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Surface Wind Nowcasting in the Penghu Islands Based on Classiﬁed Typhoon Tracks and the Effects of the Central Mountain Range of Taiwan

CHIH-CHIANG WEI Department of Digital Content Designs and Management, Toko University, Pu-Tzu City, Chia-Yi County, Taiwan

(Manuscript received 5 March 2014, in ﬁnal form 21 September 2014)

ABSTRACT

The purposes of this study were to forecast the hourly typhoon wind velocity over the Penghu Islands, and to discuss the effects of the terrain of the Central Mountain Range (CMR) of Taiwan over the Penghu Islands based on typhoon tracks. On average, a destructive typhoon hits the Penghu Islands every 15–20 yr. As a typhoon approaches the Penghu Islands, its track and intensity are influenced by the CMR topography. Therefore, CMR complicates the wind forecast of the Penghu Islands. Six main typhoon tracks (classes I–VI) are classified based on typhoon directions, as follows: (I) the direction of direct westward movement across the CMR of Taiwan, (II) the direction of northward movement along the eastern coast of Taiwan, (III) the direction of northward movement traveling through Taiwan Strait, (IV) the direction of westward movement traveling through Luzon Strait, (V) the direction of westward movement traveling through the southern East China Sea (near northern Taiwan), and (VI) the irregular track direction. The adaptive network-based fuzzy inference system (ANFIS) and multilayer perceptron neural network (MLPNN) were used as the forecasting technique for predicting the wind velocity. A total of 49 typhoons from 2000 to 2012 were analyzed. Results showed that the ANFIS models provided high-reliability predictions for wind velocity, and the ANFIS achieved more favorable performance than did the MLPNN. In addition, a de- tailed discussion on the interaction of the CMR with the Penghu Islands based on various track directions is provided. For class I, the CMR is observed to have significantly influenced variations in wind speed when typhoons approached the Penghu Islands. In addition, the winds on the Penghu Islands were observed to have been influenced by the distance from the typhoon center to the Penghu Islands for all classes except class II.

1. Introduction a destructive typhoon hits the Penghu Islands every 15– 20 yr (Wu et al. 2013). For the Penghu Islands, the wind The Penghu Islands (Fig. 1), situated in the main path data were measured by a weather station at an eleva- of western North Pacific typhoons, form an archipelago tion of 10 m above sea level, indicating highly fluctu- off the western coast of Taiwan in the Taiwan Strait. The ating wind velocities during typhoons, as evidenced Penghu Islands comprise excellent land and sea areas for by historical records. Compared with weather stations wind power generation. Recently, the Penghu Islands at this altitude, a typical wind turbine, which is ap- were selected as low-carbon islands because numerous proximately 40–60 m in height, might be subjected to researchers have found the Penghu Islands to be an relatively stronger winds. Because fluctuations in wind excellent location for developing wind power (Lee and velocity influence wind power production, accurate Huang 2004; Lin 2012). Wind power meteorology can knowledge of wind is required for the planning, design, provide information to the wind power industry over and operation of wind turbines (Akhmatov 2007; the Penghu Islands, such as the siting of wind tur- Vincentetal.2010). bines, regional wind resource assessment, and the short- As a typhoon approaches the Penghu Islands, the ty- term prediction of wind resources (Petersen et al. 1998; phoon circulation with the Central Mountain Range Hsieh and Dai 2012). According to typhoon statistics, (CMR) of Taiwan, as indicated by the yellow dotted line in Fig. 1, produces considerable mesoscale variations in Corresponding author address: Chih-Chiang Wei, No. 51, Sec. 2, pressure, wind, and precipitation distribution over and University Rd., Pu-Tzu City, Chia-Yi County 61363, Taiwan. nearby Taiwan. The CMR is the principal range of E-mail: [email protected] mountains in Taiwan, and runs from the north to the

DOI: 10.1175/WAF-D-14-00027.1

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FIG. 1. Location of the Penghu Islands and schematic diagram of the typhoon track classiﬁcations.

south of Taiwan. The tallest peak of the CMR is Jade confining the storm to a cyclonic track around the Mountain (3952 m). The CMR is 340 km long and 80 km northern end of the CMR. Bender et al. (1985) observed wide, with an average height of 2500 m. As a typhoon that the mountain range affects the decay rate through approaches Taiwan, the topography of the CMR in- reduction in the supply of latent and kinetic energy into fluences its track and intensity (Wu and Kuo 1999; Tsai the storm circulation both during and after the passage and Lee 2009). The topography increases the rainfall of the storm over the mountain. Moreover, Hsu et al. amount significantly by lifting moist air over the wind- (2013) examined the effect of topographically phase- ward side of the mountains. The topography modulates locked convection with the CMR on the westward the wind field, and the rainfall pattern adjusts with the movement of typhoons across Taiwan. They deter- wind pattern (Wu et al. 2002). mined that topographically phase-locked convection acts A number of review studies on typhoons affecting to slow the northern landfalling typhoons and accelerate Taiwan have been investigated and have indicated that, the southern landfalling typhoons. These studies have when a typhoon approaches Taiwan, the CMR signifi- shown the substantial influences of the CMR topogra- cantly affects its circulation and track (Chang et al. phy on typhoons. 1993; Tsay 1994; Wu et al. 2002; Wu and Kuo 1999). Based on historical records, the Central Weather Brand and Blelloch (1974) found that westbound ty- Bureau (CWB) of Taiwan defined 10 typical track phoons tend to move cyclonically around the northern types based on typhoon statistics. For simplicity, the side of the CMR, and experience an average intensity typhoon tracks that affected the Penghu Islands are decrease of over 40%, starting approximately 12 h be- classified into the following six main track directions fore the storm centers reach the CMR. Wang (1980) (classes I–VI) (Fig. 1): direct westward movement documented and analyzed the path, intensity, propa- across the CMR of Taiwan (class I, comprising types gation speed, and evolution of 53 westbound typhoons 2–4); northward movement along the eastern coast of that approached Taiwan, indicating that the typhoon Taiwan (class II, comprising types 6 and 8); northward center was deflected toward the north as it approaches movement traveling through Taiwan Strait (class III, Taiwan, and toward the south after its passage over comprising types 7 and 9); westward movement traveling the CMR, because of the deflection of the mean through the Luzon Strait, which is the strait between steering flow upstream of the CMR. Using a primitive Taiwan and Luzon Island of the Philippines (class IV, equation model, Chang (1982) showed that, because comprising type 5); the direction of westward movement of blocking effects, mountain-induced flow deflections traveling through the southern East China Sea (near are mainly confined to the lower levels, and the passage northern Taiwan) (class V, comprising type 1); and the of the westward-approaching typhoon induces a mean irregular track direction except classes I–V (class VI, cyclonic circulation pattern around the mountain, comprising type 10).

