Trajectory Data Mining Via Cluster Analyses for Tropical Cyclones That Affect the South China Sea

International Journal of Geo-Information

Article Trajectory Data Mining via Cluster Analyses for Tropical Cyclones That Affect the South China Sea

Feng Yang 1,2 , Guofeng Wu 1,3,* , Yunyan Du 2,* and Xiangwei Zhao 2,4

1 School of Resource and Environmental Sciences, Wuhan University, 430079 Wuhan, China; [email protected] 2 State Key Laboratory of Resources and Environmental Information System, Institute of Geographic Science and Natural Resources Research, Chinese Academy of Sciences, 100101 Beijing, China; [email protected] 3 Key Laboratory for Geo-Environmental Monitoring of Coastal Zone of the National Administration of Surveying, Mapping and Geoinformation & Shenzhen Key Laboratory of Spatial Smart Sensing and Services & College of Life Sciences and Oceanography, Shenzhen University, 518060 Shenzhen, China 4 Geomatics College, Shandong University of Science and Technology, 266590 Qingdao, China * Correspondence: [email protected] (G.W.); [email protected] (Y.D.); Tel.: +86-755-2693-3149 (G.W.); +86-10-6488-8973 (Y.D.)

Academic Editors: Jason K. Levy and Wolfgang Kainz Received: 28 April 2017; Accepted: 5 July 2017; Published: 8 July 2017

Abstract: The equal division of tropical cyclone (TC) trajectory method, the mass moment of the TC trajectory method, and the mixed regression model method are clustering algorithms that use space and shape information from complete TC trajectories. In this article, these three clustering algorithms were applied in a TC trajectory clustering analysis to identify the TCs that affected the South China Sea (SCS) from 1949 to 2014. According to their spatial position and shape similarity, these TC trajectories were classiﬁed into ﬁve trajectory classes, including three westward straight-line movement trajectory clusters and two northward re-curving trajectory clusters. These clusters show different characteristics in their genesis position, heading, landfall location, TC intensity, lifetime and seasonality distribution. The clustering results indicate that these algorithms have different characteristics. The equal division of the trajectory method provides better clustering result generally. The approach is simple and direct, and trajectories in the same class were consistent in shape and heading. The regression mixture model algorithm has a solid theoretical mathematical foundation, and it can maintain good spatial consistency among trajectories in the class. The mass moment of the trajectory method shows overall consistency with the equal division of the trajectory method.

Keywords: tropical cyclone; data mining; South China Sea; trajectory clustering

1. Introduction Tropical cyclones (TCs) are a type of intense atmospheric cyclonic eddy generated over warm tropical oceans [1]. They are one of the most globally devastating natural catastrophes and usually have a considerable socio-economic impact for countries in TC-prone areas [2–4]. The South China Sea (SCS), which is the largest semi-enclosed marginal sea in the Northwest Pacific, is also an active region of TCs. Approximately 13.2% of the TCs formed in the Western North Pacific (WNP) were generated in the SCS [5]. In addition, more than 60% of the TCs in the WNP affect countries and areas located around the SCS [6]. Previous studies have primarily focused on WNP TCs in general [7–14], whereas relatively few studies have focused on the specific characteristics of TCs affecting the SCS. With the rapid social economic development and population growth in the areas around the SCS, it is important to gain a better understanding of how TC behaviour affects the SCS.

ISPRS Int. J. Geo-Inf. 2017, 6, 210; doi:10.3390/ijgi6070210 www.mdpi.com/journal/ijgi ISPRS Int. J. Geo-Inf. 2017, 6, 210 2 of 22

TC landfall locations are primarily determined by their trajectories [15]; therefore, identifying the rules of TCs trajectories represents one of the most important aspects of TC disaster protection [16]. Previous studies have found that the characteristics of these TC trajectories can be better understood by classifying them into several clusters [9,11,14]. For example, by classifying TC trajectories into three types (straight-moving storms, re-curving-south storms, and re-curving-north storms), Harry and Elsberry [11] illustrated the relationship between TC trajectory types and anomalous 700-mb large-scale circulation patterns and TC genesis locations. Hodnish and Gray [9] investigated features of environmental wind fields at all levels of the troposphere that are related to TC re-curvature by categorizing TCs into four patterns: non-re-curving cyclones, sharply re-curving cyclones, gradually re-curving cyclones and left-turning cyclones. Lander [14] discussed the effects of the reverse orientation of the summer monsoon trough of the WNP further north and east than normal for TC motion by classifying TC trajectories into four major patterns: straight moving, re-curving, north oriented and SCS oriented. However, the results of previous studies were relatively qualitative and descriptive; therefore, more effective quantitative methods are needed to better understand the behaviour of TC trajectories. The numerical clustering method includes objective characteristics and represents a quantitative data-mining method that is widely applied in many areas, including public transportation [17,18], the humanities and social sciences (e.g., Twitter events) [19–21], and environmental pollution [22–24]. Compared with other clustering objects, TCs with different lifetimes generate tracks with different lengths; thus, they cannot be analysed through the direct use of common clustering methods. To overcome this shortcoming, different methods have been proposed. Some studies included special trajectory points and the K-means clustering method [25] to perform cluster analyses of TC trajectories. Based on the geographical position of TCs at their maximum intensity and terminal position, Elsner and Liu studied the WNP and the North Atlantic TCs by classifying them into three clusters [10,26]. Blender used six-hourly trajectory point positions over three days to cluster trajectories of extratropical TCs in the North Atlantic [27], and Corporal-Lodangco and Leslie clustered TCs affecting the Philippines based on their genesis, maximum intensity, and decay point positions [28]. However, these methods are exclusively based on limited special points of the TC track, and Gaffney [29] suggested that this method is not desirable for resolving the problem because the features of TC trajectories should be expressed by the entire TC trajectory [29,30]. To overcome the deficiencies of these methods, Gaffney proposed a Finite-Mixture-Model (FMM) clustering algorithm [29,31], which has been utilized in many TC trajectory clustering analyses of the WNP [30,32], the North Atlantic Ocean [33,34], the Eastern North Pacific Ocean [35], and the North Indian Ocean [36]. Nakamura et al. proposed the use of two mass moments of TC trajectory, namely, the centroid and the variance (x-, y-, and xy-directions), for TC trajectory clustering. These two mass moments reflect the TC position and shape separately and constitute a vector of five scalar components per TC track. By applying the mass moments to the K-means clustering method, a reliable clustering result of six clusters for the North Atlantic TCs were obtained [34]. Kim also solved this problem and analysed the WNP TCs by dividing each trajectory into M segments of equal length [6]. Through sufficient density of equal dividing sample points, the original position and shape character of each trajectory can be retained. Therefore, the common clustering method can be used to cluster the re-sampled TC tracks. TCs that affect the SCS include not only the TCs forming locally in the SCS but also the TCs forming in the WNP and then migrating into the SCS. Therefore, it would be more appropriate to incorporate all these TCs in the TC trajectory analysis to obtain a more comprehensive understanding of the trajectory characteristics of TCs that affect the SCS. However, few studies have focused on the unique TC trajectory characteristics of the SCS, especially using quantitative numeric clustering methods [37,38]. In this paper, we use the three abovementioned methods based on full TC trajectory information to perform TC trajectory clustering and analyse the TC trajectory patterns that affect the SCS. Comparisons of the results of these methods are performed, and their differences are analysed. ISPRS Int. J. Geo-Inf. 2017, 6, 210 3 of 22

2. Research Methods

2.1. Research Data In this paper, the best-track dataset for TCs from 1949 to 2014 provided by the China Meteorological Administration (CMA) was adopted. This dataset provides the longitude and latitude for the spatial location, the maximum sustained wind velocity, and lowest pressure near the centre of TCs every six hours in the WNP (to the north of the equator and the west of longitude 180◦ E, including the SCS) since 1949. Because there are more observations of TCs in the continental and surrounding sea areas of China, this dataset has more advantages in the areas surrounding China and the SCS [39,40]. The spatial range in this study is within the region (105◦–125◦ E, 0◦–27◦ N), which covers the entire SCS and the surrounding areas and countries. When a TC generated in the WNP passes through this region, it is selected as a TC that has an impact on the SCS. Only TCs with a maximum wind velocity (vmax) above the tropical storm threshold (17.2 m/s ≤ vmax) were adopted. Overall, 946 TC trajectories were selected. We also conducted a clustering analysis for the TC trajectories after 1972, the year in which satellite observation techniques began to be used. According to the results, there are no essential differences in the analysis results compared with data recorded since 1949, lending credibility to the trajectory data of the TCs recorded in the dataset.

