Abstract
Spatiotemporal patterns are one of the greatest interests and provide valuable insights into chronological events occurring in space. A tropical cyclone (TC) track is defined as a sequence of successive points, and several different types of analyses are performed to explore the temporal and spatial patterns of the TCs in the Northwest Pacific and along the coastline of China during 1949–2014. Results show that (1) the number of TCs is getting more frequent from April to August and less frequent from August to October with the peak occurring in August almost every year; (2) the mean of the sizes of the annual temporal clusters during 1949–2014 is 52.5 (days), the standard deviation is 17.0 (days), and the average starting point is the 210.5th day; (3) the spatial clusters are located in two areas: the boundary of Guangxi and Guangdong provinces and the boundary of Fujian and Zhejiang provinces; and (4) the within-strata variance is less than the between-strata variance, which implies the locational and seasonal factors are the potential determinants of the heterogeneity of the TCs. Furthermore, several maps representing the hazards of TCs are produced. According to the resultant maps, 12 coastal prefectures (Zhanjiang, Maoming, Fuzhou, Huizhou, Yangjiang, Qinzhou, Ningde, Quanzhou, Jiangmen, Nanning, Zhangzhou, and Hangzhou) have return periods of less than two years, and the two island provinces of Hainan and Taiwan are visited by TCs the most. Guangdong, Guangxi, Fujian, and Zhejiang provinces in particular suffered severely from the destructive TCs.
1. Introduction
A tropical cyclone (TC) is a rapidly rotating storm system characterized by a low-pressure center, strong winds, and a spiral arrangement of thunderstorms that produce heavy rain. Depending on the strength and the location where the storm occurs, tropical cyclones have some synonyms such as tropical storm, hurricane, typhoon, tropical depression, cyclonic storm, and simply a cyclone [1]. An intense tropical cyclone, which brings gales, heavy rain, and storm surge in the course of its landfall, is among the most devastating of all natural hazards and causes huge losses every year all over the world, especially in some coastal areas [2]. China is located in the West Pacific and has a length of continental coastline more than 18,000 km in the east and south parts of the country. There are numerous cities (including Tianjin, Shanghai, Guangzhou, Shenzhen, etc., metropolises) distributed in 14 coastal provinces (autonomous regions, municipalities, and special administrative regions) (12 continental ones and 2 island ones). Due to suitable natural and climate conditions, more than 600 million people live in these coastal provinces, which amount to 43% of the total population of the country. In terms of the national statistics yearbook of 2014, the accumulated GDP (Gross Domestic Product) of the 10 continental coastal provinces (data are unavailable for Hongkong and Macau) are 36,952 billion RMB (Ren Min Bi) Yuan which is even more than 54% of the total GDP of Mainland China. The nation standard of China “Grade of tropical cyclones” that was put in practice since June 15, 2006 divides tropical cyclones into six scales: TD (tropical depression), TS (tropical storm), STS (severe tropical storm), TY (typhoon), STY (severe typhoon), and SuperTY (super typhoon). Although the fatality of tropical cyclones has been significantly reduced by a highly successful program of warnings and advanced building construction over the last decades, economic losses are escalating rapidly owing to the accelerated construction in TC-prone areas. The main affected areas in China by tropical cyclones are concentrated in coastal cities where population density and economic level are universally higher than other areas. These areas suffer huge losses from typhoons every year. 16 (including 10 coastal and 6 inland) out of 28 provinces in China are affected by TC-induced disasters [3]. In recent decades, the number of casualties caused by hazardous TCs in China has slightly decreased, but the property loss has significantly increased. Since the year of 2000, direct and indirect economic loss from hazardous TCs exceeds tens of billion RMB every year. Densely populated and well-developed coastal areas have suffered high casualty and property loss.