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TABLE 1. Typhoons affecting the Penghu Islands during 2000–12 and typhoon information.

Track Period affected Max wind in Max wind in class the Penghu Magong typhoon center Intensity 2 2 (type) Typhoon Islands (LST) (m s 1) (m s 1) category Class I Bilis 22–23 Aug 2000 15.9 53 Category 3 (types 2–4) Toraji 29–31 Jul 2001 9.3 38 Category 1 Lekima 26–28 Sep 2001 12.7 35 Category 1 Morakot 3–4 Aug 2003 6.7 23 Tropical storm Haitang 17–19 Jul 2005 16.8 55 Category 3 Talim 31 Aug–1 Sep 2005 17.0 53 Category 3 Longwang 1–3 Oct 2005 10.8 51 Category 3 Bilis 13–15 Jul 2006 12.9 25 Tropical storm Kaemi 24–26 Jul 2006 13.8 38 Category 1 Bopha 8–9 Aug 2006 8.0 23 Tropical storm Pabuk 7–9 Aug 2007 8.4 28 Tropical storm Sepat 17–19 Aug 2007 13.7 53 Category 3 Krosa 6–7 Oct 2007 12.6 51 Category 3 Kalmaegi 17–18 Jul 2008 8.9 33 Category 1 Fung-Wong 27–29 Jul 2008 15.9 43 Category 2 Sinlaku 12–14 Sep 2008 10.1 51 Category 3 Jangmi 27–29 Sep 2008 13.4 53 Category 3 Morakot 7–9 Aug 2009 15.4 40 Category 1 Fanapi 19–20 Sep 2010 18.9 45 Category 2 Nanmadol 28–31 Aug 2011 10.6 53 Category 3 Saola 31 Jul–3 Aug 2012 12.3 38 Category 1 Class II Kai-Tak 8–9 Jul 2000 8.2 35 Category 1 (types 6 and 8) Prapiroon 27–30 Aug 2000 7.1 33 Category 1 Xangsane 30 Oct–1 Nov 2000 12.0 38 Category 1 Cimaron 11–13 May 2001 9.9 23 Tropical storm Melor 2–3 Nov 2003 9.0 25 Tropical storm Mindulle 30 Jun–2 Jul 2004 9.0 45 Category 2 Haima 12–13 Sep 2004 5.6 18 Tropical storm Nock-Ten 24–25 Oct 2004 8.9 43 Category 2 Class III Chebi 22–24 Jun 2001 25.8 35 Category 1 (types 7 and 9) Nanmadol 3–4 Dec 2004 9.9 38 Category 1 Nakri 9–10 Jul 2002 11.9 18 Tropical storm Chanchu 17–18 May 2006 14.6 45 Category 2 Linfa 20–22 Jun 2009 14.8 28 Tropical storm Lionrock 31 Aug–2 Sep 2010 8.5 23 Tropical storm Megi 21–23 Oct 2010 12.3 48 Category 2 Talim 19–21 Jun 2012 19.3 25 Tropical storm Class IV Utor 3–5 Jul 2001 12.6 38 Category 1 (type 5) Dujuan 1–2 Sep 2003 11.7 43 Category 2 Kompasu 14–15 Jul 2004 2.7 20 Tropical storm Molave 16–18 Jul 2009 5.5 28 Tropical storm Class V Sinlaku 4–8 Sep 2002 5.8 40 Category 1 (type 1) Aere 24–26 Aug 2004 7.5 38 Category 1 Matsa 3–6 Aug 2005 5.9 40 Category 1 Wipha 17–19 Sep 2007 9.0 48 Category 2 Class VI Bopha 9–10 Sep 2009 9.2 23 Tropical storm (type 10) Nari 16–19 Sep 2001 11.1 40 Category 1 Parma 3–6 Oct 2009 11.5 43 Category 2 Tembin 22–28 Aug 2012 10.3 45 Category 2

The purposes of this study were 1) to forecast the hourly intelligence models can be applied to formulate wind ve- typhoon wind velocity over the Penghu Islands and 2) to locity prediction models. Since the renaissance of artiﬁcial understand the effects of the CMR terrain over the Penghu neural networks (ANNs) in the late 1980s (caused by the Islands based on typhoon tracks. Numerous artiﬁcial introduction of the back-propagation training algorithm

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TABLE 2. Hurricane wind scale and number of collected events approaching Taiwan during 2000–12.

2 Wind intensity scale Range (m s 1) No. of event Saffir–Simpson 5 $70 0 wind category 4 58–70 0 3 50–58 9 2 43–50 10 1 33–43 16 Additional Tropical 18–33 14 classifications storm Tropical ,18 0 FIG. 2. Numbers of the six classified typhoon directions (classes depression I–VI) during 2000–12. for feed-forward ANNs, such as multilayer perceptron 2. Geographical area and typhoons neural networks; MLPNN), they have become the most The Penghu Islands (Fig. 1), consisting of 64 small frequently used prediction approach. Recently, ANNs have islands and islets off the western coast of Taiwan, have been widely applied in the hydrology and hydrometeorol- a meteorological environment characterized by a sub- ogy fields (e.g., Chau et al. 2005; Chen and Chau 2006; tropical marine monsoon climate with hot summers and Muttil and Chau 2006; Taormina et al. 2012; Wei 2012; Wei dry winters. The Penghu Islands, comprising an area of and Roan 2012; Wu et al. 2009; Wu and Chau 2013). 141 km2, are located over the Taiwan Strait, which is be- Additionally, the application of another popular technol- tween China and Taiwan. The spatial range of the Penghu ogy, the adaptive network-based fuzzy inference system Islands spans 238120–238470Nand1198190–1198430E. We (ANFIS), has also become widespread. Neurofuzzy sys- considered island-based gauges at the Magong weather tems (e.g., the ANFIS) are fuzzy systems that apply ANN station of the Penghu Islands. The Magong weather station theory to determine the properties of fuzzy sets and fuzzy is at an elevation of 10.7 m, and at a position of 2383400200N rules by processing data samples (Jang 1992, 1993). The and 11983301900E. The following complete dataset of ty- major advantage of this network is that it can tune the phoon characteristics and ground weather data were ob- complicated conversion of human intelligence to fuzzy tained from the CWB. systems. ANFIS has been shown to be powerful in modeling numerous processes, such as civil engineering a. Recorded typhoons (Emiroglu et al. 2012), and hydrological time series (Chang and Chang 2006; Lohani et al. 2012; Özger et al. 2012; We collected 49 typhoon events that affected the Sfetsos 2000; Smiatek et al. 2013). As indicated in Bilgehan studied station over the past 13 yr (2000–12). Table 1 lists (2011), both ANN and fuzzy logic techniques have ad- the typhoon intensities of the collected events. Moreover, vantages and disadvantages. ANNs are highly efficient in Fig. 2 shows the numbers of the six track classes for adapting and learning, but the disadvantage is that the the examined typhoons. For classes I–VI, the numbers trained models are much more difficult to interpret than is of typhoons were 21 (42.9%), 8 (16.3%), 8 (16.3%), the ‘‘black box’’ model. Conversely, fuzzy logic is not 4 (8.2%), 4 (8.2%), and 4 (8.2%), respectively. We iden- particularly efficient in learning but presents the advantage tified class I as the most frequent track direction. of approximate reasoning. Neurofuzzy systems combine The Saffir–Simpson hurricane wind scale is used to the advantages of both techniques without having any of define typhoon intensity. Table 2 shows the hurricane their disadvantages (Vassilopoulos and Bedi 2008). wind scale on a 1–5 basis determined by the sustained In this study, ANFIS was used as the forecasting wind velocity of a hurricane. This scale estimates po- technique to predict the wind velocity on the Penghu tential property damage. To be classified as a hurri- Islands based on the classified typhoon tracks. Neuro- cane, a tropical cyclone must have maximum sustained 2 fuzzy systems are currently among the most widely winds of at least 33 m s 1 (category 1). Hurricanes studied hybrid systems because of the advantages of two reaching category 3 and higher are considered major highly popular modeling techniques: ANNs and fuzzy hurricanes, because of their potential for a substantial logic. Moreover, we compared them with a benchmark loss of life and damage. The highest classification in the MLPNN model. In addition, the effects of the CMR scale, category 5, is reserved for storms with winds 2 terrain were discussed in-depth because the CMR sig- exceeding 70 m s 1. Table 2 also displays the numbers nificantly influences variations in wind speed when ty- of different typhoon intensities. In total, 8 typhoons phoons approach the Penghu Islands. (16.3%) fall into category 3, 11 typhoons (22.4%) fall