2.2. Equal Division of TC Trajectory Method Equally dividing a trajectory into M parts is a simple and straightforward method of processing trajectory data of different lengths. In the actual application, the equivalent trajectory division points can be extracted using available tools, such as the ICurve.QueryPoint method of the ArcGIS Engine. For random variables that obey the Gaussian distribution, more than 99% of the values of the random variable are contained in the range of (µ − 3σ, µ + 3σ), where µ is the average, and σ is the standard deviation of the random variable. According to the central limit theorems, the lifetime of a TC can be assumed to obey the Gaussian distribution. The statistical result shows that the average lifetime of TCs in the dataset is µ = 178 h, and the standard deviation is σ = 80 h. Because the TC trajectory obtains each sampling point for every six-hour time interval, we selected 80 equal division sample points for each TC track. Therefore, the coordinate points of each TC trajectory are organized into a

1 × 160 row vector, Trji = [xe1, ye1, ··· , xe80, ye80]1 × 160. The ensemble of all TC tracks in the dataset T will constitute a k × 160 matrix, Xek = [Trj1, ··· , Trjk] , and k = 946 is the number of TC trajectories.

2.3. Mass Moment of the TC Trajectory Method Using the mass moment of the trajectory, the shape and length of the entire trajectory can be comprehensively considered in the clustering process. This method includes two mass moments, the ﬁrst of which is represented by the coordinates (x, y) for the central point position of the trajectory. The equation is as follows:

Z 1 1 n M1 = w(r)rdxdy = n ∑ i=1w(ri)ri, (1) A ∑i=1 w(ri) where r is the coordinate vector (x, y) for a point on the trajectory, w(r) is the value corresponding to the selected weight variable (such as the intensity of TC) at that point, and A is a constant represented by the integral of the selected weight variable on the overall trajectory. The form of the polynomial sum on the right side of the equation is an approximate simpliﬁed calculation of this value using n discrete observation points in the trajectory. M1 is the geometric centre of the trajectory, representing its location. The second matrix represents the variance of coordinates x, y of the trajectory, and the corresponding mathematical form is as follows: ISPRS Int. J. Geo-Inf. 2017, 6, 210 4 of 22

Z 1 2 1 n 2 M2 = w(r)(r − M1) dxdy = n ∑ i=1w(ri)(ri − M1i) . (2) A ∑i=1 w(ri)

The variable symbols in this equation are equivalent to the corresponding symbols in the equation for M1 [34]. In this paper, we cluster the TC trajectories according to the shape characteristics of the trajectory, and the value of w at different points is set to one. The expression form of matrix M2 is " 2 # σx σxy M2 = 2 . This matrix corresponds to a variance ellipse that represents the shape of the σyx σy trajectory. The long axis of the ellipse reflects the direction and range for the maximum distribution of the trajectory points, and the short axis of the ellipse reflects the degree of concentration for the distribution of the trajectory points in this direction. The angle of the long axis is determined by the covariance, which reflects the overall moving trend of the trajectory. Through this transformation, each trajectory is expressed by a five-dimensional vector, i.e., h 2 2 i x, y, σx , σy , σxy . For the coordinate elements and variance elements in the vector to have the same order of magnitude, the variables must be normalized. In addition, we assign the weight for each coordinate variable as ρ1 = 0.5/2 and the weight for each variance variable as ρ2 = 0.5/3. Thus, the position and shape factors of the trajectory have the same effect on the clustering results. Kim [6] suggested that compared with hard clustering methods such as K-means, fuzzy clustering methods allow each object to belong to all clusters with assigned corresponding membership coefficients (ranging from 0 to 1) that evaluate the degree to which an object belongs to each of clusters. Thus, fuzzy clustering can better manage fuzzy datasets such as TC trajectories, which are too complex to determine the potential boundaries and discrete different patterns. Chu [41] also argues that the fuzzy c-means (FCM) algorithm is more suitable for TC track data. Therefore, in this paper, the FCM clustering algorithm is selected to perform cluster analyses of TC trajectories in both the mass moment method and the equal division method.

2.4. Mixed Regression Model Method The mixed regression model uses the linear combination of a ﬁnite number of density functions to express the distribution of data, and the Expectation Maximum (EM) algorithm is used to perform the clustering analysis of the trajectory data. In the regression mixture model, coordinates x and y of each observation point in the trajectory are expressed in the form of a p-order polynomial function p p−1 1 with respect to observation time t, z = βpt + βp−1t + ··· + β1t + β0. The form of the function for the regression polynomial ﬁtting of each trajectory is as follows:

zi = Ti β + εi, (3) where z = [X, Y] , X, Y are the column vector of the x coordinate and the y coordinate for the i ni × 2 trajectory, respectively; Ti is the ni × (p + 1) Vandermonde determinant; and β is the (p + 1) × 2 matrix of the regression coefficients. The first column in the matrix is the regression coefficient of the x coordinate on the TC trajectory, the second column is the regression coefficient of the y coordinate. εi is the ni × 2 error term that obeys the normal distribution; its average is 0, and ni is the number of points in the trajectory. According to the number of observation points in the trajectory, ni can take different values. Based on the qualitative artificial method and the quantitative analysis used to determine the fitting results for the TC trajectory, Gaffney suggested that the quadratic polynomial has the best fitting result for the TC trajectory [42]. Therefore, quadratic polynomials are typically used for clustering analyses of TC trajectories. In this paper, we also adopt the quadratic polynomial method to perform the clustering analysis of TCs in the SCS. The conditional density function for the ith trajectory is as follows:

" −1 # − 1 0 p(z |t , θ) = f (z |T β, ) = (2π) ni/2exp − tr(z − T β) (z − T β) . (4) i i i i ∑ 2 i i ∑ i i ISPRS Int. J. Geo-Inf. 2017, 6, 210 5 of 22

According to the deﬁnition of the mixture model, when there are k functions of probability density, the probability density function of the trajectory i is as follows:

K K p(zi|ti, ψ) = ∑ k αk pk(zi|ti, θk) = ∑ k αk fk(zi|Ti βk, ∑ k). (5)

For the dataset that contains n typhoon trajectories, Z = {z1, ··· , zn}, the overall probability densityISPRS is Int. the J. productGeo-Inf. 2017 of, 7, the210 different trajectory probability densities in set Z, such as Equation5 of 22 (6), where Ti = {t1, ··· , tn} is the observation time of different typhoon trajectories: For the dataset that contains n typhoon trajectories, 푍 = {푧1, ⋯ , 푧푛}, the overall probability n K density is the product of thep (differentZ|T, ψ) trajectory = ∏ i ∑ probabilityk αk fk(zi| Tdensitiesi βk, ∑ k in). set Z, such as Equation (6), (6) where 푇푖 = {푡1, ⋯ , 푡푛} is the observation time of different typhoon trajectories: Using the observed coordinate data of TC trajectories푛 퐾 and the EM algorithm, the probability for 푝(푍|푇, 휓) = ∏푖 ∑푘 훼푘푓푘(푧푖|푇푖훽푘, ∑푘). (6) each trajectory as the member of the kth density function is obtained. By dividing the trajectory into the functionUsing with the the observed largest coordinate probability, data the of clusteringTC trajector ofies TC and tracks the EM is algorithm, achieved. the probability for each trajectory as the member of the kth density function is obtained. By dividing the trajectory into 2.5. Selectionthe function of the with Number the largest of Clusters probability, the clustering of TC tracks is achieved. Determining2.5. Selection of thethe Number optimum of Clusters number of clusters is an important process performed in clustering analysis. ToDetermin determineing the the optimum optimum number number of clusters of clusters, is an important Figure1 shows process the performed coefficients in clustering of variation indexanalysis values. obtainedTo determine by thethe equaloptimum division number of of the clusters, trajectory Figure and 1 shows the mass the coefficient moments of of thevariation trajectory methods.index Thevalues coefficient obtained by of the variation equal division represents of the the trajectory ratio between and the mass the standardmoment of deviation the trajectory and the averagemethods. of the The total coefficient distances of of variation all the TCrepresents trajectories the ratio to their between cluster the centres,standard and deviation this value and the reflects the overallaverage degree of the total of dispersion distances of forall the TC TC trajectories trajectories to to theirtheir cluster class centres.centres, and Smaller this value values reflects for the indexthe correspond overall degree to better of dispersion clustering for TC results. trajectories The indexto their shows class centre thats when. Smaller the values number for the of clustersindex is set tocorrespond five or six, to relativelybetter clustering good clusteringresults. The resultsindex shows can be that obtained. when the Wenumber also of used clusters indices is set such to as five or six, relatively good clustering results can be obtained. We also used indices such as average average similarity [43], the partition index [44], and the log-likelihood index [30], and a comprehensive similarity [43], the partition index [44], and the log-likelihood index [30], and a comprehensive comparisoncomparison of different of different indices indices was was performed performed toto determine the the optimum optimum number number of clusters of clusters [45]. [45]. All theseAll these indices indices showed show consistented consistent results results with with thethe coefficientcoefficient of of variation variation index. index. Compared Compared with with previousprevious studies studies on theon the clustering clustering analysis analysis of of TCs TCs inin the entire entire WNP WNP,, both both Camargo Camargo [30] [ 30and] andKim Kim[6] [6] selectedselected seven seven as the as the optimum optimum number number of of clusters. clusters. However, this this paper paper includes includes only only the theTCs TCsthat that affectaffect the region the region of the of the SCS. SCS. Therefore, Therefore, by by summarizing summarizing the the above above analyses, analyses, we we select select five five classes classes as as the optimumthe optimum number number ofclusters. of clusters.

