (+50%) m s

^{−1}. If the foehn identification criteria go up to

*T*≥ 30°C and

_{x}*T*−

_{x}*T*≥ 10°C, the wind speed averages become 3.22, 2.98, and 3.54 m s

_{d}^{−1}, respectively. These results show that the leeward wind speed is higher when flow is over the mountain. (i.e., an unblocked flow regime).

In a parallel flow regime the flow is parallel to the mountains and the rainfall is relatively small. For types 1–3, the parallel flows can be seen over southwestern, eastern, and northwestern Taiwan, respectively. The averages of wind and rainfall patterns for type 4 also show parallel flow and include light rainfall. After division of type-4 data into four regions (defined in Fig. 14) and computation of the surface wind and rainfall averages for each domain, the features are shown in Fig. 15. These figures indicate that the parallel flow regime will occur most easily when a typhoon enters the NE, SE, and SW subdomains for type-4 cases. For the NW region, mean wind directions are generally southeastern because the typhoons in the NW domain are usually heading northwest toward southeastern China.

The wind pattern variations of type-4 cases are examined further, and the RVPCA method is applied (Webber et al. 1997; Kaihatu et al. 1998; Ludwig et al. 2004). Figure 16a shows the results of the wind field RVPCA results for all type-4 cases. The pattern of RVPCA mode 1 exhibited the parallel flow pattern over the northwestern and southeastern regions, and it explains 32% of the variance. Therefore, the variations in the type-4 wind patterns are mainly along the longitudinal axis of the mountains. For mode 2, the explained variance is 11%, and parallel flows can be seen on the western coast of Taiwan. However, the flow direction is toward the northern SMR and southern tip of the CMR; therefore, the rainfall averages for northeastern and southeastern Taiwan are a bit larger than for other areas (Fig. 15a).

RVPCA on the type-4 cases within the four subdomains is performed separately. The results are shown in Figs. 16b–e. The explained variances of RVPCA mode 1 for the NE, SE, NW, and SW subdomains are 37%, 33%, 27%, and 31%, respectively. The major portions of the type-4 wind pattern variations inside these subdomains are mainly along the mountains; thus, the rainfall amounts are generally small.

### e. Case study and implications for forecasting

Most statistical methods that infer typhoon rainfall utilize typhoon center position and intensity as predictors (Wang 1983; Lee et al. 2000, 2006). These statistical models were developed to obtain a typhoon rainfall climatological description for real-time forecast applications (Wu and Kuo 1999). They assume that typhoons with similar coordinates and low intensities may have similar rainfall observations. However, rainfall patterns may vary if the flow regimes are different, even if the center positions are alike.

To investigate the coherent relations of wind–rain patterns and the classification results for typhoons with comparable center positions, we chose the historical typhoon cases whose center positions were inside the domain of 26.0°–27.0°N, 120.5°–121.5°E, which is located on the northwestern side of Taiwan (Fig. 8). There are 24 cases inside the 1° × 1° grid. According to the categorization results, there are 13 cases (54%) categorized as type 2. The remaining cases include five cases (21%) that are categorized as type 1, one case (4%) that is categorized as type 3, and five cases (21%) that belong to type 4. The details are shown in Table 2.

Figure 17a is the rainfall average over Taiwan when typhoon centers are inside this 1° × 1°grid. Heavy rainfalls are observed over the southwestern mountain area, especially around the southwestern SMR. Figures 17b–e are the rainfall averages when these 24 cases are divided into the four types according to the wind patterns. The rainfall average patterns are altered when the wind patterns are changed. Therefore, four (or more) possible types of rainfall patterns should be considered.

Three cases are selected as examples. Figures 18a–c are the patterns of wind and rainfall observations at 1)1100 UTC 9 July 2007 for Typhoon Kai-Tak (type 1), 2)1800 UTC 22 September 1992 for Typhoon Ted (type 2), and 3) 1800 UTC 2 July 2004 for Typhoon Mindulle (type 2). The rainfall observations at the automatic rainfall stations of the Central Weather Bureau were collected to reveal the detailed rainfall patterns. These stations were installed successively beginning from 1996. The normalize distance *d _{k}*, wind mode value

*Z*, and rainfall mode value

_{x}*Z*are also shown in Fig. 18. The wind pattern at 1100 UTC 9 July 2007 (Typhoon Kai-Tak) is type 1 (Fig. 18a); thus, the wind mode-1 value (