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TABLE 3. Statistics of attributes for typhoon characteristic and ground weather data.

Data Attribute Unit Min–max Mean Std dev Typhoon Pressure at typhoon center 102 Pa 912–1000 968.74 20.57 Lat of typhoon center 8N 15.20–28.50 23.05 2.34 Lon of typhoon center 8E 113.90–131.40 121.49 2.68 Typhoon radius km 50–350 200.34 65.32 2 Typhoon moving speed km h 1 0–50 15.68 7.32 2 Max wind intensity of ms 1 18–55 32.66 9.84 typhoon center Ground Air pressure on the ground 102 Pa 975.1–1016.8 998.81 6.61 Air pressure at sea level 102 Pa 976.4–1018.1 1000.11 6.61 Ground temperature 8C 18.9–33.4 26.94 2.10 Dewpoint temperature 8C 15.2–27.6 24.15 1.88 Relative humidity % 55–100 85.16 8.33 Vapor pressure on the ground 102 Pa 17.3–36.9 30.26 3.24 Rainfall duration within 1 h h 0–1 0.31 0.44 2 Global solar radiation MJ m 2 0–3.3 0.31 0.60 2 Surface wind velocity m s 1 0.1–25.8 6.05 2.99 Surface wind direction 8 0–360 168.32 133.02 2 Precipitation on the ground mm h 1 0–94.5 1.52 5.37 into category 2, 16 typhoons (32.7%) fall into category c. Typhoon track classification and data division 1, and 14 typhoons (28.6%) are classified as tropical Because the typhoon tracks in class VI are constantly storms. changing and abnormal, this track class might be not b. Datasets suitable for deducing rules for data-driven modeling. Thus, a prediction model was not developed for class VI A total of 2892 hourly records for the collected ty- typhoons. Before the prediction models were trained and phoons were available. The climatologic typhoon data and tested, the datasets were classified into independent the ground weather data of the Magong station were training and validation subsets. Table 4 lists five classified collected. The six attributes of typhoon climatologic data typhoon tracks (i.e., classes I–V). For class I, depending consist of the pressure at the typhoon center, the location on typhoon date, the first several typhoons (Table 1) of the typhoon center (latitude and longitude), the radius were used for training, whereas the last typhoons (i.e., of the typhoon, the moving speed, and the maximal wind Fanapi in 2010, Nanmadol in 2011, and Saola in 2012) intensity of the typhoon center. The 11 attributes of the were used for validation. The data of classes II–V were ground weather data are the air pressure on the ground, divided in the same manner (Table 4). air pressure on the sea level, ground temperature, dewpoint temperature, relative humidity, vapor pressure on the ground, rainfall duration within 1 h, global solar ra- 3. Theorem of algorithm diation, surface wind velocity (maximum 10-min mean, a. ANFIS 10 m above the surface), surface wind direction, and precipitation on the ground. All the data were measured Based on the types of fuzzy reasoning and fuzzy IF/ basedonanhourlyscale. THEN rules employed, various types of fuzzy reasoning

TABLE 4. Typhoon track classes and data division.

Track class (type) Training set Validation set Class I (types Bilis (2000), Toraji (2001), Lekima (2001), Morakot (2003), Haitang (2005), Fanapi (2010), 2–4) Talim (2005), Longwang (2005), Bilis (2006), Kaemi (2006), Bopha Nanmadol (2011), (2006), Pabuk (2007), Sepat (2007), Krosa (2007), Kalmaegi (2008), Saola (2012) Fung-Wong (2008), Sinlaku (2008), Jangmi (2008), Morakot (2009) Class II (types Kai-Tak (2000), Prapiroon (2000), Xangsane (2000), Cimaron (2001), Nock-Ten (2004) 6 and 8) Melor (2003), Mindulle (2004), Haima (2004) Class III (types Chebi (2001), Nakri (2002), Nanmadol (2004), Chanchu (2006), Linfa (2009), Talim (2012) 7 and 9) Lionrock (2010), Megi (2010) Class IV (type 5) Utor (2001), Dujuan (2003), Kompasu (2004) Molave (2009) Class V (type 1) Sinlaku (2002), Aere (2004), Matsa (2005) Wipha (2007)

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FIG. 3. The structure of an ANFIS. have been proposed in the literature (e.g., Mamdani and Therefore, we employed TS fuzzy inference systems, Assilian 1975; Tsukamoto 1979; Takagi and Sugeno which can be easily implemented in the form of an 1985). The most widely applied in ANFIS is the Takagi– adaptive neurofuzzy network structure. Figure 3 pres- Sugeno (TS) fuzzy model (Sugeno and Kang 1988). ents the ﬁve-layer structure of the neurofuzzy network,

FIG. 4. Flowchart of the proposed methodology for formulating an artiﬁcial intelligence-based wind velocity model.