0.52 0.75 0.50 0.70 0.48 0.65 0.46 0.60 0.44 0.55 0.42 0.50 2 4 6 8 10 12 14 2 4 6 8 10 12 14

(a) (b)

Figure 1. Variation of the coefficients of variation index with the number of clusters. The left side Figure 1. Variation of the coefﬁcients of variation index with the number of clusters. The left side shows the result of the equal division of the trajectory method, and the right side is the result for the shows the result of the equal division of the trajectory method, and the right side is the result for the mass moment of the trajectory method. (a) Equal division of the trajectory method. (b) Mass moment massof moment the trajectory of the method. trajectory method. (a) Equal division of the trajectory method. (b) Mass moment of the trajectory method. 3. Results 3. Results 3.1. Clustering Results for the TC Trajectories 3.1. ClusteringThe c Resultslustering for centre the TC represents Trajectories the overall characteristics and tendency of elements in the class. TheFigure clustering 2 shows the centre clustering represents centre thes obtained overall by characteristics various clustering and methods tendency. Th ofis elementsfigure shows in thethat class. Figurethe2 showsclustering the centres clustering of the centres equal obtained division of by the various trajectory clustering method methods.(Figure 2a) Thisand the ﬁgure mixed shows regression model method (Figure 2b) are both curved, representing the average spatial location and moving features of their class. The results for the mass moment of the trajectory method (Figure 2c) show the average of variance ellipses for the different element trajectories in the class, and the average ellipses provide an expression of the spatial distribution of the trajectory. To facilitate the comparison among the results of the three methods, classes with similar location and shape properties are sorted ISPRS Int. J. Geo-Inf. 2017, 6, 210 6 of 22 that the clustering centres of the equal division of the trajectory method (Figure2a) and the mixed regression model method (Figure2b) are both curved, representing the average spatial location and moving features of their class. The results for the mass moment of the trajectory method (Figure2c) ISPRS Int. J. Geo-Inf. 2017, 7, 210 6 of 22 show the average of variance ellipses for the different element trajectories in the class, and the average ellipses provide an expression of the spatial distribution of the trajectory. To facilitate the comparison into the same group, and a class number is assigned and sequentially marked as class A, class B, class amongC, class the results D, and ofclass the E. three methods, classes with similar location and shape properties are sorted into the sameIn general group,, the and different a class algorithms number is all assigned obtain three and sequentiallyclasses of westward marked straight as class-moving A, class B, classtrajectories C, class D, and and two class classes E. of northward re-curving trajectories for the TCs affecting the SCS. The classIn general, centres of the the differentthree straight algorithms-moving classes all obtain are sequentially three classes shifted of east westward from the SCS straight-moving basin to trajectoriesapproximately and two 150° classes E. Therefore of northward, the corresponding re-curving trajectories average length for the of the TCs trajectory affecting also the gradually SCS. The class centresincreases of the (Table three 1). straight-moving Among them, class classes A and class are B sequentially are the two main shifted classes east: the fromsum of the the SCSelements basin to approximatelyin these two 150 classes◦ E. account Therefore, for more the corresponding than 50% (Table average2). For the length two re of-curv theing trajectory classes, the also average gradually length of the trajectories in class D is less than the average length of the trajectories in class E (Table increases (Table1). Among them, class A and class B are the two main classes: the sum of the elements 1). in these two classes account for more than 50% (Table2). For the two re-curving classes, the average Although classes in the same group show great consistency in their spatial character, some lengthdifferences of the trajectories remain. These in class differences D is less will than be analysed the average in detail length in the of thefollowing trajectories discussion. in class E (Table1).

(a) (b)

(c)

Figure 2. Clustering centres of the tropical cyclone (TC) trajectory obtained by different clustering Figure 2. Clustering centres of the tropical cyclone (TC) trajectory obtained by different clustering algorithms: (a) clustering centre for the equal division of the trajectory method, (b) clustering centre algorithms: (a) clustering centre for the equal division of the trajectory method, (b) clustering for the mixed regression model method, and (c) clustering centre for the mass moment of the trajectory centremethod. for the mixed regression model method, and (c) clustering centre for the mass moment of the trajectory method. Table 1. Statistics for the length of the tropical cyclone (TC) trajectories in each category. Table 1. Statistics for the length of the tropical cyclone (TC) trajectories in each category. Equal Division of the Mixed Regression Model Mass Moment of the TC Trajectory Method Method Trajectory Method Trajectory AverageEqual DivisionStandard of the AverageMixed RegressionStandard Model AverageMass MomentStandard of the Trajectory Method Method Trajectory Method TCClass Trajectory Length Deviation Length Deviation Length Deviation Class (kmAverage) (kmStandard) (kmAverage) Standard(km) Average(km) Standard(km) Class A 1804.77Length 824.79Deviation 1939.48Length Deviation900.28 2014.61Length Deviation1007.87 Class B 3297.24(km) 971.83(km) 3429.85(km) 966.40(km) 3318.78(km) 1066.28(km) ClassClass C A4604.63 1804.77 1297.13 824.79 5118.53 1939.48 1275.13 900.28 5239.34 2014.61 1007.871416.27 ClassClass D B4049.65 3297.24 1846.76 971.83 5216.37 3429.85 1945.33 966.40 3812.19 3318.78 1066.281529.89 ClassClass E C7526.23 4604.63 2210.65 1297.13 4331.05 5118.53 2545.40 1275.13 8489.51 5239.34 1416.271930.25 Class D 4049.65 1846.76 5216.37 1945.33 3812.19 1529.89 Class E 7526.23 2210.65 4331.05 2545.40 8489.51 1930.25

ISPRS Int. J. Geo-Inf. 2017, 6, 210 7 of 22

Table 2. Number of TC trajectories in the different classes and the proportion relative to the total TC number.

Equal Division of the Mixed Regression Model Mass Moment of the ISPRS Int. J. Geo-Inf. 2017, 7, 210Trajectory Method Method Trajectory Method 7 of 22 TC Trajectory Class Number of Number of Number of Trajectories Percentage Trajectories Percentage Trajectories Percentage Table 2. Numberin of the TC Class trajectories in the differentin the classes Class and the proportionin therelative Class to the total TC number. Class A 227 24% 260 27% 261 28% Class BEqual 266Division of the 28% Mixed 208 Regression Model 22% 243Mass Moment 26% of the Class C 203 21% 119 13% 186 20% TC Trajectory Method Method Trajectory Method Class D 166 18% 163 17% 204 21% TrajectoryClass ENumber 84of 9%Number 196 of 21%Number 52 of 5% ClassOverall Trajectories 946 in Percentage 100% Trajectories 946 in Percentage 100% Trajectories 946 in Percentage 100 the Class the Class the Class Class A 227 24% 260 27% 261 28% AlthoughClass B classes266 in the same28% group show208 great consistency22% in their243 spatial character,26% some differencesClass remain. C These203 differences21% will be analysed119 in detail13% in the following186 discussion.20% Class D 166 18% 163 17% 204 21% 3.2. TrajectoryClass E Features of84 Different TC9% Classes 196 21% 52 5% Overall 946 100% 946 100% 946 100 Figure3 shows the TC trajectories contained in the different classes and the corresponding class centres.3.2. TheTrajectory clustering Features results of Different for the TC sameClasses group obtained by the different clustering algorithms are placed on the same row, and the corresponding frequency distribution of the heading of TC trajectories Figure 3 shows the TC trajectories contained in the different classes and the corresponding class in thecentre classs. isThe shown clustering at the results lower for part. the same This group frequency, obtained which by the reveals different the clustering heading algorithms distribution are of TC ◦ movementplaced at on a the 10 sameinterval, row, is and an accumulationthe corresponding of the frequency angle between distribution any two of the adjacent heading points of TC in the TC trajectory.trajectories in the class is shown at the lower part. This frequency, which reveals the heading distributionThe TC tracks of TC in movement classes A, at B, a and10° interval C are primarily, is an accumulation in found of a straightthe angle westward between any movement. two Fromadjacent the perspective points in the of spatialTC trajectory distribution,. these straight-moving classes are primarily distributed in the regionThe TC to tracks the south in class ofes 30 A◦, BN., and Class C are A primarily is primarily in found concentrated a straight westward in the region movement of the. From SCS, i.e., the trajectoriesthe perspective were of generatedspatial distribution locally, inthese the straight SCS. The-moving trajectories classes are contained primarily in distributed class B and in the class C region to the south of 30° N. Class A is primarily concentrated in the region of the SCS, i.e., the represent TCs generated in the WNP that move into the SCS. The heading frequencies for these three trajectories were generated locally in the SCS. The trajectories contained in class B and class C categories show obvious single-peak distribution and are primarily distributed in the range near 280◦. represent TCs generated in the WNP that move into the SCS. The heading frequencies for these three In addition,categories different show obvious clustering single algorithms-peak distribution show relativelyand are primarily high consistency distributed in the their range clustering near 280 results.°. InThe addition, class centre different curve clustering pattern algorithm for classs show D and relatively class E high show consistency that these in two their classes clustering are result re-curvings. TC classes:The TCs class in centre these curve two pattern classes for move class to D highand class latitudes E show after that turningthese two near classes the are SCS. re-curving The overall movementTC classes: distances TCs in of these the trajectoriestwo classes inmove class to E high are greater,latitudes reaching after turning approximately near the SCS. 60 ◦TheN. overall In addition, thesem twoovement classes distances both have of the a trajectoriesrelatively large in class spatial E are distribution greater, reaching range. approximately Moreover, the60° N.frequency In distributionsaddition, of these heading two classes for these both two have classes a relatively are the large double-peak spatial distribution distributions range. in theMoreover, northwest the and northeastfrequency direction. distributions However, of heading the heading for these frequency two classes distribution are the double of trajectories-peak distributions in class D in(middle the of northwest and northeast direction. However, the heading frequency distribution of trajectories in Figure3d) obtained by the mixed regression model shows a signiﬁcant single-peak structure moving in class D (middle of Figure 3d) obtained by the mixed regression model shows a significant single-peak the northwest direction. In contrast, the results obtained by the equal division of the trajectory method structure moving in the northwest direction. In contrast, the results obtained by the equal division of and massthe trajectory moment method of the and trajectory mass moment method of have the trajectory two obvious method peaks have in twothe northwestobvious peaks and in northeast the directions,northwest indicating and northeast that for directions, class D, obtained indicating by that the for mixed class regression D, obtained model, by the westernmixed regression movement is the predominantmodel, western moving movement trend is the for predominant TCs, although moving the classtrend centrefor TCs, curve although pattern the class shows centre a northwardcurve re-curvingpattern motion shows a pattern. northward re-curving motion pattern.