Analysis of spatiotemporal characteristics for TCs is useful to recognize distributional patterns, identify clusters, and predict spatial variables based on historical data, which is able to provide useful support for prevention and response of hazardous TCs, including comprehensive risk assessment, evacuation planning, resource allocation, among others. For example, Wang et al. [4] show the interdecadal variation in TC tracks over the Northwest Pacific taking landfalling locations of TCs in Xiamen as study objects. The results from Gu et al. [5] suggest that since the early 1960s, there has been an overall decreasing trend in the frequency of occurrence, intensity, peak intensity, length of movement, and lifetime of TCs. Chan and Liu [6] explored interannual variations of typhoon activity and concluded these variations appear to be largely constrained by the large-scale atmospheric factors that are closely related to the El Niño—Southern Oscillation (ENSO) phenomenon. Tang et al. [7] analyzed the annual and monthly variations of TC from 1951 to 2006 statistically, including frequencies, intensities, and wind intensity indices. By calculating the TC frequency and wind intensity indices in each 1° × 1° longitude-latitude grid, Tang et al. [7] also analyzed the spatial distribution and the influence extent of TCs. In summary, in spatiotemporal characteristics of TCs, currently existing literature are mainly focused on summary statistics on different scales. Though some temporal and spatial patterns are presented in these papers, it is necessary to get deep insight into spatiotemporal characteristics of TCs with advanced techniques of spatial pattern analysis. Temporal analysis helps ones effectively get insights into chronological phenomena through establishing references of activity and discover periodic patterns in which data are presented by different scales (e.g., hour, day, month, and year). Temporal analyses are often shown in simple linear and circular charts to illustrate chronological order and cycle [8]. Different from the charts, some statistical methods can be used to detect clusters of events along a timeline and assert the confidence level of the results. Whether the occurrences of chronological events have significant anomalies along a timeline is essentially a problem how to identify the clusters of points along a line. There are some existing methods able to solve this problem [9–11]. These kinds of one-dimensional scan statistic methods are also widely applied in cluster detection of temporal data such as disease, drought, and forest fire. There are two kinds of commonly used techniques for exploring spatial patterns: global clustering and local clustering. Global clustering is to judge whether there exists significant spatial clustering trends in spatial phenomena (represented by observed events), which is generally determined by global test statistics [12, 13]. However, global clustering cannot obtain the specific locations of clusters. Local clustering is capable of identifying the centers of clusters and even their sizes and shapes [14–17]. Stratified heterogeneity, which refers to the within-strata variance less than the between-strata variance, is ubiquitous in spatial phenomena. Stratified heterogeneity may imply the determinants of events [18].
To visualize the hazard of disasters, an alternative approach is to evaluate the spatial density of disasters. While point density estimation is widely used to quantify hazard of disasters with concentric impact, a line-based density estimation is imperative to map the hazard of disasters with linear distribution. Density estimation techniques have been applied to examine spatiotemporal dynamics in some domains [19–24]. These types of techniques generally use a density kernel to spread the values of the samples out over a surface. The magnitude at each sample is distributed throughout the study area, and a density value is estimated for each cell in the output surface. Steiniger and Hunter [22] extend the point-based kernel density estimation (KDE) approach to work with sequential GPS-point tracks, the outcome of which is a line-based KDE. Demšar et al. [23] present an alternative geovisualization method for spatiotemporal aggregation of trajectories of tagged animals: stacked space-time densities. Given tracks of tropical cyclones are represented as lines, and in this study, we propose a track density algorithm to map the density of tropical cyclones.
Some GIS tools of mapping and analysis are widely used in manipulation of georeferenced data. Through adding a few geographic elements into the tornado definition and then characterizing tornado density as a density field in GIS, Deng et al. [25] examine how GIS factors function in the process of tornado density mapping. Liu et al. [26] resort to the extension of ArcGIS (a proprietary GIS software package developed by Esri Corporation): Geostatistical Analyst to carry out interpolation analysis of flood risk factors. Also, in those widely used proprietary GIS software packages like ArcGIS, some commonly used methods of spatial analysis and visualization have been devised. Moreover, almost all products also provide script languages to facilitate end-users to glue all kinds of functions (including built-in and customized ones) for domain-oriented problem solving. As will be seen, in our study, we will make full use of these kinds of capability devised by the proprietary GIS.
For purpose of discovering temporal and spatial characteristics of TCs along the coastline of China in the Northwest Pacific, following the exploratory data analysis, this paper mainly explores temporal and spatial clusters with advanced spatial techniques of spatiotemporal cluster analysis and density mapping coupled with GIS based on the TCs record data between 1949 and 2014. In the remainder of this paper, we first explore the temporal clusters of the TCs in the Northwest Pacific during 1949–2014 and the spatial clusters of the landfalling TCs along the coast of China to identify the clustering durations in these years and the clustering areas along the coastal prefectures, respectively. Following these explorations, the degree of temporal and spatial stratified heterogeneity is measured and its significance is tested. Then, the exceedance probabilities (EP) and the return periods of the landfalling TCs in the coastal prefectures are rendered. Next, we map the hazards of the TCs in the Northwest Pacific. In the end, the paper summaries the main conclusions, proposes some problems to be solved, and suggests further research aspects.