Unauthenticated | Downloaded 10/05/21 02:09 PM UTC DECEMBER 2014 W E I 1431 ! kx 2c k2 O 5u (x )5exp 2 i ji 1,ji ji i s2 2 ji 5 ... 5 ... i 1, 2, ,Nj 1, 2, , Mi, (1)

where uji(xi) is the membership function, cji and sji are the antecedent parameters, N is the number of

inputs, Mi is the number of the fuzzy membership function of input i,andkk denotes the Euclidean distance. In the rule layer, an AND or OR operator is applied to obtain one output that represents the results of the antecedent for a fuzzy rule or, in other words, firing strength. This indicates the degree to which the antecedent part of the rule is satisfied and the shape of the output function for that rule. Here, the AND operator is applied to obtain the outputs, called firing strengths

O2,p, which are the products of the corresponding de- grees obtained from layer 1, as follows:

N 5 5 5 ... O2,p wp P upi(xi) p 1, , P, (2) i51

FIG. 5. Sensitivity analysis of ANFIS and MLPNN model parameters on classes I–V. where wp is the weighted value and P is the number of rules. The node of the normalization layer computes the composed of an input layer, a rule layer, a normalization output ratio between the node and all nodes, as follows: layer, a consequent layer, and an output layer, creating the TS fuzzy model. The computation and transmission w O 5 w 5 p . (3) of each layer are described as follows. 3,p p P å The input layer projects the input to a group of fuzzy wp 5 sets and estimates the values of a group of membership p 1 functions. The shapes of membership functions are criti- The output of the consequent layer node is the prod- cal because they affect fuzzy inference systems. These uct of the output of the normalization layer and the membership functions can be any appropriate functions commonly used ﬁrst-order TS fuzzy model (Takagi and that are continuous and piecewise differentiable (e.g., Sugeno 1983), and is as follows: Gaussian, generalized-bell-shaped, trapezoidal-shaped, and triangular-shaped functions; Lohani et al. 2012). ! N Gaussian functions have been widely used in various stud- 5 5 å O4,p wp fp wp rpi xi , (4) ies (e.g., Ichihashi et al. 1995; Li et al. 2002; Oh and Pedrycz i50 2000). Here, we adopted a group of Gaussian function as the membership function, expressed as follows: where rpi is the consequent parameters and x0 5 1.

FIG. 6. Processes of real-time forecasting wind velocity.

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ANFIS is a feed-forward neural network, and is con- structed through supervised learning. The network parameters can be divided into antecedent parameters

(nonlinear parameters: cji and sji) and consequent parameters (linear parameters: rpi)(Jang 1993). Various methods have been proposed for tuning fuzzy membership functions, such as the gradient descent, least squares, and back-propagation algorithms. If these learning algorithms are applied, being trapped in local minima is highly probable (Eftekhari and Katebi 2008). Moreover, when the input variables increase, the number of parameters in ANFIS that must be determined is large because of the increasing fuzzy rules. Therefore, the computing efficiency of these learning algorithms is low (Kiran and Rajput 2011). To solve these problems, the subtractive clustering method developed by Chiu (1994), a type of fuzzy clustering approach, was used to establish the rule base relationship between the input and output variables. This method has the advantage of avoiding the explosion of the rule base, a problem FIG. 7. Performance levels of prediction models for 1-h-ahead known as the ‘‘curse of dimensionality.’’ The subtrac- predictions using a validation dataset. tive clustering method assumes that each data point is a potential cluster center, and based on the density of The output layer sums the outputs of the previous the surrounding data points, it calculates a measure of layer to compute the model output, as follows: the likelihood that each data point would be defined P as the cluster center (Chen 2013). The density measure å w f P p p Di at a data point xi is defined as p51 " # O 5 å w f 5 . (5) 2 5,p p p P m kx 2 x k p51 5 å 2 i j å w Di exp , (6) p 5 2 p51 j 1 (ra/2)

FIG. 8. Typhoon track of Fanapi during 2010 (UTC).

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FIG. 9. Satellite infrared images of Fanapi during 2010. where m is the total number of data points in the where h is a constant greater than 1 to prevent cluster

N-dimensional space and ra is a positive constant de- centers from being in too close a proximity. A recom- ﬁning a neighborhood radius. mended value of setting h is 1.5 (Chang and Chang

The first cluster center is chosen as the c1 data point 2006). with the highest potential density value, D*; for the According to Eq. (7), data points near the first cluster c1 second cluster center, the effect of the first cluster center center c1 reduce the potential measurement substantially. is subtracted to determine the new density values, as Thedatapointc2, corresponding to the larger potential follows: value, was selected for the second cluster center. After 2 3 determining the kth cluster center ck, the density measure 2 2 of each data point x is typically revised as kxi xc k i D 5 D 2 D* exp42 1 5 and (7) i i c1 2 (rb/2) " # kx 2 x k2 D 5 D 2 D* exp 2 i k , (9) 5 h i i k (r /2)2 rb ra , (8) b

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FIG. 10. Typhoon intensity hydrograph of Fanapi during 2010 and comparison of wind observations and predictions on the Penghu Islands. where D*k is the largest potential density value. Cluster 4. Methodology and modeling centers were selected iteratively until the stopping cri- To resolve the problem in predicting the wind velocity teria were achieved. The r is a critical parameter a in the Penghu Islands during typhoons, we presented (ranging between 0 and 1) that determines the number a procedure to conceptualize the forecasted processes. of cluster centers or locations (Chen 2013). The model constructions are described in this section. b. MLPNN a. Procedures of the methodology MLP network models are popular network architec- Figure 4 shows a flowchart of the proposed method- tures used in most of the research applications related to ology for formulating an artificial-intelligence-based medicine, engineering, and mathematical modeling. An wind-velocity model during typhoon periods. The fore- ANN was created to simulate the nervous system and casting horizon is 1 h. The required hydrometeorological brain activity. In general, the architecture of neural information is as follows: 1) typhoon tracks and typhoon networks comprises an input layer, a hidden layer, an landfall warning, as well as the typhoon climatologic output layer, and a connection system. In a feed-forward data; and 2) the ground-based weather data from weather network, information flows in only one direction (i.e., gauges (as described in section 2b). In the data pre- from the neurons of a layer to the neurons of the suc- processing stage, the typhoon track classifications (classes ceeding layer). A gradient descent procedure, known I–V) were designed (section 2c).Inthemodelingpro- as generalized error back propagation, is typically cedure, ANFIS and MLPNN were used as the forecasting employed to train the MLPNN. Thus, the MLP network techniques. The artificial-intelligence-based wind-velocity is also known as a back-propagation network (BPN; prediction model can be formulated as Sajikumar and Thandaveswara 1999; Wei et al. 2014). As training progresses, the weights are updated systemati- 0 5 Vt f (fAgt21), (10) cally and the network output is compared with the target 0 output by using the BPN. More details can be found in where Vt is the predicted surface wind velocity at time t, Bishop (1995). fAgt21 is the attribute set of typhoon climatologic data

