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An Objective Track Similarity Index and Its Preliminary Application to Predicting Precipitation of Landfalling Tropical Cyclones

a a,b a,c a,d b FUMIN REN, WENYU QIU, CHENCHEN DING, XIANLING JIANG, LIGUANG WU, e a YINGLONG XU, AND YIHONG DUAN a State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing, China b Key Laboratory of Meteorological Disaster, Ministry of Education, Nanjing University of Information Science and Technology, Nanjing, China c College of Atmospheric Sciences, Chengdu University of Information Technology, Chengdu, China d Hainan Meteorological Observatory, Haikou, China e National Typhoon and Marine Weather Forecast Center, Beijing, China

(Manuscript received 22 January 2018, in ﬁnal form 4 September 2018)

ABSTRACT

Combining dynamical model output and statistical information in historical observations is an innovative approach to predicting severe or extreme weather. In this study, in order to examine a dynamical–statistical method for precipitation forecasting of landfalling tropical cyclones (TC), an objective TC track similarity area index (TSAI) is developed. TSAI represents an area of the enclosed scope surrounded by two TC tracks and two line segments connecting the initiating and ending points of the two tracks. The smaller the TSAI value, the greater the similarity of the two TC tracks, where a value of 0 indicates that the two tracks overlap completely. The TSAI is then preliminarily applied to a precipitation forecast test of landfalling TCs over South China. Given the considerable progress made in TC track forecasting over past few decades, TC track forecast products are also used. Through this test, a track-similarity-based landfalling TC precipitation dynamical–statistical ensemble forecast (LTP_DSEF) model is established, which consists of four steps: adopting the predicted TC track, determining the TC track similarity, checking the seasonal similarity, and making an ensemble prediction. Its application to the precipitation forecasts of landfalling TCs over South China reveals that the LTP_DSEF model is superior to three numerical weather prediction models (i.e., ECMWF, GFS, and T639/China), especially for intense precipitation at large thresholds (i.e., 100 or 250 mm) in both the training (2012–14) and independent (2015–16) samples.

1. Introduction is one of the major challenges facing today’s TC scientific community (Chen et al. 2010; Woo et al. 2014), is still very There has been considerable progress made in the nu- limited—especially in predicting the area coverage, in- merical forecasting of tropical cyclone (TC) tracks during tensity, and finescale distribution of precipitation (Tuleya the past few decades (Fraedrich et al. 2003; Langmack et al. 2007; Marchok et al. 2007; Huang et al. 2009;Wang et al. 2012; Cangialosi and Franklin 2015). This forecast et al. 2012). Therefore, improving the reliability and ac- improvement can be attributed mainly to better numerical curacy of LTC precipitation forecasts remains as one of weather prediction (NWP) model performance, such as our most challenging tasks. the reasonable representation of the large-scale circulation The first solution to the above challenging task is to as well as ensemble forecasting (Fraedrich et al. 2003; improve the NWP models. It is well known that there Zhang and Krishnamurti 1997; Goerss 2000). However, have been considerable advances in model core devel- our ability to predict precipitation associated with land- opment, parameterization of physical processes, and falling tropical cyclones (LTCs) with NWP models, which data assimilation (Chen and Xue 2004; Bauer et al. 2015), which have resulted from a steady accumula- Denotes content that is immediately available upon publica- tion of scientific knowledge and technological advances tion as open access. over many years (Bauer et al. 2015). It is becoming in- creasingly difficult to improve the forecasting skill of Corresponding author: Dr. Fumin Ren, [email protected] NWP models (Wang and Chen 2007).

DOI: 10.1175/WAF-D-18-0007.1 Ó 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses). Unauthenticated | Downloaded 10/03/21 01:41 AM UTC 1726 WEATHER AND FORECASTING VOLUME 33