2. Study Area and Data
2.1. Study Area
The Northwest Pacific is one of the international TC zones with an annually average number of 35 TCs, which amounts to 31% of all the hazardous TCs in the world, two times more than any other zone [27]. Moreover, about 80% of TCs in the Northwest Pacific develop into more severe ones (tropical storm or above). Figure 1 shows the administration map of China at the provincial level and its surrounding areas. For an intuitional recognization of the hazard of TCs, the population and GDP of 2014 are symbolized with graduated colors and graduated symbols, respectively, in Figure 1.
2.2. TC Track Data
The TC track data used in this study are obtained from the China Typhoon Web (http://www.typhoon.gov.cn). These data are published by Shanghai Typhoon Institute (STI) which is entrusted by the China Meteorological Administration (CMA) to compile the Best Track Dataset for Tropical Cyclones over the Northwest Pacific (CMA-STI Best Track Dataset for Tropical Cyclones over the Northwest Pacific) (http://www.typhoon.org.cn). The basin is to the north of the equator and to the west of 180°E, including the South China Sea, and the time span is from 1949 to 2014. In the data set, the data are organized track by track. Each TC track starts with a header and records a sequence of points (the location of the TC head at that time) every 6 hours. Each file in the data set contains the annual data, which is saved as a text format (with a .txt extension). For detailed information, please refer to the data set and its document.
In order to import and analyze the data in ArcGIS (a proprietary GIS software) [28], we wrote a program to parse the original text files into XY Data files (required by the Add XY Data operation of ArcGIS as input), and then these resultant files are imported into ArcGIS and transferred into point features. Finally, the Points To Line tool is executed to obtain the TC tracks of line features.
2.3. TC Landfall Data
As mentioned above, the time interval of the adjacent track points recorded is 6 hours. Thus, it is difficult to determine the accurate landfall locations of the TCs. To obtain the most accurate landfall locations, some materials are collected from various sources (such as statistics yearbooks, news reports, memorandum, and the literature). In these materials, generally the landfall locations of TCs are recorded as addresses (e.g., Putuo, Zhoushan, Zhejiang Province). The geocoding technique is applied to interpret the addresses into coordinates of longitude and latitude. Given the abundant gazetteer possessed by some online maps like the Baidu map, we created a Baidu map API-based program to automatically geocode the landfall addresses of TCs of interest in batch.
3. Methods
3.1. Workflow
The study of temporal and spatial characteristics of tropical cyclones is performed with the following steps:(1)Data collection and preprocessing: The methods and procedure are explained in the above sections.(2)Data analysis: Exploratory analysis, temporal pattern analysis, and spatial pattern analysis are done with some selected methods. A Monte Carlo simulation is employed to support the hypothesis test of the temporal and spatial cluster methods. To visualize the hazard of TCs, the track density is mapped through a track density estimation algorithm (line-based KDE).(3)Result interpretation: From the results of data analysis, the temporal and spatial characteristics of TCs are summarized.
A brief overview of the methodology is shown in Figure 2.
The main data analysis techniques will be explained in Sections 3.2–3.5.
3.2. Temporal Cluster Detection of TC Occurrences
Let be TC occurrences on a time period (e.g., one year) ordered according to occurrence dates. A scan statistic with a variable window (interval) is as follows [11]:where is the scan window width, is the number of TC occurrences contained in the scan window, and is the minimum number of occurrences contained in the clusters to be detected.
This test is the generalized likelihood ratio test for a uniform Null distribution against an alternative of nonrandom clustering which will detect the most likely cluster (interval) whose observed value of the likelihood ratio is maximum. This method allows for clusters of variable width. For more details, please refer to Appendix A.
3.3. Spatial Clustering Analysis of TC Crossing Number
Spatial clusters are those regions (prefectures in this study) whose values are significantly higher than their neighbors. Identifying spatial clusters allows one to map “hot” areas and “cold” areas of TCs. The local Moran’s I statistic is an index for identifying clusters and outliers and computed according to the following formula:where is an attribute of region , is the mean of the corresponding attribute, is the spatial weight between region and , andwith equating to the total number of regions in a study area.