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number of clusters only when the parameter ra is set. Sensitivity analysis was adopted to determine the suit-

able ra values necessary to train ANFIS. The nine segments were set using an ra value between 0.1 and 0.9 (i.e., in increments of 0.1). The relative root-mean-square

errors (RRMSEs) were calculated, and the ra values were set using favorable performance levels. The RRMSE was defined as FIG. 11. Model performance levels during different periods of sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi, Fanapi during 2010. n 5 1 å pre 2 obs 2 obs RRMSE (Oi Oi ) O , (11) n i51 and the ground weather data at time t 2 1, and f() is the pre obs artificial-intelligence-based model. where Oi is the predicted value at record i, Oi is the Subsequently, the ANFIS- and MLPNN-based pre- observed value at record i, Oobs is the average of the diction models were trained, and the model parameters observations, and n is the number of records. The were calibrated using the training subset. The same smaller the RRMSE value, the better the performance validation subset was used to test both models. Finally, of the predicted outcomes is. the optimal models were compared and verified based After several numbers of clustering were evaluated, on various levels of performance. an appropriate ra value was adopted for each model case. In Fig. 5a, the optimal r values are shown to be 0.4, b. Models calibration a 0.3, 0.2, 0.3, and 0.2 for classes I–V, respectively. As mentioned, ANFIS using the subtractive clustering To train an MLP network, a three-layer feed-forward method can be used to automatically determine the network was created. The Levenberg–Marquardt

FIG. 12. Correlation coefﬁcient between distance from Magong to the typhoon center and wind velocity of Magong in Fanapi during 2010.

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FIG. 13. Typhoon track of Nock-Ten during 2004 (UTC).

training function, which appears to be the fastest 2—using the obtained attribute data as inputs in the method and is performed until the error reaches artificial-intelligence-based models (ANFIS and a minimum and remains stable (Iphar 2012), was used in MLPNN) to determine real-time wind velocity at this study. The training was stopped when the maximum time t; of 2000 iterations was reached. As indicated by Kim 3—forecasting real-time wind velocity at the end of (2008), a low learning rate ensures a continuous descent period t; and on the error surface and a high momentum accelerates 4—updating the time step t 5 t 1 1 and verifying the training process; the selected values are typically whether the CWB has lifted the typhoon warning used in ANN training. Therefore, we set the learning rate for sea and land. If so, the prediction process is and momentum to 0.1 and 0.9, respectively. Moreover, stopped; otherwise, steps 1–3 are repeated. the hyperbolic tangent function was selected as the ac- tivation function for use in the hidden layer because this The wind velocity forecast simulation can be contin- function provides higher accuracy than do other sigmoid ued after the CWB has lifted the typhoon warning for functions (Maier and Dandy 1998). The number of nodes sea and land in step 4. However, to facilitate an objective in the hidden layer was based on the sensitivity analysis comparison, we terminated the simulation process when in the interval of [1, 20]. As shown in Fig. 5b, the suitable the CWB lifted the typhoon warning. numbers of nodes were 13, 15, 13, 14, and 14, respectively, for classes I–V. 5. Model results and comparisons c. Concept of real-time forecast processes a. Performance definition After calibrating models, real-time wind velocity can To assess the model performance levels completely, in be predicted in a series of iterative hourly calculation addition to RRMSE, the criteria of the relative mean steps (Fig. 6). The steps involved in processing real-time absolute error (RMAE) and the coefficient of correla- simulating runs are listed as follows: tion r were used: 1—obtaining hydrometeorological information n 1 pre (dataset fAgt21) when the observed data at time 5 å 2 obs obs RMAE jOi Oi j O and (12) t 2 1 are available; n i51

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FIG. 14. Typhoon intensity hydrograph of Nock-Ten during 2004 and comparison of wind observations and predictions on the Penghu Islands. n å obs 2 obs pre 2 pre (Figs. 10b, 14b, 17b, 21b, and 25b), are discussed later. (Oi O )(Oi O ) 5 This discussion demonstrates that ANFIS is more pre- r 5 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffii 1 , (13) n n cise than MLPNN. The reason might be that, as indi- å obs 2 obs 2 å pre 2 pre 2 (Oi O ) (Oi O ) cated in Übeyli (2009), neurofuzzy systems couple the i5 i5 1 1 power of the two paradigms, fuzzy logic and ANNs, by using the mathematical properties of ANNs in tuning pre where O is the average of the predictions. Smaller rule-based fuzzy systems that approximate how humans RMAE values and larger r values typically indicate fa- process information. Therefore, ANFIS combines the vorable performance levels. The accurate models should advantages of both techniques, rendering it superior to have RMAE and RRMSE values close to 0, and r values MLPNN for wind prediction. In addition, the various close to 1. discussions regarding the CMR effects on classes I–V are described in the next section. b. Model evaluation In this section, to identify the suitable model, the 6. Effects of CMR terrain RMAE, RRMSE, and r were employed. Figure 7 displays an ANFIS-based model with corresponding typhoon The interaction of the typhoon circulation with the performance levels for the various track classes to enable CMR produces significant mesoscale variations in pres- a comparison with the MLPNN-based model. The results sure, wind, and precipitation distribution over and near showed that ANFIS-based models achieved more fa- Taiwan. The CMR complicates the wind forecast of the vorable performance (lower RMAE and RRMSE, and Penghu Islands. The effects of CMR were discussed on higher r for the five individually modeled track classes) the six typhoons. than did the MLPNN-based models. Although a model for class VI typhoons was not The observations and forecasts of the validation ty- generated, these typhoons are severe hazards. As an phoons, comprising Fanapi in 2010, Nock-Ten in 2004, alternative method, we attempted to divide typhoon Talim in 2012, Molave in 2009, and Wipha in 2007 tracks into multiple segments that can be categorized