Figure 3. Cont. ISPRS Int. J. Geo-Inf. 2017, 6, 210 8 of 22 ISPRS Int. J. Geo-Inf. 2017, 7, 210 8 of 22

0 600 0 800 0 800 330 30 330 30 330 30 600 600 400 300 60 300 400 60 300 400 60 200 200 200

270 90 270 90 270 90

240 120 240 120 240 120

210 150 210 150 210 150 180 180 180 (a) Class A

0 1500 0 1500 0 1500 330 30 330 30 330 30 1000 1000 1000 300 60 300 60 300 60 500 500 500

270 90 270 90 270 90

240 120 240 120 240 120

210 150 210 150 210 150 180 180 180 (b) Class B

0 1500 0 1000 0 1500 330 30 330 30 330 30 1000 1000 300 60 300 500 60 300 60 500 500

270 90 270 90 270 90

240 120 240 120 240 120

210 150 210 150 210 150 180 180 180 (c) Class C

Figure 3. Cont. ISPRS Int. J. Geo-Inf. 2017, 6, 210 9 of 22 ISPRS Int. J. Geo-Inf. 2017, 7, 210 9 of 22

0 500 0 1000 0 500 330 30 330 30 330 30

300 250 60 300 500 60 300 250 60

270 90 270 90 270 90

240 120 240 120 240 120

210 150 210 150 210 150 180 180 180 (d) Class D

0 300 0 400 0 200 330 30 330 30 330 30 300 150 200 300 60 300 200 60 300 100 60 100 100 50

270 90 270 90 270 90

240 120 240 120 240 120

210 150 210 150 210 150 180 180 180 (e) Class E Equal division of the trajectory Mixed regression model Mass moment of the trajectory method. method. method.

FigureFigure 3. (3.a– (ea)–e TC) TC trajectory trajectory clustering clustering results results andand correspondingcorresponding heading heading frequency frequency distribution distribution of of TC movement obtained by the different trajectory clustering methods. TC movement obtained by the different trajectory clustering methods.

3.3. Genesis Locations of Different TC Classes 3.3. Genesis Locations of Different TC Classes The spatial location of TC generation is connected—to a certain extent—to the movement mode ofThe its trajectory spatial location [11]. It can of TCbe seen generation from the is kernel connected—to density distribution a certainextent—to (KDE) of the the genesis movement positions mode of its(Figure trajectory 4) that [11 the]. Itspatial can be distribution seen from theof TC kernel genesis density locations distribution for three (KDE) westward of the straight genesis-moving positions (Figureclasses4) that(class thees A, spatial B, and distributionC) obtained through of TC genesis different locations methods forare threeessentially westward consistent straight-moving (Figure 4a– classesc). T (classeshe average A, B,longitude and C)s obtained for the genesis through locations different ofmethods classes A, are B, essentiallyand C are approximately consistent (Figure 118°4 a–c).E, The135 average° E, and longitudes 150° E, respectively for the genesis(Table 3) locations, which correspond of classess to A, the B, three and major C are source approximately regions for 118 TC◦ E, 135generation◦ E, and 150 in the◦ E, WNP respectively, namely, (Tablethe SCS3), basin, which the corresponds Philippine Basin, to the and three the Mariana major source Islands regions [46], forrespectively TC generation. in the WNP, namely, the SCS basin, the Philippine Basin, and the Mariana IslandsHowever, [46], respectively. for the TC trajectories in classes D and E, considerable differences are observed. Figure 4dHowever, shows that for the the spatial TC trajectories distribution in of classesTC genesis D and locations E, considerable for class D differences obtained by are the observed. equal Figuredivision4d shows of the thattrajectory the spatial method distribution and mass moment of TC genesisof the trajectory locations method for class is relatively D obtained scattered by the equalanddivision primarily of restricted the trajectory to the west method of 140° and E, mass with the moment main concentration of the trajectory in the method Philippine is relatively Basin, the SCS, and the area around Taiwan Island. Moreover, the average longitude for the genesis scattered and primarily restricted to the west of 140◦ E, with the main concentration in the Philippine locations is located near 130° E (Table 3). In contrast, for class D obtained by the mixed regression Basin, the SCS, and the area around Taiwan Island. Moreover, the average longitude for the genesis model method, the TC genesis location is more concentrated and primarily distributes to the east of locations is located near 130◦ E (Table3). In contrast, for class D obtained by the mixed regression 140 °E, near the region of the Mariana Islands. According to the previous analyses, the class D modelobtained method, by the the mixed TC genesis regression location model is method more concentratedis a mixed cluster, and containing primarily both distributes straight to and the re east- ◦ of 140curvingE, nearTC trajectories the region forming of theMariana to the east Islands. of 140° According E, and shows tothe a significant previous westanalyses,-moving the trend class D obtainedFigure by3d). the Compared mixed regressionwith class C model obtained method by the ismix aed mixed regression cluster, model containing method, both which straight is also anda ◦ re-curvingclass that TC primarily trajectories contain formings west tostraight the east-moving of 140 TCE, trajectories and shows form a signiﬁcanting to the east west-moving of 140° E, the trend Figuremain3d). difference Compared is that with the classaverage C obtained latitude of by TC the genesis mixed position regressions in class model D are method, located which in a more is also a classnortherly that primarilyposition, located contains at approximately west straight-moving 12° N. Class TC C trajectories is located at forming approximately to theeast 7° N of (Table 140◦ E, ISPRS Int. J. Geo-Inf. 2017, 6, 210 10 of 22 the main difference is that the average latitude of TC genesis positions in class D are located in a moreISPRS northerly Int. J. Geo-Inf. position, 2017, 7, 210 located at approximately 12◦ N. Class C is located at approximately10 of 22 7◦ N (Table3). Therefore, classes C and D obtained by the mixed regression model generate a division of western-moving3). Therefore, class TCses based C and on D obtained latitude difference,by the mixed which regression leads model to the membergenerate a TCs division in class of western C obtained- bymoving the mixed TCs regression based on latitude model method difference representing, which lead onlys to the 13% member of theoverall TCs in numberclass C obtained of TCs, relativelyby the mixed regression model method representing only 13% of the overall number of TCs, relatively less less than the results obtained by the other two methods (Table2). than the results obtained by the other two methods (Table 2). The spatial distributions of TC genesis locations in class E (to the left and right of Figure4e) The spatial distributions of TC genesis locations in class E (to the left and right of Figure 4e) obtained by the equal division of the trajectory and the mass moment of the trajectory methods are obtained by the equal division of the trajectory and the mass moment of the trajectory methods are more dispersive, and they are widely distributed from the SCS to 150◦ E. This means that TCs in this more dispersive, and they are widely distributed from the SCS to 150° E. This means that TCs in this classclass present present shapes shapes that that are are more more similar similar inin trajectorytrajectory than than the the genesis genesis position positions.s. In Incomparison, comparison, class class E (seenE (seen in thein the middle middle of of Figure Figure4e) 4e obtained) obtained by by the the mixed mixed regression regression mode mode shows shows moremore consistencyconsistency in spatialin spatial distribution distribution of TC of genesisTC genesis positions position ands and is relativelyis relatively similar similar to to that that of of class class D D (seen (seen on on the the left andleft right and of right Figure of 4Figured) obtained 4d) obtained by the equalby the division equal division of the trajectoryof the trajectory method method and the and mass the momentmass of themoment trajectory of the method.trajectory method.