Generally, the distribution of does not meet normality. Though the mean and standard deviation are roughly consistent with those for a standard normal distribution, the kurtosis and the skewness are not [14]. In this study, it is more unlikely that the distribution of the Null hypothesis is normal since we are going to explore the spatial clusters of TCs along the coastal regions that is a zonary area. A Monte Carlo simulation is employed to construct a Null hypothesis (see Section 3.5 for the explanation of the simulation process), and further by a classic hypothesis test procedure, the value for each region is obtained. The values represent the statistical significance of the computed index values. A Moran’s scatterplot can be used to explore the clusters of attributes of regions in a study area in which the X axis denotes the normalized observed attributes and the Y axis is the spatial lags [14].
3.4. Stratified Heterogeneity of TC Crossing Number
Wang et al. [29] define a -statistic to measure stratified heterogeneity. The -statistic distribution is defined aswhere is the number of regions in a study area, is the number of stratum, follows a noncentral -distribution with the 1st df , the 2nd df , and noncentrality , and is the probability of . For more information, please refer to Appendix B.
According to the -statistic, a hypotheses test is carried out by defining the Null hypotheses and alternative hypotheses, respectively. The procedure can be implemented by a software: GeoDetector, which is freely downloadable from http://www.geodetector.org.
3.5. Test Statistical Significance
To assess the significance of a cluster (including temporal and spatial), a Monte Carlo method of inference is used to implement the hypothesis tests. First, the test statistic value is computed according to the observed data. Secondly, the same statistic is calculated with a given quantity of realizations drawn independently from the Null hypothesis (generally a uniform distribution). Next, a distribution can be fitted by some methods (e.g., histogram and kernel density), which provides an estimate of the distribution of the test statistic under the Null hypothesis. The proportion of test statistic observed for the actual data set provides a Monte Carlo estimate of the upper-tail value for a one-sided hypothesis test [30]. Specifically, suppose that denotes the test statistic value for the sample data and denote the test statistic values for the simulated data of realizations. If , then the estimated value iswhere one is added to the denominator since the estimate is based on values . The lower-tail values can be calculated in an analogous manner.
3.6. Track Density Estimation
To visualize the hazard of TCs, an alternative approach is to evaluate the spatial density of the TC tracks. The algorithm for track density can be considered an extension of the widely used 1D kernel density on point data [31] into 2D kernel density on polyline data (tracks). The contribution of each track to the estimated density is calculated separately, which represents the influence of the particular track on its neighborhood in space. Then, those contributions from all tracks are added up to obtain the total density. The contribution of each track (polyline) to the density is defined within a buffer whose centerline is the projection of the track on the plane space. A value is assigned to each point in the buffer according to the distance of the point to the centerline (the perpendicular distance). This value needs to be normalized using the user-specified kernel size, so that the point on the centerline is assigned a maximum value, and the density value decreases with distance from the centerline and reaches a minimum value at the limit of the kernel. Furthermore, in order to be consistent with the probability density function (pdf), the integral of the kernel function along the perpendicular segment must be equal to 1. For the computation detail, please refer to Appendix C.
4. Results and Discussion
4.1. Temporal Analysis of the TC Occurrences
There are a total of 2233 recorded TCs in the Northwest Pacific and 816 landfalling TCs along the continental coastline during 1949–2014. The landfalls are more than 12 in an average year. The landfalls amount to 25 in 1961 with 17 as tropical storms or above. The annual number of the TC occurrences and their landfalls are shown in Figure 3.
Several radar plots (also called sample circular plots or spider plots in some literature) are presented in Figures 4 and 5. Figure 4 shows the monthly pattern of the recorded TC occurrences in the Northwest Pacific during 1949–2014. Figure 5 shows the monthly pattern of the landfalling TCs along the coastline of China during 1949–2014. These two figures show that the number of TCs increased from April to August and decreased from August to October with the peak occurring in August. According to Figure 5, fortunately, STY and SuperTY, the most destructive TCs, occupy a relatively small proportion in all TCs. Nonetheless, the tremendous consequences caused by STY and SuperTY indicate that the need for prevention and response to them cannot be overemphasized.