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irregular direction of class VI (Table 1), to simulate. Based on its historical track (Fig. 25), we separated the typhoon track into two subtracks, which can be categorized as classes I and II, and employed the corresponding class models to predict their wind speeds. a. Class I (Fanapi in 2010) Fanapi, classified as a category 2 typhoon (Fig. 8), created a landfall over Hualien, Taiwan, early on 19 September in coordinated universal time (UTC). The UTC time can be converted to local standard time (LST) and is calculated by LST 5 UTC 1 8 h. The interactions between typhoon circulation and mountainous terrain brought rainfall and strong winds over eastern Taiwan. After Fanapi passed the CMR of Taiwan, it weakened into a category 1 typhoon. On 20 September, Fanapi created a second landfall over Zhangpu in Fujian, China, and weakened into a tropical storm. Figure 9 FIG. 15. Correlation coefficient between distance from Magong to the typhoon center and wind velocity of Magong during shows a satellite infrared (IR) image taken between 18 Nock-Ten in 2004. and 20 September (LST). As shown in the first IR image in Fig. 9, the typhoon eye was apparent, and the structure of the typhoon continued to strengthen before according to their direction (i.e., classes I–V). Thus, Fanapi traversed the CMR of Taiwan. It then moved combining the track segments of these irregular tracks over the ridge of the CMR approximately 12 h later. In by using the tracks of classes I–V might be suitable (e.g., the IR image of Fig. 9b, Fanapi crossed over the CMR at Tembin in 2012), but some tracks might not be suitable 1400 LST 19 September, and the track deflections tend (e.g., Bopha in 2000, Nari in 2001, and Parma in 2009). In to be larger for weaker and slower-moving storms. Af- this section, we selected Typhoon Tembin, which oc- terward, the typhoon center passed the Penghu Islands curred in 2012 and was classified as moving in an at 2000 LST 19 September (Fig. 9c).

FIG. 16. Typhoon track of Talim during 2012 (UTC).

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FIG. 17. Typhoon intensity hydrograph of Talim during 2012 and comparison of wind observations and predictions on the Penghu Islands.

We separated four periods (periods A–D) by three which the structure and the intensity of the typhoons time points (Fig. 10a), including at 1100 LST 19 Sep- were destructed and dissipated by the CMR. This might tember (the typhoon crossing over the CMR), 2000 LST have been because the wind forecast for the Penghu 19 September (the typhoon center passing Magong), and Islands during periods B and C was more complex than 0000 LST 20 September (the typhoon center departing that in period A. To elucidate the influence of the CMR Magong). As shown in Fig. 10a, when Fanapi traversed further, the relationship of the distance factor and winds the CMR (period B), its measured intensity decreased in Magong should be analyzed. In this study, we defined 2 from 45 to 35 m s 1 from 1000 to 1400 LST 19 Septem- r 0 as the correlation coefficient between the wind ve- ber. At 2000 LST 19 September (period C), the typhoon locity in Magong and the distance from Magong to the eye passed the Penghu Islands directly, and the wind typhoon center. 2 velocity in Magong decreased to approximately 0 m s 1. In Fig. 12, strong negative correlations (20.8277 and At 0100 LST 20 September, the wind velocity in Magong 20.9419) are exhibited in periods A and D, whereas 2 reached a maximal velocity of 18.9 m s 1 because of the moderate (0.6549) and strong (0.9284) positive correla- typhoon circulation. tions are shown in periods B and C, respectively. Regarding the CMR terrain effects, we considered the model performance across four periods (Fig. 10a). The numbers of data are 11, 9, 5, and 13, respectively, for periods A–D, which were utilized for the calculation of model performance. Figure 11 displays the predicted wind velocity in Magong, which was determined using ANFIS- and MLPNN-based models. The results showed that, regardless of whether the ANFIS or MLPNN was applied, the performance level in period A (with the blocking effect of the CMR for Magong) provided more FIG. 18. Model performance levels in different periods of Talim favorable predictions than did that in periods B and C, in during 2012.

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FIG. 19. Correlation coefﬁcient between distance from Magong to the typhoon center and wind velocity of Magong in Talim during 2012.

Typically, jr0j . 0:7 represents a strong correlation, slower-moving storms. This situation might continue to whereas jr0j , 0:3 represents a weak correlation (Taylor weaken typhoon intensity during period B, and the wind 1990). As in periods A and D, it can be anticipated that velocity at Magong might gradually decrease until the the wind velocity in Magong is inverse to the distance typhoon approaches Magong. from Magong to the typhoon center. A positive corre- During period C, the wind velocity varied when the lation is shown in period B when the typhoon was 50– typhoon center passed, possibly because the typhoon 150 km from Magong, whereas the wind velocity in redeveloped (without regaining its original strength 2 Magong decreased from 11 to 5 m s 1. As indicated by because of the terrain effect) when it traveled over the Yeh and Elsberry (1993a,b), when a westward-moving Taiwan Strait. Thus, the highest wind speeds were ob- typhoon track approaches the mountainous terrain of served when the typhoon center passed over Magong. Taiwan, the deﬂections tend to be larger for weaker and Moreover, period C in Fig. 12 reveals a strong positive

FIG. 20. Typhoon track of Molave during 2009 (UTC).

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FIG. 21. Typhoon intensity hydrograph of Molave during 2009 and comparison of wind observations and predictions on the Penghu Islands. correlation between the distance from Magong to the passed close to Taipei on 25 October. The system then typhoon’s center and the wind velocity of Magong. began to lose strength, and was downgraded to tropical When the distance from Magong to the typhoon center storm intensity. was approximately 50 km and the typhoon intensity was Because the direction of typhoons in class II is north- 2 35 m s 1 (Fig. 10a), the wind velocity in Magong in- ward along the eastern coast of Taiwan, the Magong wind 2 creased from 2 to 19 m s 1 (Fig. 10b). This might have velocity was slightly affected by Nock-Ten because of the occurred because the mesoscale structure of the ty- effects of the mountain barrier and being a distance of phoon was a critical factor as the typhoon approached 280kmfromMagong(Fig. 14a). Thus, the correlation Magong, which might explain which period C exhibited coefficient in Fig. 15 displays a weak r 0 value. the worst performance compared with the other periods c. Class III (Talim in 2012) in Fig. 11 in terms of RMAE and RRMSE by ANFIS and MLPNN models (Fig. 11). Consequently, the model Talim was classified as a tropical storm from 1800 UTC parameters might be difficult to learn when training the 17 June to 1800 UTC 20 June. On 17 June, a low pres- ANN-based models. Thus, the factor was overlooked by sure area near the east of Hainan Island started to the ANN-based models. absorb the surrounding convection (Fig. 16). Late on 17 June, Talim was upgraded to a tropical storm (Fig. 17a). b. Class II (Nock-Ten in 2004) Early on 20 June, the convection of Talim soon wrapped Nock-Ten originated from a disturbance that formed around the center as it began to merge with a monsoon among the Marshall Islands early on 13 October trough. Early on 21 June, Talim was downgraded to (Fig. 13). Nock-Ten passed 260 km south of Guam on 20 a tropical depression as the system weakened in the 2 October. Nock-Ten reached a peak intensity of 43 m s 1 Taiwan Strait. Shortly afterward, the tropical depres- late on 23 October, and was classified as a category 2 sion was absorbed into the same monsoon trough. typhoon. On 24 October, the storm track curved north- We separated two periods (periods A and B) at west. Turning to a northerly track, Typhoon Nock-Ten 1200 LST 20 June (the typhoon center approaching