(a) Class A

(b) Class B

(d) Class D

Figure 4. Cont. ISPRS Int. J. Geo-Inf. 2017, 6, 210 11 of 22 ISPRS Int. J. Geo-Inf. 2017, 7, 210 11 of 22

(e) Class E Equal division of the trajectory Mixed regression model Mass moment of the trajectory method. method. method.

FigureFigure 4. 4.(a –(ae–)e kernel) kernel density density distribution distribution of genesis locations locations for for the the TC TC trajectories trajectories in the in the different different classes according to the different trajectory clustering methods. The density is the number of TC classes according to the different trajectory clustering methods. The density is the number of TC genesis genesis points per square kilometre, and the unit is 10−5 events /km2. points per square kilometre, and the unit is 10−5 events /km2.

Table 3. Average longitude and latitude coordinates of the starting TC trajectory points in different Table 3. Average longitude and latitude coordinates of the starting TC trajectory points in classes. different classes. Equal Division of the Mixed Regression Model Mass Moment of the TC Trajectory Trajectory Method Method Trajectory Method Class Equal Division of the Mixed Regression Model Mass Moment of the TC Trajectory LongitudeTrajectory Latitude Method LongitudeMethod Latitude LongitudeTrajectory MethodLatitude Class Class A 117.38Longitude 14.914 Latitude Longitude118.99 Latitude14.47 Longitude118.90 Latitude14.72 Class B 134.01 11.81 135.94 10.79 135.09 10.28 Class A 117.38 14.914 118.99 14.47 118.90 14.72 Class C 148.93 9.78 150.84 7.87 150.04 9.62 Class B 134.01 11.81 135.94 10.79 135.09 10.28 ClassClass D C130.67 148.93 16.06 9.78 142.38 150.84 12.43 7.87 150.04130.66 9.6217.00 ClassClass E D132.75 130.67 13.75 16.06 127.75 142.38 17.05 12.43 130.66132.96 17.0013.89 Class E 132.75 13.75 127.75 17.05 132.96 13.89 3.4. Landfall Locations for Different TC Classes 3.4. LandfallLandfall Locations locations forDifferent are direct TCly Classes associated with TC disasters. Therefore, to obtain a better understandingLandfall locations for landfall are rules directly of TCs associated in different with classes, TC disasters.a hot-spot analysis Therefore, of landfall to obtain location a betters understandingwas performed for for landfall different rules TC of categories TCs in different. The analysis classes, identif a hot-spotied statistically analysis significantof landfall spatial locations wasclusters performed of hot forspots different and cold TC spots, categories. which correspond The analysis to frequent identified landfall statistically locationssignificant and infrequent spatial landfall locations, respectively. The analytical results are shown in Figure 5. In the figure, the red clusters of hot spots and cold spots, which correspond to frequent landfall locations and infrequent areas indicate frequent landfall locations, and the green areas indicate infrequent landfall locations. landfall locations, respectively. The analytical results are shown in Figure5. In the figure, the red areas Figure 5 shows that the frequent landfall locations for different classes of TCs can be divided into two indicate frequent landfall locations, and the green areas indicate infrequent landfall locations. Figure5 types. The frequent landfall locations for westward straight-moving TCs are the surrounding showscountries that theand frequentregions of landfall the SCS locations to the south for of different 22° N. The classes frequent of TCs landfall can belocations divided for into northward two types. There frequent-curving TCs landfall are located locations in the for eastern westward coastal straight-moving region of China TCs to the are north the surrounding of 22° N. countries and ◦ regionsFrom of the the SCS perspective to the south of different of 22 N. trajectory The frequent categories landfall, for TCs locations in class for A northward(Figure 5a), re-curvingthe frequent TCs ◦ arelandfall located locations in the eastern are primarily coastal concentrated region of China in the to coastal the north regions of 22 ofN. South China and the northern regionFrom of the Vietnam perspective. The Philippines of different is trajectory an obvious categories, infrequent for landfall TCs in location class A. (Figure For TCs5a), in theclass frequentes B landfall(Figure locations 5b) and C are (Figure primarily 5c), the concentrated most obvious in frequent the coastal landfall regions locations of South are concentrated China and thealong northern the regioncoast of of Vietnam.the Philippines The; Philippines the coastal region is ans obvious of South infrequentChina and Vietnam landfall are location. comparatively For TCs infrequent in classes B (Figurelandfall5b) locations and C (Figure. Compared5c), the to mostthe average obvious latitude frequent of the landfall genesis locations location areof TCs concentrated in class C obtained along the coastby ofthe the equal Philippines; division of the the coastal trajectory regions and ofthe South mass China moment and of Vietnam the trajectory are comparatively methods, the infrequentclass C landfallgenesis locations. location Comparedobtained by to the the mixed average regression latitude ofmodel the genesisis located location in a more of TCs southerly in class position C obtained by( theTable equal 3), and division therefore of,the it does trajectory not form and a significant the mass frequent moment landfall of the trajectorylocation in methods,the north of the Luzon class C genesisIsland location, unlike class obtained C obtained by the by mixedthe other regression two methods model. is located in a more southerly position The frequent landfall location for class D is mainly concentrated in the eastern and southeastern (Table3), and therefore, it does not form a significant frequent landfall location in the north of Luzon areas of China. Because class D obtained by the mixed regression model is a mixed TC trajectory class Island, unlike class C obtained by the other two methods. with a dominant westward heading, the frequent landfall location for this class occurs more to the The frequent landfall location for class D is mainly concentrated in the eastern and southeastern south, extending only to Zhejiang Province in China (in the middle of Figure 5d). In contrast, the areasfrequent of China. landfall Because location class of class D obtained D obtained by the by the mixed other regression two trajectory model clustering is a mixed algorithms TC trajectory extends class withfurther a dominant northward westward and reaches heading, Jiangsu the Province frequent of landfallChina (on location the left and for thisright class of Figure occurs 5d more). to the south, extending only to Zhejiang Province in China (in the middle of Figure5d). In contrast, the ISPRS Int. J. Geo-Inf. 2017, 6, 210 12 of 22 frequent landfall location of class D obtained by the other two trajectory clustering algorithms extends furtherISPRS northward Int. J. Geo-Inf. and 2017 reaches, 7, 210 Jiangsu Province of China (on the left and right of Figure125d). of 22 The frequent landfall location of class E obtained by the mixed regression model (in the middle of Figure5e) isThe consistent frequent landfall with that location of class of class D obtainedE obtained byby the mixed equal regression division model of the (in trajectory the middle and the mass momentof Figure of5e) the is consistent trajectory with methods that of class (on D the obtained left and by rightthe equal of Figuredivision5 d)of the for trajectory their similarity and the in TC trajectorymass shape moment and of genesis the trajectory position, methods as mentioned (on the left inand the right previous of Figure section. 5d) for However,their similarity class in E TC obtained by the equaltrajectory division shape of and the genesis trajectory position and, as mass mentioned moment inof the the pr trajectoryevious section methods. However forms, class only E a finite obtained by the equal division of the trajectory and mass moment of the trajectory methods forms frequent landfall location in the eastern coast region of China. only a finite frequent landfall location in the eastern coast region of China.

(a) Class A

(b) Class B

(d) Class D

Figure 5. Cont. ISPRS Int. J. Geo-Inf. 2017, 6, 210 13 of 22 ISPRS Int. J. Geo-Inf. 2017, 7, 210 13 of 22

(e) Class E Equal division of the trajectory Mixed regression model Mass moment of the trajectory method. method. method.