Next, we try to detect the most likely clusters of the TC occurrences during 1949–2014 in the Northwest Pacific, which is able to be achieved through a scan over the period with a variable window. For each year, the most likely cluster of points (the times of the TC occurrences) along the whole year (from January 1 to December 31) is detected. The cluster detection of points along line is implemented to look for the most likely clusters. The algorithm presented in (1) and Appendix A is coded with Matlab to find the most likely cluster. Meanwhile, the algorithm of the Monte Carlo simulation is coded to test the significance of the most likely cluster. In our analysis, is set to 5, the max length of the clusters is limited to 178 (days), and the simulation times are set to 999. After finishing the computation, the starting position, the number of points, and value are output.
Figure 6 shows the detection result. From the visual examination, these clusters are obviously concentrated in a certain range of time. The mean of the durations of all 66 clusters from 1949 to 2014 is 52.5 (days) and the corresponding standard deviation is 17.0 (days). The average starting point is the 210.5th day. The mean of the centers of these clusters is the 237th day which is consistent with Figure 4.
4.2. Spatial Clusters of Landfalling TCs along the Coastline
The local Moran’s I statistic aforementioned is used to analyze clusters of TCs traveling across those prefectures along the continental coastline of China. The landfall times of TCs for every city are summarized. This operation is accomplished through the Spatial Join tool of ArcGIS, which can join the tracks to the prefectures according to the spatial topological relationship of Interaction (meaning that the TC passes through the prefectures). ArcGIS also has been devised with several spatial cluster analysis tools including the Local Moran’s I and Getis-Ord [15, 32]. The tools produce a map in terms of the calculated results of the statistic itself and value. Here, we define the spatial weight with Rook contiguity [33]. Figure 7(a) shows the clusters of the times of TCs traveling across the continental coastal prefectures of China, and the corresponding values are shown in Figure 7(b). As seen, the clusters are located in two areas (filled with red in Figure 7(a)): the boundary of Guangxi and Guangdong provinces and the boundary of Fujian and Zhejiang provinces. These two areas are the most frequently stroke ones that can be easily confirmed by comparison with the historical TC records. Other prefectures do not have statistically significant clusters according to the analysis results. A Moran’s scatterplot is drawn from the results of local Moran’s I (Figure 8). In a Moran’s scatterplot, a point is drawn in one of the four phases according to its X value and Y value. The first phase of the plot contains the HH (High-High) values of the observed data, that is, the attribute of a region is high and the attributes of its neighboring region are also high, which means these regions are a cluster. Similarly, the second phase contains LH (Low-High) values, the third phase contains LL (Low-Low) values, and the fourth phase contains HL (High-Low) values. Here, our interest obviously is on the first phase in order to learn the spatial clusters of the visiting frequencies of TCs. As expected, the dots for detected clusters are drawn in the first phase and have greater observation values and expected mean neighbor values.
(a)
(b)
4.3. Stratified Heterogeneity of TCs
Two tests of stratified heterogeneity of TCs are carried out. One is for spatial stratified heterogeneity of landfall counts of TCs in the coastal prefectures. In this case, we divide the coastal prefectures into three strata: Low-Low, High-High, and Not Significant according to the analysis results of local Moran’s I. In the other, we test the temporal stratified heterogeneity of the TC occurrences in different seasons, that is, we divide the TC occurrences into four strata: January–March, April–June, July–September, and October–December. We assessed these assumptions by the -statistic to the landfall counts and TC occurrences of the spatial and temporal strata. We also tested the significance of the stratified heterogeneity. The results are shown in Tables 1 and 2. In the spatial case, because F = 24.52 > F0.01 (2, 63, 3.9082) = 10.96 and , we conclude that the spatial stratified heterogeneity is significant. In the temporal case, because F = 54.77 > F0.01 (3, 32, 3.2549) = 8.06 and , the temporal stratified heterogeneity is significant. We can also identify the most likely boundary of strata by -statistic to test various stratifications to reach the one with the maximum value, which should be performed in a future work [29].
4.4. Track Mapping of TCs
The landfall counts of TCs in the coastal prefectures are by year. Assume the landfall counts for a certain prefecture obey Poisson distribution with intensity , that is,
The exceedance probability (EP) can be calculated as follows:
According to the exceedance probability, the return period of TCs in prefecture can be obtained by (8)
The annual intensities for every prefecture are estimated according the landfall counts of TCs from 1949 to 2014.where is the observed landfall times of TCs for prefecture in year .