_{y}*Z*

_{x}^{1}) is the largest. Also, the corresponding rain mode 1 (

*Z*

_{y}^{1}) is the largest among the three modes; thus, the rainfall pattern is similar to that in Fig. 4d. The wind patterns at 1800 UTC 22 September 1992 (Typhoon Ted) and 1800 UTC 2 July 2004 (Typhoon Mindulle) are shown in Figs. 18b and 18c. The wind patterns of these two cases are classified as type 2. The wind directions on the west and southwest coasts are near southern or southwestern; therefore, the wind mode-2 values (

*Z*

_{x}^{2}) are significant. The corresponding heavy rainfalls are observed over the southwestern mountain region (i. e., similar to Fig. 4e), so that the rain mode-2 values (

*Z*

_{y}^{2}) in these two cases are large. Furthermore, the rain mode-2 value (

*Z*

_{y}^{2}) of the case on 1800 UTC 2 July 2004 is prominent because Typhoon Mindulle induced strong and moist southwesterly flow toward southwestern Taiwan. Even though Typhoon Mindulle was far away from Taiwan, the southwesterly-flow-induced heavy rainfall caused tremendous damage on the leeward side, such as debris flows, landslides, and severe floods. Therefore, wind pattern is an important factor for inferring typhoon rainfall pattern. The results of wind–rain MCA from this study can provide useful information for analysis and forecasts. The examples in this session show that, even in a confined domain, wind and the accompanying rainfall pattern may still vary. Therefore, it is recommended that wind information should be considered when analyzing the typhoon rainfall pattern in Taiwan.

## 5. Conclusions

In this study, JTWC best tracks, hourly rainfall, and wind field observations at surface stations were used to analyze the relationships between wind and rainfall during typhoons affecting Taiwan. Maximum covariance analysis was applied to characterize the leading modes of the surface wind and rain observations. We also proposed an MCA-supervised categorization method to classify historical typhoon cases into major wind pattern types. The analysis results show that the three leading modes consist of 53% of the data and explain 70%, 20.6%, and 7.6% of the SCF, respectively. The wind directions of the three leading positive modes are 1) flow that is northwesterly and perpendicular to the SMR, 2) southwesterly flow toward the river valleys of the southwestern CMR and the southern SMR, and 3) easterly flow perpendicular to the northeastern CMR. The rainfall patterns of these three principal modes are all bipolar, with the positives (negatives) occurring on the windward (leeward) sides of the mountain ranges. The correlation coefficients of the three leading MCA modes are 0.59, 0.48, and 0.49. The results are raised to 0.69, 0.66, and 0.58 after wind pattern clustering.

Also, because of topographic effects, the air temperature and relative humidity anomaly patterns of these types show that *T _{x}* is increased and RH is decreased on the leeward sides. The surface pressure contrast pattern of type-1 cases also shows the contrast between the windward and leeward sides. The differences between the unblocked flow regime and the blocked flow regime can be differentiated by the foehn phenomenon on the leeward sides. If a foehn pattern can be seen on the leeward side (i.e., the unblocked flow regime), then the analysis results show that wind directions are more perpendicular to the SMR and heavy rainfall appears on the windward side. In addition, wind speeds on the leeward side are higher.

The allocation of the chosen surface stations may have impacts on the wind–rain MCA results. However, it is difficult to use evenly distributed stations at present. To provide representative statistical results and to present the main features of typhoon rainfall in Taiwan, the stations located over SMR are included first. As mentioned above, our research can complement the rainfall information that has been lacking in previous studies. The rainfall observations over SMR are very important because of the dense population downstream of the watersheds, and there are also several important reservoirs located around the area. Thus, this is valuable information for flood disaster prevention and reduction.

The proposed analysis procedures would be useful for diagnosing the rainfall anomalies caused by wind pattern variations. Furthermore, correctly categorizing the wind and rainfall data can help to clarify the interaction mechanism among typhoon wind, rainfall, and topography. This is an important step in further improving the skill of typhoon rainfall inferences.

## Acknowledgments

The authors thank the Central Weather Bureau for providing the surface observation data. We also thank three anonymous reviewers and the editor for their valuable comments.

## REFERENCES

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## Footnotes

*Corresponding author address:* Dr. Hsiao-Chung Tsai, Weather Forecast Center, Central Weather Bureau, No. 64, Gongyuan Rd., Taipei City 10048, Taiwan. Email: hctsai@cwb.gov.tw