FigureFigure 5. (a– e5). Spatial(a–e) Spatial distribution distribution of of landfall landfall locationslocations for for the the TCs TCs in different in different classes classes according according to to the different trajectory clustering methods. Red indicates the frequent landfall locations, and green the different trajectory clustering methods. Red indicates the frequent landfall locations, and green indicates the infrequent landfall locations. A value of ±3 is statistically significant at a confidence level ± indicatesof 99%, the infrequent ±2 is statistic landfallally significant locations. at a confidence A value of level3 of is 95%, statistically and ±1 is significant statistically atsignificant a confidence at a level of 99%,confidence±2 is statistically level of 90%; significant 0 indicates at that a confidence the results are level not of significant. 95%, and ±1 is statistically significant at a confidence level of 90%; 0 indicates that the results are not significant. 3.5. Intensity and Lifetime of Different TC Classes 3.5. IntensityThe and distribution Lifetime ofof Different maximum TC intensity Classes levels reached by the TCs in the various classes over the lifetime of the TC is shown in Figure 6. TCs are categorized into tropical storm (TS, 17.2 ≤ 푣 ≤ The distribution of maximum intensity levels reached by the TCs in the various푚푎푥 classes 32.6 m/s), typhoon (TY, 32.7 ≤ 푣푚푎푥 ≤ 50.9 m/s) and super typhoon (STY, 푣푚푎푥 ≥ 51.0 m/s) over thecategories lifetime according of the to TC their is grade shown of maximumin Figure wind.6. TCs For all are the categorized TCs shown intoin Figure tropical 6, the storm (TS, 17.2proportion≤ vmax of≤ tropical32.6 m/s storm),s typhoon and typhoon (TY,s is 32.7essentially≤ vmax the≤ same50.9: both m/s )account and for super approximately typhoon (STY, vmax ≥40%51.0 of m/s the) overall categories TCs. accordingThe proportion to their of TCs grade reaching of maximum the level wind.of super For typhoon all the is TCs approximately shown in Figure 6, the proportion20%. of tropical storms and typhoons is essentially the same: both account for approximately 40% of the overallThere are TCs. some The differences proportion in the of intensity TCs reaching distribution the level of TCs of superin different typhoon classes is. approximatelyAmong these 20%. results, relatively high consistency in the intensity distribution tendency of TCs can be seen in the There are some differences in the intensity distribution of TCs in different classes. Among these clustering results obtained by the equal division of the trajectory method (Figure 6a) and the mass results,moment relatively of the high trajectory consistency method in(Figure the intensity 6c). The maximum distribution intensity tendency level of of the TCs TCscan in class be seenA is in the clusteringrelatively results low obtained because by of the equallimited division spatial scale of the of trajectory the SCS basin method and the(Figure influence6a) and of the mass momentsurrounding of the trajectory land. The method tropical (Figurestorm type6c). accounts The maximum for the vast intensity majority (> level70%) of of thethe TCs in in class class A is relativelyA, lowfollowed because by the of thetyphoon limited level spatial, which scale accounts of the for SCS approximately basin and the 26% influence; however, of few the super surrounding- land. Thetyphoon tropical TCs are storm observed type in accounts this class for. The the TCs vast in class majorityes B and (>70%) D are similar of the, and TCs the in proportion class A, followedof tropical storm and typhoon-level TCs is essentially the same and comprises the vast majority of TCs by the typhoon level, which accounts for approximately 26%; however, few super-typhoon TCs are (>80%) in the classes. A few super-typhoon TCs occur in classes B and D. observed inIn this class class. C, the The super TCs-typhoon in classes TCsB and and typhoon D are similar,TCs account and for the the proportion vast majority of tropical(>80%). One storm and typhoon-levelsignificant TCs difference is essentially is that the the proportion same and of comprises super-typhoon the vastTCs in majority this class of exceeds TCs (>80%) the proportion in the classes. A few super-typhoonof the other two types TCs of occur TCs, inaccounting classes Bfor and more D. than 40%. The TCs in class C have longer moving Indistance class C,s and the lifetime super-typhoons in general TCs because and of typhoon their easternmost TCs account genesis for regions the near vast the majority Mariana (>80%). One significantIslands (on differencethe right side is ofthat Figure the 6a) proportion; therefore, these of TCs super-typhoon are more likely TCs to reach in thishigher class intensities exceeds the [47–49]. The opposite situation is true for TCs in class A, which have the shortest lifetime and lowest proportion of the other two types of TCs, accounting for more than 40%. The TCs in class C have strength distribution. longer moving distances and lifetimes in general because of their easternmost genesis regions near the Mariana Islands (on the right side of Figure6a); therefore, these TCs are more likely to reach higher intensities [47–49]. The opposite situation is true for TCs in class A, which have the shortest lifetime and lowest strength distribution. The average lifetime is longest for class E TCs. Therefore, TCs in this class also have a relatively strong intensity. The proportion of TCs reaching typhoon intensity is approximately 50%, and the proportion of super typhoons exceeds 20%. The proportion of super typhoons that is relatively lower than class C may be related to the re-curving north movement of TCs in class E, where cooler sea surface temperature inhibits the development of intense TCs [50]. ISPRSISPRS Int. Int. J. J. Geo Geo-Inf.-Inf. 20172017, ,76, ,210 210 1414 of of 22 22

TS TY STY 80% 20

60% 15

40% Days 10

20% 5

0% 0 A B C D E All A B C D E All

(a)

TS TY STY 80% 20

60% 15

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(b)

TS TY STY 20 80%

60% 15

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0% 0 A B C D E All A B C D E All

(c)

Figure 6. The statistics of intensity distribution and lifetime of TCs in different classes obtained by the Figure 6. The statistics of intensity distribution and lifetime of TCs in different classes obtained by the different trajectory clustering methods. The histograms on the left side of the figure show the intensity different trajectory clustering methods. The histograms on the left side of the ﬁgure show the intensity distribution of TCs in different classes; the corresponding boxplot on the right side shows the lifetime distribution of TCs in different classes; the corresponding boxplot on the right side shows the lifetime statistics of TCs in the classes. The line and the diamond within the box represent the median value statistics of TCs in the classes. The line and the diamond within the box represent the median value and the mean value of the lifetime of TCs in the class, separately. (a) Intensity and lifetime statistical and the mean value of the lifetime of TCs in the class, separately. (a) Intensity and lifetime statistical resultsresults obtained obtained by by e equalqual division division of of the the trajectory trajectory method method;; (b (b)) Intensity Intensity and and lifetime lifetime statistical statistical results results obtainedobtained by by m mixedixed regression regression model model method; method; ( (cc)) Intensity Intensity and and lifetime lifetime statistical statistical results results obtained obtained by by mmassass moment moment of of the the trajectory trajectory method. method.

The average lifetime is longest for class E TCs. Therefore, TCs in this class also have a relatively For TCs in classes obtained by the mixed regression model (Figure6b), the intensity statistical strong intensity. The proportion of TCs reaching typhoon intensity is approximately 50%, and the results exhibit different features. The intensity of TCs in class D also have the highest proportion proportion of super typhoons exceeds 20%. The proportion of super typhoons that is relatively lower of strong TC intensity, similar to that of TCs in class C. This is an embodiment of the similarity of than class C may be related to the re-curving north movement of TCs in class E, where cooler sea TCs in intensity distribution in these two classes, which show a relatively high consistency in the surface temperature inhibits the development of intense TCs [50]. trajectory movement trend and genesis position. The lifetime statistics show that the TCs in class For TCs in classes obtained by the mixed regression model (Figure 6b), the intensity statistical D are the second-longest (on the right of Figure6b) among the TC groups obtained by the mixed results exhibit different features. The intensity of TCs in class D also have the highest proportion of regression model. The northward re-curving TCs in class E show similarity in intensity distribution strong TC intensity, similar to that of TCs in class C. This is an embodiment of the similarity of TCs in intensity distribution in these two classes, which show a relatively high consistency in the trajectory ISPRS Int. J. Geo-Inf. 2017, 6, 210 15 of 22 and lifetime to those in class D obtained by the equal division of the trajectory and the mass moment of the trajectory methods. Both of these classes have main genesis locations restricted to the west of 140 ◦E concentrated in the Philippine Basin and the SCS. The tropical storm and typhoon-level TCs comprise the vast majority (~90%), and the average lifetime is approximately seven days, which is close to the total average value.