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respectively, for periods A and B, which were utilized for the calculation of model performance. The results (Fig. 18) indicated nearly the same performance scores in periods A and B (regardless of whether ANFIS or MLPNN was applied). This might have been caused by the wind forecast of the Penghu Islands without the CMR factor (or slightly affected by the CMR) for both periods. We calculated the r 0 values for both periods. In Fig. 19, without the blocking effects of the CMR, the moderate and strong negative correlation coefﬁcients between the distance from Magong to the typhoon center and the Magong wind velocity were observed in periods A and B, respectively. This implies the distance factor might be the most important consideration for the winds in Magong.

d. Class IV (Molave in 2009) FIG. 22. Correlation coefficient between distance from Magong to the typhoon center and wind velocity of Magong in Molave during 2009. Molave was classified as a tropical depression during 14–16 July (Fig. 20). On 16 July, Molave was classified as Magong) (Fig. 17a). Talim moved along the Taiwan a tropical storm as it was crossing the Luzon Strait. Later Strait without being blocked by the CMR. Talim was that day, Molave moved swiftly toward the South China active in the Penghu Islands from 19 to 20 June. The Sea. On 19 July, Molave made landfall over China. high wind variability appeared from 0800 to 1800 LST The direction of the typhoon was westward through 20 June, and exhibited two protruding peak wind epi- the Luzon Strait, and the Magong wind velocity was sodes (Fig. 17b). Early on 21 June, Talim passed over the slightly affected by the typhoon because of its distance, Taiwan Strait. at least 270 km between the typhoon center and Magong Similarly, we compared the model performance levels (Fig. 21a). Therefore, the correlation coefficient in in periods A and B. The numbers of data are 31 and 17, Fig. 22 is a weak r 0 value.

FIG. 23. Typhoon track of Wipha during 2007 (UTC).

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FIG. 24. Satellite infrared images of Wipha during 2007.

2 e. Class V (Wipha in 2007) Although the Wipha peak intensity reached 48.06 m s 1 from 0200 to 1300 LST 18 September (Fig. 25a), Magong 2 Wipha was classified as a tropical depression on winds showed low values, ranging from 4 to 6 m s 1 15 September (Fig. 23). Wipha quickly developed into a (Fig. 25b), and the correlation coefficient was a weak r 0 tropical storm on 16 September, and intensified into value (Fig. 26). The typhoon intensity did not sub- a typhoon early on 17 September with the appearance of stantially affect Magong winds in this case, possibly be- an eye feature. Later that day, Wipha continued moving cause the winds are a function of the distance factor toward north Taiwan (Fig. 24a). After a period of rapid (great distance from the typhoon center to Magong) and intensification, Wipha attained its peak intensity on because of the CMR blocking effects. In other words, 2 18 September, with winds of 48.06 m s 1 (category 2) a distance of 401–528 km between the typhoon center (Fig. 24b). Later that day, Wipha began to weaken as it and Magong (from 0200 to 1300 LST 18 September) was interacted with the mountainous terrain of Taiwan before greater than the radius of the typhoon (200 km), reducing reaching the northern edge of the island (Fig. 24c). Wipha the wind velocity at Magong. Moreover, the CMR bar- subsequently made landfall over China (Fig. 24d). rier effects obstructed the fringe circumfluence of the

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FIG. 25. Typhoon intensity hydrograph of Wipha during 2007 and comparison of wind observations and predictions on the Penghu Islands. typhoon when Typhoon Wipha reached maximum in- We separated five periods (periods A–E) by four time tensity (from 0200 to 1300 LST 18 September). points (Fig. 29a), including 0500 LST 24 August (as the typhoon landed along the southern tip of Taiwan), f. Class VI (Tembin in 2012) 2000 LST 24 August (as the typhoon center approached Tembin, classified as a category 4 typhoon, was un- Magong), 1800 LST 26 August (as the typhoon center usual for a strong tropical cyclone in that it affected moved far from Magong), and 0200 LST 28 August (as southern Taiwan twice, on 22 and 28 August (Fig. 27). the typhoon center approached the southern tip of After making landfall over the southern tip of Taiwan Taiwan). For a comparison of the terrain effects, Fig. 30 late on 23 August, Tembin weakened but regained shows a visual assessment of the model performance strength in the South China Sea. On 28 August, Tembin scores regarding periods A–E. The numbers of data are impacted southern Taiwan as a category 1 typhoon. At 54, 15, 46, 32, and 11, respectively, for the five periods that time, Tembin accelerated east-northeastward and utilized for the calculation of the model performance. traveled around eastern Taiwan in loops. Afterward, As shown in Fig. 30, the performance in period A (with Tembin did not regain strength in the East China Sea, the CMR blocking effect for Magong) provided more and made landfall over South Korea on 30 August be- favorable predictions than did that in periods B and C, in fore becoming an extratropical cyclone. which the structure and intensity of the typhoon were Figure 28 shows a satellite IR image of Tembin taken dissipated by the CMR. This outcome was similar to that between 23 and 28 August. As shown in Fig. 28a, satel- of Fanapi in 2010 (class I). lite IR imagery revealed that the typhoon eye was ap- In addition, we calculated the r 0 values for the five parent, and that the structure of the typhoon continued periods to determine the distance factor of the typhoon. to strengthen before Tembin traversed the CMR of Figure 31 displays the r’ values for the five periods. As Taiwan. At 2000 LST 24 August, the intensity of Tembin shown in Fig. 31, a strong negative correlation (20.9086) decreased significantly as it traversed mountainous ter- was observed before the typhoon landed along the rain in Taiwan (Fig. 28c). southern tip of Taiwan (period A). When Tembin

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wind continued to decrease to a minimal value of 2 0.2 m s 1 at 2000 LST 24 August. In addition, a moderate (0.6739) positive correlation was observed during period B(Fig. 31). Subsequently, the wind speed increased to 2 a second peak of 9.9 m s 1 at 0000 LST 25 August because of the weakened blocking effect, and the structure and intensity of Tembin were redeveloped during period C (causing a negative r 0 value of 20.9820). Meanwhile, the wind velocity of Magong was inverse to the distance from Magong to the typhoon center when the typhoon traveled into the South China Sea. At 0200 LST 28 August, Tembin approached southern Taiwan for the second time. However, the wind peak over the Penghu Islands did not occur. It might have been affected by the decreased typhoon intensity, the radius of the typhoon, and the distance factor.