Figure 9 depicts the exceedance probabilities of the 66 coastal prefectures of China for landfall counts of TCs. According to Figure 9, 12 coastal prefectures (Zhanjiang, Maoming, Fuzhou, Huizhou, Yangjiang, Qinzhou, Ningde, Quanzhou, Jiangmen, Nanning, Zhangzhou, and Hangzhou) have return periods of less than two years. We also observe that: (1) Zhanjiang, Maoming, and Fuzhou rank highest in modeled levels of EP; (2) Huizhou, Yangjiang and Qinzhou are at lesser, but still relative to the remaining prefectures, high EP; and (3) of all 66 selected coastal prefectures, Lincang has no landfalling TCs according to historical records.
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(b)
Furthermore, a track density map is produced to visualize the continuous impact of TCs around the coastline of China (Figure 10). A Gaussian kernel function is selected here. The formation of the kernel function is defined as , where is the center of the kernel, and is window width (a value of is specified). Through simply a visual investigation, we can find out that there are two peaks in the track density map. One peak is over the South China Sea, the other is located to the southeast of China in the Western Pacific. Furthermore, there is a dominant northwest gradient of the density. We inferred that large-scale atmospheric circulation causes this result. Further statistical and mechanism analyses are required to ascertain the underlying fact. The analysis results show that the two island provinces of Hainan and Taiwan are located near the peaks. Guangdong, Guangxi, Fujian, and Zhejiang provinces suffered severely from destructive TCs. In comparison, several northern coastal provinces have significantly less TC landfalls. These results show consistency with existing literature [34–36]. The track density map provides a continuous presentation of TC hazards of “places” across China, which will be helpful for preparedness and mitigation of TCs such as hazard hotspot identification and risk assessment.
5. Conclusions
Spatiotemporal patterns of TCs are one of the greatest interests in prevention and control of the destructive disasters. While the accurate behavior of a certain TC is difficult to determine thanks to our limited cognition for the complex dynamic mechanism [37, 38], data-oriented analysis provides a kind of feasible approach to mining hidden patterns implied in the massive tracks. Time stamps and geographical locations are two types of substantial attributes for TC track data. As stated in the first law of geography, in a spatial context, spatial (spatiotemporal) correlation must be taken into consideration, which is an essential difference between spatial and nonspatial analysis. Since some proprietary GIS software packages are devised with powerful spatiotemporal analysis tools, some traditional methods of identifying TC patterns in time and space are complemented and enhanced when coupled with GIS. Visualization-based approaches provide an intuitive survey for observations and are widely put in practice, while they usually fail to be accepted in some occasions due to their imprecisions and inherent weakness. In order to discover real potential patterns, some robust methods are used in spatial data analysis. When faced with a question like what methods are appropriate for our analysis, the representation of spatial data is also of great concern. As a typical kind of linear features composed of a sequence of points, linear feature specific methods are usually preferred for track analysis of TCs and the like.
The typical periodicity and centralization of TCs encourages us to explore the potential patterns of TCs. Through plotting the circular map on different time scales (month, season), an obvious monthly and seasonal difference is presented. Point cluster analysis along line (temporal interval) is carried out to confirm the exploratory results by a rigorous approach. The cluster analysis demonstrates not only the consistency, but also the detailed analysis of statistical characteristics of these clusters through a Monte Carlo simulation, which is impossible to be perceived by visualization-based analysis methods. The detected temporal clusters are consistent with empirical knowledge. Since the temporal dimension can only describe the marginal features of TCs, several spatial aspects are explored. At this time, our focus is on the landfall locations of TCs. First, a local Moran’s I index is used to detect spatial clusters of TCs. The analytical results are consistent with the intuitive realization of TC clustering along the coastline of China. Additionally, statistical significance is calculated according to the spatial Monte Carlo algorithm. This extended analysis helps refine the visual estimation of clusters and provides a rigorous approach to result assessment. Next, to evaluate the stratified heterogeneity of TCs, both spatial and temporal stratified heterogeneity is carried out according to a -statistic. The tests show that stratified heterogeneity is significant, which means the within-strata variance is less than the between-strata variance. The results imply the locational and seasonal factors are the potential determinants of the heterogeneity of TCs. Sequentially, the exceedance probabilities and the return periods for the coastal prefectures are rendered. Finally, a line-based kernel density estimation is performed on the TC tracks generated in the Northwest Pacific. Coupled with some referable data such as population and GDP, the resultant map is intended to quantitatively evaluate the hazard of TCs and further provide substantial reference for preparedness and mitigation of future TCs along the coastline of China. Furthermore, compared to some findings in existing literature related to the TC mechanisms, these spatial and temporal patterns are consistent with several universally accepted mechanisms that have been deeply studied by some researchers. For example, the TC swarm occurring in space or time is closely related to atmospheric circulation conditions of the tropical Northwest Pacific [39]. The status of the warm pool in the West Pacific largely affects the interannual change of the moving tracks of TCs [40]. Therefore, those comprehensive effects lead to the patterns.