3.6. Seasonal Distribution of Different TC Classes The seasonal distribution for class A (Figure7a) is primarily concentrated in June–November, and relatively high consistency is reached for the results obtained by the different algorithms for this class. TCs in class B obtained by the equal division of the trajectory method (on the left of Figure7b) are primarily distributed from July–November. The relatively larger spread time is likely related to the relatively high sea surface temperature of the Philippine Sea, which are higher than 26 ◦C[30]. In contrast, for class B obtained by the mass moment of the trajectory method (on the right of Figure7b), more TC activities are observed for October–November. The average genesis position statistic results show that TCs in class B obtained by the mass moment of the trajectory method are located in a relatively more southerly location than those obtained by the equal division of the trajectory method (Table3). This reflects that the average generation position of TCs in the WNP gradually moves northward from June to August and begins to retreat southward beginning in September [6,51]. For the TCs in class C obtained by the equal division of the trajectory and the mass moment of the trajectory methods, the seasonal distribution has obvious double peaks in July, August, October and November (left and right of Figure7 c). This distribution follows the straight-moving TCs, which are mostly distributed in the early and late stages of the TC season in the WNP [6,51]. The northward re-curving moving trajectory of class D is primarily concentrated during July-September (on the left and right of Figure7d). Although class D obtained by the mixed regression model method has a similar form of seasonal distribution (in the middle of Figure7d), it is important to remember that this class is a mixture class and contains numerous westward straight-moving TC trajectories. Compared to the genesis position with class C, which was also obtained by the mixed regression model method, TCs in class C shifted more southward (Table3). In addition, the seasonal distribution of class C displays a pronounced winter active mode concentrated in October-December (in the middle of Figure7c). Accordingly, these two classes obtained by the mixed regression model method together also reflect the north-south oscillation of the genesis positions of TCs with the change of seasonality in the WNP. The seasonality distribution of TC activity in class E (on the left and right of Figure7e) exhibits a bimodal pattern and is concentrated during the conversion from spring to summer and summer to fall in May, June, August, September, and October. This seasonal distribution reflects the seasonal distribution of the extratropical transition of TC in the WNP, which is related to large-scale circulation modes and high-altitude trough activity in the mid-high latitude region over the WNP [52,53]. The statistical analysis indicates that 82% of the TCs in class E obtained by the equal division of the trajectory method experienced an extratropical transition process, and 94% of the TCs in the class obtained by the mass moment of the trajectory method experienced an extratropical transition process. The seasonal distribution of class E obtained by the mixed regression model method has more similarity to that of class D obtained by the equal division of the trajectory method and the mass moment of the trajectory method. This result is consistent with the similarity of class features for these classes as analysed previously. ISPRS Int. J. Geo-Inf. 2017, 6, 210 16 of 22 ISPRS Int. J. Geo-Inf. 2017, 7, 210 16 of 22

25% 25% 25% 20% 20% 20% 15% 15% 15% 10% 10% 10% 5% 5% 5% 0% 0% 0% 1 2 3 4 5 6 7 8 9 101112 1 2 3 4 5 6 7 8 9 101112 1 2 3 4 5 6 7 8 9 101112 (a) Class A 20% 25% 25%

15% 20% 20% 15% 15% 10% 10% 10% 5% 5% 5% 0% 0% 0% 1 2 3 4 5 6 7 8 9 101112 1 2 3 4 5 6 7 8 9 101112 1 2 3 4 5 6 7 8 9 101112 (b) Class B 20% 30% 20% 25% 15% 15% 20% 10% 15% 10% 10% 5% 5% 5% 0% 0% 0% 1 2 3 4 5 6 7 8 9 101112 1 2 3 4 5 6 7 8 9 101112 1 2 3 4 5 6 7 8 9 101112 (c) Class C 30% 30% 30% 25% 25% 25% 20% 20% 20% 15% 15% 15% 10% 10% 10% 5% 5% 5% 0% 0% 0% 1 2 3 4 5 6 7 8 9 101112 1 2 3 4 5 6 7 8 9 101112 1 2 3 4 5 6 7 8 9 101112 (d) Class D 25% 30% 30% 20% 25% 25% 20% 20% 15% 15% 15% 10% 10% 10% 5% 5% 5% 0% 0% 0% 1 2 3 4 5 6 7 8 9 101112 1 2 3 4 5 6 7 8 9 101112 1 2 3 4 5 6 7 8 9 101112 (e) Class E Equal division of the trajectory Mixed regression model Mass moment of the trajectory method. method. method.

Figure 7. (a–e) Seasonal distributions of of TCs in different classes according to the different trajectory clustering methods.

4. Discussion In this paper, three clustering methods were applied to analyse the trajectory of TCs that affect the SCS. Among these methods, the equal division of the trajectory method and the mass moment of the trajectory method preprocess the original trajectory data into a structure that can express the characteristics of the original trajectory and satisfy the data-processing requirements of normal clustering algorithms. In contrast, the mixed regression model method can conduct clustering operations on the original trajectory data with different lengths based on a special mathematical regression model. The form of the clustering centre provides a preliminary understanding of the overall characteristics of the elements in the class. The TC cluster centre obtained by different methods are different (Figure2). Among these cluster centres, the mass moment of the trajectory method obtains a variance ellipse class centre, which provides a good expression of the spatial distribution of the trajectory. Both the equal division of the trajectory method and the mixed regression model method acquired a line-type class centre. However, the class centre for the mixed regression model still produced curve lines in the cases of classes A and B (Figure2b), even though these classes primarily consist of straight-moving TC trajectories. This observation produces a confusing expression for the TC trajectory mode of the classes. However, the class centres acquired by the equal division of the trajectory method provide a relatively simple and clear expression (Figure2a) corresponding to the TC trajectory mode of classes A and B. The reason may be that the mixed regression model method is essentially based on a quadratic polynomial curve fitting process, which may be more susceptible to the effect of abnormal trajectories in the class. Thus, the cluster centre takes the form of a curve, and it cannot accurately reflect the overall characteristics of TC trajectories in the class. In contrast, the class centre obtained by the equal division of the trajectory method is a result of an averaging operation of all TC trajectory data in the class. Therefore, the influences of abnormal trajectories in the class are eliminated by the averaging process. In addition, the cluster centre can better embody the overall tendency of the moving trend of TCs in the class. The previous analysis shows that differences are observed in the results obtained from the different models. These differences reflect the methods’ individual features. Table4 summarizes the main characteristics of the different algorithms. For the equal division of the trajectory method, the velocity information contained in the original trajectory cannot be retained after the equal division of the trajectory is performed. The mass moment of the trajectory method retains the velocity information of the original trajectory, at least to an extent. However, this transformation process also produces biases in the space and shape information expression of the TC trajectory and may induce some deviation in the clustering result. Figure8 shows a re-curving trajectory mixed in the straight-moving trajectory class C obtained by the mass moment of the trajectory method. The left side of the figure shows the original observation points of the TC trajectory, and the right side is the equal division point of the trajectory. It can be seen from Figure8a that when the TC moved to a high latitude, the accelerated velocity caused a decrease in the number of observation data points in the trajectory obtained in the same time interval; therefore, the central point of the trajectory is more to the south and closer to the side of the trajectory with dense sampling points. In addition, the long axis direction of the variance ellipse is consistent with the distribution direction of the dense trajectory points. In Figure8b, because the equal division sampling points are uniformly distributed, the central point is shifted to the north, closer to the geometric centre of the trajectory, and the variance ellipse indicates the overall distribution trend of the trajectory. Therefore, the central point and the variance ellipse are more susceptible to the sample points in the trajectory, which may influence the clustering result and result in some mixture of trajectory types in the TC trajectory cluster. However, the overall clustering results show that, for TC trajectory, it is not the velocity but the shape and spatial location that are the main factors in determining the clustering results. This finding is consistent with the previous view [6,30]. Moreover, in comparison, relatively high consistency is observed for the clustering results obtained by the mass moment of the trajectory method and the equal division of the trajectory method. ISPRS Int. J. Geo-Inf. 2017, 6, 210 18 of 22

The mixed regression model method has a solid theoretical mathematical basis. The clustering operation can be conducted for the original trajectory data without preprocessing. By expanding the dimension of the polynomial coefficient matrix, this method can conveniently add variable factors that are likely to play a role in clustering results into the model. Through regression fitting, the clustering results show relatively good concentration for the TC spatial location. However, the ISPRSquadratic Int. J. Geo polynomial-Inf. 2017, 7, used210 to fit the TC trajectory will likely cause a mixture of the various types18 of of22 ISPRS Int. J. Geo-Inf. 2017, 7, 210 18 of 22 TC trajectory. Figure9 shows the quadratic polynomial fitting of the TC trajectories with different movements contained in class D according to the mixed regression model method. The red trajectory movements contained in class D according to the mixed regression model method. The red trajectory represents the fittedfitted quadratic quadratic polynomial polynomial curve. curve. F Foror the the straight trajectory and the re-curvingre-curving represents the fitted quadratic polynomial curve. For the straight trajectory and the re-curving trajectory with with relatively relatively high high local local similarity, similarity, we can achieve a relatively good fit fit through the same trajectory with relatively high local similarity, we can achieve a relatively good fit through the same quadratic polynomial curve. quadratic polynomial curve.

(a) (b) (a) (b) Figure 8. Central point and variance ellipse of the trajectory obtained by the (a) original trajectory Figure 8. Central point and variance ellipse of the trajectory obtained by the ( a) original trajectory points and (b) equal division trajectory points for Typhoon Emma (November 1959). points and ( b) equal division trajectory points for Typhoon EmmaEmma (November(November 1959).1959).