7. Summary and conclusions FIG. 26. Correlation coefficient between distance from Magong to the typhoon center and wind velocity of Magong in Wipha The Penghu Islands off the western coast of Taiwan during 2007. have excellent land and sea areas for wind power generation. Wind power production is subject to fluc- passed over the CMR, its intensity decreased from 43 to tuations in wind velocity and, therefore. requires ac- 2 30 m s 1 during period B (Fig. 29a). Figure 29b shows curate knowledge regarding the wind. As a typhoon the two wind peaks appearing over the Penghu Islands. approaches the Penghu Islands, the typhoon circula- 2 The first wind peak (10.3 m s 1 at 0600 LST 24 August) tion with CMR produces considerable mesoscale vari- occurred after the landfall over the southern tip of ations in winds. In this study, the major objective was to Taiwan (at 0500 LST 24 August). Because the typhoon develop accurate wind speed prediction models during structure and intensity were dissipated by the CMR, the typhoon periods in the Penghu Islands and to discuss

FIG. 27. Typhoon track of Tembin during 2012 (UTC).

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FIG. 28. Satellite infrared images of Tembin during 2012.

the effects of the CMR terrain of Taiwan on the Penghu interpretation of neural networks is unsatisfactory, and Islands, based on typhoon tracks. their underlying mechanisms remain unclear. Moreover, This study formulates wind prediction models over because ANNs are parallel computing models, which the Penghu Islands based on classified typhoon tracks. are still a statistical method, when the typhoon tracks are This study employed ANFIS and MLPNN to predict very different from those in the sample pool (i.e., the wind velocity based on classified typhoon tracks training data set of typhoons), the ANN-based model (classes I–VI), and to examine their feasibility. The forecast results could be worse than those of numerical dataset consisted of 49 typhoons that affected the model simulations. Penghu Islands from 2000 to 2012. The data included In addition, we obtained the following results re- 2892 hourly records. We employed the performance garding the interactions between the CMR and the levels of RMAE, RRMSE, and r to assess the forecasts. Penghu Islands based on track directions. The results showed that the ANFIS models provided highly reliable 1-h-ahead predictions for wind velocity, d For direct westward movement across the CMR of and the five individually classified ANFIS-based models Taiwan (class I), prior to the typhoon passing over achieved more favorable performance than did the the CMR, the CMR has only a minor impact on the MLPNN-based models. The ANFIS combines the ad- Penghu Islands because it is blocked by the CMR. In vantages of both ANN and the fuzzy inference system, this phase, the winds of the Penghu Islands could be and, therefore, it is superior to MLPNN wind predic- affected slightly by typhoons. When typhoons cross tion. Although ANN-based models might exhibit over the steep and high CMR, the typhoons often promising 1-h-ahead wind speed prediction ability, make track deflections and structure modifications.

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FIG. 29. Typhoon intensity hydrograph of Tembin during 2012 and comparison of wind observations and predictions on the Penghu Islands.

After the typhoon center passes over the CMR, the typhoons move along the Taiwan Strait without be- winds over the Penghu Islands rise, possibly because ing blocked by the CMR. We also observed that the the typhoon redeveloped (without regaining its orig- winds on the Penghu Islands were directly affected inal strength because of the terrain effect) when it by the distance from the typhoon center to the Penghu traveled over the Taiwan Strait. Thus, the highest Islands, exhibiting two peak winds (e.g., Talim in wind speeds were observed when the typhoon center 2012). passed over Magong. Fanapi, which occurred in 2010, d For the track direction of the westward movement demonstrated that the wind forecast for the Penghu through the Luzon Strait (class IV), the winds on the Islands before the typhoon crossing over the CMR Penghu Islands were slightly affected by the typhoon was more complex than that after the typhoon center because of a distance of at least 270 km (e.g., Molave passed the CMR. This might be due to the mountain- in 2009) between the typhoon center and the Penghu induced flow deflections being mainly confined to Islands. Similarly, for the westward movement the lower-level vortex, and the typhoon’s passage induced a mean cyclonic circulation pattern around the CMR. In other words, the steep and high CMR causes typhoon track deflections and structure modifications. d For the track direction of the northward movement along the eastern coast of Taiwan (class II), because of the blocking effect of the typhoon and a distance of at least 280 km (e.g., Nock-Ten in 2004) from the Penghu Islands to the typhoon, relatively weak winds occur.

In contrast, for the track direction of the northward FIG. 30. Model performance levels during different periods of movement along the western coast of Taiwan (class III), Tembin during 2012.

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FIG. 31. Correlation coefﬁcient between distance from Magong to the typhoon center and wind velocity of Magong in Tembin during 2012.

traveling through the southern East China Sea (near Acknowledgments. The support given by the Ministry northern Taiwan) (class V), we observed that typhoon of Science and Technology of Taiwan, under Grant intensity was not a vital factor affecting the Penghu MOST103-2111-M-464-001, is greatly appreciated. The Islands winds. This is because the typhoon was far author acknowledges typhoon data provided by the Cen- from the Penghu Islands, and was slightly affected by tral Weather Bureau (CWB) of Taiwan and the Joint the CMR blocking effects. Typhoon Warning Center (JTWC). The author is also d For irregular track directions (class VI), we selected grateful for the constructive comments of the referees. Tembin in 2012, according to which separating the track into two subtracks (categorized as classes I and II) REFERENCES is suitable, and employed the corresponding class Akhmatov, V., 2007: Influence of wind direction on intense power models to predict wind velocity. For the first subtrack, fluctuations in large offshore wind farms in the North Sea. the variability of winds was similar to the case in the Wind Eng., 31, 59–64, doi:10.1260/030952407780811384. track of the westward movement across the CMR. Bender, M. A., R. E. Tuleya, and Y. Kurihara, 1985: A numerical It also indicated that the performance in the period study of the effect of a mountain range on a landfalling before the typhoon landed along the southern tip of tropical cyclone. Mon. Wea. Rev., 113, 567–582, doi:10.1175/ 1520-0493(1985)113,0567:ANSOTE.2.0.CO;2. Taiwan provided more favorable predictions than Bilgehan, M., 2011: Comparison of ANFIS and NN models—With did the performance in the period after the typhoon a study in critical buckling load estimation. Appl. Soft Com- passed over the CMR. Possible explanations are sim- put., 11, 3779–3791, doi:10.1016/j.asoc.2011.02.011. ilar to those related to Fanapi in 2010. For the second Bishop, M., 1995: Neural Networks for Pattern Recognition. Oxford subtrack, we observed that a wind peak over the University Press, 504 pp. Brand, S., and J. W. Blelloch, 1974: Changes in the character- Penghu Islands did not occur, possibly because the istics of typhoons crossing the island of Taiwan. Mon. Wea. winds have been affected by the decreased typhoon Rev., 102, 708–713, doi:10.1175/1520-0493(1974)102,0708: intensity, the typhoon radius, and the distance factor. CITCOT.2.0.CO;2.

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