Overall, this paper systematically explored temporal and spatial patterns and mapped the hazards of TCs, through the integrated application of advanced spatial techniques. This work can help obtain insight into temporal and spatial characteristics of TCs compared to previous efforts. These kinds of findings can assist with proactive destructive prevention activities, thereby enhancing the preparedness and mitigation capacity in a predisaster phase. While the present findings offer useful insights into the spatiotemporal patterns of TCs along the coastline of China, further work is clearly required both to reinforce the results and to extend our understanding of the problems. For example, satellite remote sensing techniques enable retrieval of meteorological parameters from remotely sensed data since 1970s, which makes it necessary to compare between data from meteorological stations and satellites. In prevention and response, a continued effort by researchers, the authorities, and the public is imperative in order to enhance prevention ability and reduce the loss of lives and property damage caused by TCs.
Appendixes
A. Cluster Detection of Points along a Line
Let be points independently drawn from the uniform distribution on a line segment (or timeline) ordered according to size. The joint p.d.f. at is and , the probability that no points are contained in a length , is the multiple integral of over in the region: , and , for all . Naus derived , the c.d.f. of , and the size of the smallest interval that contains out of the points. This calculation gave rise to a test statistic for detecting clusters, namely, the scan statistic.
Assume be a random sample of points from the density:
For the hypothesis test problem,where is the scan window width and is the start location of the scan window. Obviously, if , then the sample is drawn from a uniform distribution in [0, 1]. Otherwise, when , the sample has higher density in than in . This is the basic principle of the hypothesis test.
According to the above notation, the scan statistic is formulated as follows:where is the minimum number of points of the clusters to be detected.
B. Test for Stratified Heterogeneity
Assume that a study area is composed of regions and is stratified into stratum; stratum is composed of regions; and and denote the value of region in the population and in stratum , respectively.
The -statistic is defined as follows:where the total sum of squaresand the within sum of squares
The value of the statistic is within [0, 1] (0 if there is no stratified heterogeneity and 1 if the population is fully stratified) and increase monotonously with the increase of stratified heterogeneity.
Letwhere is the between-strata sum of squares, then follows a noncentral -distribution with the 1st df , the 2nd df , and noncentrality as follows:
C. Calculation of Track Density
Let are the tracks and for a certain location , the distances (perpendicular distances) from to these tracks are , then the track density of can be calculated as follows:where is a distance decay function (kernel function). Figure 11 illustrates how to calculate the track density at a certain location (two tracks are shown in Figure 11).
Kernel estimation methods originally are used to estimate a probability density function. With respect to the track data set, a density function defines the probability of observing a track at a location . In this sense, only a function conforming to some certain conditions can be adopted as a kernel [30].
The pseudocode in Table 3 presents a more detailed description of the calculation procedure of the track density. For each cell in a tessellation of the area to be kernelled, first calculate the normalized distances (TrackDensity) to its neighboring tracks, second, add the densities for each separate track up to a summarized density, and finally, the summarized density (SumDensity) is normalized with the number of tracks. Once all cells are processed according to the steps, a raster map of track density will be produced.
In the algorithm, a track is represented as a list of successive points in 2D space, that is, a 2D polyline consisting of points , where , , and are geographic coordinates. Though a track in the real world is always a continuous line, this discretized representation of the track is a kind of widely used data structure in GIS, which enables storage and analysis of real-world objects in computers. We adopt this standard assumption in our study: a series of straight-line segments between sample points are able to represent an original continuous track approximately.
Conflicts of Interest
No potential conflicts of interest were reported by the authors.
Acknowledgments
The authors acknowledge the support from the National Natural Science Foundation of China (Grant nos. 70901047 and 91224004) and Project in the National Science and Technology Pillar Program during the Twelfth Five-Year Plan Period (Grant nos. 2015BAK10B01 and 2015BAK12B03). The authors also appreciate support for this paper from the Collaborative Innovation Center of Public Safety.