Figure 9. Quadratic polynomial fitting result of the TC trajectories. Figure 9. Quadratic polynomial fitting ﬁtting result of the TC trajectories. To compare the trajectory motion modes in the clustering results obtained by the various To compare the trajectory motion modes in the clustering results obtained by the various algorithms,To compare cosine thesimilarity trajectory statistics motion between modes the in trajectories the clustering in the resultsdifferent obtained classes were by the conducted various algorithms, cosine similarity statistics between the trajectories in the different classes were conducted (algorithms,Table 5). The cosine statistical similarity results statistics show betweenthat, in general, the trajectories the algorithms in the different all obtain classes relatively were conducted good TC (Table 5). The statistical results show that, in general, the algorithms all obtain relatively good TC trajectory(Table5). The clustering statistical results. results The show result that,s of in the general, equal the division algorithms of the all trajectory obtain relatively method goodare more TC trajectory clustering results. The results of the equal division of the trajectory method are more consistenttrajectory in clustering TC trajectory results. movement, The results especially of the for equal the re division-curving of trajectories the trajectory in class methodes D and are E. more The consistent in TC trajectory movement, especially for the re-curving trajectories in classes D and E. The averageconsistent cosine in TC similarities trajectory movement,of these two especially classes are for 0.988 the re-curving and 0.987 trajectories for the equal in classes division D andof the E. average cosine similarities of these two classes are 0.988 and 0.987 for the equal division of the trajectoryThe average method cosine. For similarities the mixed of regression these two model classes method, are 0.988 the and similar 0.987ities for are the 0.981 equal and division 0.982, which of the trajectory method. For the mixed regression model method, the similarities are 0.981 and 0.982, which aretrajectory the lowest method. among For these the mixed three regressionmethods. The model statistical method, results the similarities are significant are 0.981 at the and 0.05 0.982, level. which are the lowest among these three methods. The statistical results are significant at the 0.05 level. are theThe lowest above among analyses these suggest three methods.that the equal The statisticaldivision of results the trajectory are signiﬁcant method at theprovides 0.05 level. a simple The above analyses suggest that the equal division of the trajectory method provides a simple and directThe above solution analyses to the suggest problem. that This the equal algorithm division also of reach the trajectoryes a relative methodly better provides clustering a simple result and and direct solution to the problem. This algorithm also reaches a relatively better clustering result fromdirect the solution standpoint to the of problem. the characteristic This algorithm expression also reaches and consistency a relatively of better the clusteringTC trajectory result movement from the from the standpoint of the characteristic expression and consistency of the TC trajectory movement instandpoint the class. of For the the characteristic mass moment expression of the trajectory and consistency method, of the the spatial TC trajectory distribution movement of TC trajectories in the class. in the class. For the mass moment of the trajectory method, the spatial distribution of TC trajectories inFor different the mass classes moment is well of the displayed trajectory through method, a variance the spatial ellipse distribution form class of centre TC trajectories. It may be in somewhat different in different classes is well displayed through a variance ellipse form class centre. It may be somewhat difficult to select the proper length of the clutter centre for the mixed regression model method to difficult to select the proper length of the clutter centre for the mixed regression model method to more accurately express the characteristics of TC tracks in the class. A relatively greater mixture of more accurately express the characteristics of TC tracks in the class. A relatively greater mixture of different types of TC trajectories may be caused in the clustering result. However, a relatively high different types of TC trajectories may be caused in the clustering result. However, a relatively high spatial concentration of TC trajectories in the clustering result is achieved with this algorithm, which spatial concentration of TC trajectories in the clustering result is achieved with this algorithm, which may be a priority option in the case of TC trajectory spatial consistency being retained. may be a priority option in the case of TC trajectory spatial consistency being retained.

Table 4. Comparison of three clustering methods for the trajectory. Table 4. Comparison of three clustering methods for the trajectory. Clustering Equal Division of the Mixed Regression Model Mass Moment of the Clustering Equal Division of the Mixed Regression Model Mass Moment of the Method Trajectory Method Method Trajectory Method Method Trajectory Method Method Trajectory Method ISPRS Int. J. Geo-Inf. 2017, 6, 210 19 of 22 classes is well displayed through a variance ellipse form class centre. It may be somewhat difﬁcult to select the proper length of the clutter centre for the mixed regression model method to more accurately express the characteristics of TC tracks in the class. A relatively greater mixture of different types of TC trajectories may be caused in the clustering result. However, a relatively high spatial concentration of TC trajectories in the clustering result is achieved with this algorithm, which may be a priority option in the case of TC trajectory spatial consistency being retained.

Table 4. Comparison of three clustering methods for the trajectory.

Clustering Equal Division of the Mixed Regression Model Mass Moment of the Method Trajectory Method Method Trajectory Method Combination with the general Combination with the general Cluster the original Type of clustering model after the clustering model after the trajectory data based on the method transformation of the transformation of the mathematical model original trajectory original trajectory Model Simple Complicated Relatively complicated complexity Spatial location, shape Information Spatial location and shape Original complete trajectory information and some velocity contained information of the trajectory information information of the trajectory Clustering Trajectory shape consistency is Trajectory spatial consistency Essentially similar to the equal results relatively good is relatively good divide method Class centre Average trajectory in the class Quadratic curve Variance ellipse

Table 5. Cosine similarity statistics of TC trajectories in different classes obtained by the various trajectory clustering methods.

Equal Division of the Trajectory Mixed Regression Model Mass Moment of the Trajectory Clustering Method Method Method Method Mean Maximum Minimum Mean Maximum Minimum Mean Maximum Minimum Class A 0.991 1.000 0.914 0.990 1.000 0.924 0.991 1.000 0.914 Class B 0.993 1.000 0.944 0.994 1.000 0.963 0.992 1.000 0.928 Class C 0.992 * 1.000 0.950 0.991 * 1.000 0.939 0.986 1.000 0.898 Class D 0.988 1.000 0.911 0.981 1.000 0.877 0.986 1.000 0.922 Class E 0.987 * 1.000 0.940 0.982 1.000 0.885 0.987 * 1.000 0.940 Note: The asterisk * indicates the difference is not signiﬁcant at the 0.05 level.

5. Conclusions In this article, three trajectory clustering algorithms were applied to analyse the trajectories of TCs that affected the SCS from 1949 to 2014. Based on the complete spatial position and trajectory shape information of the TC trajectories, ﬁve trajectory clusters were obtained, including three western straight-line movement trajectory clusters and two northward re-curving trajectory clusters. The TC trajectories in different clusters show different characteristics in their properties, such as lifetime, strength, movement distance, landfall location, and seasonality distribution. For the TCs in class A, which were generated in the most western region, within the SCS, the intensity is weaker overall. The TCs in class C, which were generated in the most eastern region at approximately 145 ◦E near the Mariana Islands, have the highest proportion of super-typhoon grade TCs for their longer movement distance and extended lifetimes. The landfall location analysis shows that the northward re-curving TCs were primarily concentrated along the coasts of the eastern provinces of China. Two landfall types are observed for the westward straight-moving TCs. For the TCs in class A, the landfall locations were primarily concentrated in the coastal regions of South China and north of Vietnam. For the TCs from the WNP in classes B and C, the most affected area was the Philippines. The monthly activity frequency distribution of TCs in classes A and B were primarily distributed during June–November. There are no obvious peak seasons for the TCs generated east of the ISPRS Int. J. Geo-Inf. 2017, 6, 210 20 of 22

Philippines in class B. For the TCs in class C, two obvious peak seasons are observed in the early and late stages of the TC season. The northward re-curving TCs in class D are primarily concentrated in the period from July–September. In contrast, the TCs in class E obtained by the equal division of the trajectory and the mass moment of the trajectory methods are primarily concentrated during the conversion from spring to summer and summer to fall, reﬂecting the seasonality distribution characteristics of TCs experiencing extratropical transition. A comparison of the results obtained by these trajectory-clustering algorithms shows that the equal division of the trajectory method provide a better clustering result generally. The class centre provides a simple and clear expression for the pattern of TC tracks in the class. In addition, the heading of TC tracks maintains a relatively good consistency in the class. The results obtained by the trajectory mass moment algorithm are more consistent with the results obtained by the equal division of the trajectory method. The mixed regression model method, which presents higher sensitivity in the trajectory position, can obtain TC clusters with a more concentrated spatial distribution.

Acknowledgments: This study was funded by the National Science Foundation of China (Grant Number: 41671445) and the National Science Foundation of China (Grant Number: 41421001). Author Contributions: This research was primarily conducted by Feng Yang, Guofeng Wu, Yunyan Du and Xiangwei Zhao. Feng Yang collected the data; Guofeng Wu and Yunyan Du designed the experiments; and Feng Yang performed the experiments, analysed the data and wrote the manuscript. Xiangwei Zhao helped process the data. Conﬂicts of Interest: The authors declare no conﬂicts of interest.

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