On the other hand, dynamical–statistical models, which factors. Chen and Ding (1979) summarized three criteria are the combination of a dynamical model and a statistical that TC track similarities should meet: seasonal, geo- relation, have been developed as one important step for- graphical, and TC moving direction and speed similarity. ward in weather prediction. For example, some statistical– Zhong (2002) and Zhong et al. (2007, 2012) defined a dynamical models, for example, SHIPS (DeMaria and nonlinear TC track similarity index based on multiple Kaplan 1994, 1999; DeMaria et al. 2005), Logistic Growth similarities, including landfalling time, the initial posi- Equation Model (LGEM; DeMaria 2009), and extensions tion of a TC, TC central pressure, and environmental for rapid intensification (Kaplan and DeMaria 2003; fields. Wang et al. (2006) proposed a spatial similarity Kaplan et al. 2010, 2015; Rozoff and Kossin 2011; Rozoff index (SSI) based on GIS technology, which is the ratio et al. 2015), have been developed for TC intensity pre- of a polygon area constituted by two TC tracks inside a diction. For the prediction of LTC precipitation, the specific region to an area of interest. Xu et al. (2013) studies adopting dynamical–statistical models can be sor- proposed a track similarity criterion by averaging the ted into three types. First, using historical observations of Euclidean distance at all key points, such as sharp LTC precipitation and applying a climate mean, LTC turning points, between two TCs. Liu et al. (2006) precipitation forecasts can be obtained, based on the NWP studied the algorithm of TC track similarity deviation. forecast of LTC tracks (Marks et al. 2002; Lee et al. 2006; Based on GIS and distance functions, Scheitlin et al. Lonfat et al. 2007). Second, assuming constant rainfall (2010, 2013) developed a polyline averaging technique, rates during the landfalling process, the LTC precipitation which has the potential to identify track similarity. In prediction can be estimated by integrating the rainfall rates operational TC prediction in China, whether or not obtained at the initial time along the NWP forecast LTC TCs pass through a fixed region is also used as a crite- track for the forecast period (Kidder et al. 2005; Liu 2009; rion for identifying TC track similarity. Among the Ebert et al. 2011). A third type of the LTC precipitation above indices, some deal with only the geometric shape forecasts involves applying analog forecast techniques. between two TC tracks, while others take into consid- Based on analog analyses of a target TC within a forecast eration not only the geometric shape between two TC period with historical cases mainly in the large-scale cir- tracks but also other elements such as the seasonal, culation fields, previous studies (e.g., Zhong et al. 2009; Li TC moving direction, and speed similarities, and even and Zhao 2009) have made LTC precipitation forecasts environmental fields. Although the studies above using historical LTC precipitation and an index-based have examined TC track similarity indices, few suitable ensemble scheme of LTC similarity but without in- indices have been developed with comprehensive cluding LTC tracks. One good example is the Climatology- consideration of the realistic processes involved in Based Quantitative Rainfall tool (CLIQR; http://www. TC tracks and with direct application in an operational wpc.ncep.noaa.gov/tropical/rain/web/cliqr.html)thathas setting. been operationally used at the Weather Prediction Center. Thus, the major purpose of this study is to develop a Nevertheless, it still remains uncertain as to how the new index for identifying TC track similarity, which we dynamical–statistical approach could improve LTC pre- call the tropical cyclone track similarity area index cipitation forecasts. Clearly, a key issue is determining (TSAI). TSAI refers to areas enclosed by two TC tracks how to effectively combine the advantages of dynamical with a segment connecting the two initiating points and models with the valuable information from historical another segment connecting the two ending points of the observations. The abovementioned first two types of two TC tracks. As compared to the previous research studies focus on the NWP forecasts of LTC tracks, which into track similarity techniques, an advantage of the is one of the most important factors for TC precipitation, TSAI is its simple physical implication (i.e., an area whereas the third type focuses on analog forecast tech- between two tracks). Section 2 describes the TSAI niques but without using the model-predicted LTC concept and presents the algorithms in terms of geom- tracks. Since today’s model-predicted TC tracks have etries to calculate the areas (TSAI) covered by two TC become more reliable (Fraedrich et al. 2003; Langmack tracks on an (x, y) plane. Section 3 shows an application et al. 2012; Cangialosi and Franklin 2015), it is highly to LTC precipitation forecasting. A summary and con- desirable to incorporate the model-predicted LTC tracks cluding remarks are given in the final section. into any analog forecast technique. To achieve this, the first step is to identify the analog 2. Tropical cyclone track similarity area index TC tracks from historical data for a target TC track. a. Zonal and meridional similarity patterns Then, a suitable TC track similarity index must be found. It is well known that a TC track is an end product TCs move mainly northward in the western North of multiscale interactions with a variety of physical Pacific (WNP) basin. For 2115 TCs during 1949–2012

Unauthenticated | Downloaded 10/03/21 01:41 AM UTC DECEMBER 2018 R E N E T A L . 1727 observed by the Shanghai Typhoon Institute, 2004 TCs (94.7% of the total) travel northward, which means that the latitude of the initiating point of a TC is less than that of its ending point, or both of the two points are located at the same latitude. Only 112 TCs (5.3% of the total) move southward. To determine the similarity patterns, we define a latitudinal extreme point, which is the northernmost point or the southernmost point within a cyclone track. There are two latitudinal extreme points for each track. There FIG. 1. Schematic diagram of the enclosed scope (shaded area) are 1092 TCs (51.6% of the total TCs) with endpoints surrounded by two TC tracks (dotted line) and the two line seg- (either the initiating point or the ending point of a TC ments (thick broken line) connecting the first two points and the track) coincident with latitudinal extreme points. A last two points of the two TC tracks for the (left) meridional and (right) zonal patterns. concept of ‘‘the segmentation ratio of the latitudinal extreme point,’’ which can be used to define how close to the endpoints a latitudinal extreme point is, has been effectively represent their similarity. This area, as a proposed and is discussed in further detail in the ap- similarity index of TC tracks, is named TSAI. pendix, section b(1). If the criteria are not strict, which b. TSAI calculation method means that we are not only considering the endpoints to be the latitudinal extreme points, there are 1667 TCs The detailed calculation method of TSAI is pre- (78.8% of the total TCs) whose latitudinal extreme sented in the appendix, and the calculation of TSAI points are close to the endpoints of the tracks (defined as includes five steps (Fig. 2): preprocessing TC tracks, where the segmentation ratio of the latitudinal extreme identification of a track pattern, track idealization, and point is less than 0.2). Then, these TCs can be taken as calculation and determination of the similarity index. north–south-moving cases, which belong to a meridional Taking Typhoons Nina (197506) and Talim (200513), pattern (Fig. 1, left). Meanwhile, the remaining TCs here we show how to calculate the TSAI of the two (22.2% of the total), which have no latitudinal extreme typhoons. The two observed TC tracks are shown in points close to the endpoints, are considered as cases of Fig. 3a. east–west movement, which belong to a zonal pattern The first step is preprocessing TC tracks, including (Fig. 1, right). Only when the general directions1 of the determining the tracks within a designated region and two tracks are the same, is it meaningful to discuss track the simplification of complex tracks. The designated similarity. That is, for a zonal pattern, the general di- region is indicated by the blue rectangle in Fig. 3b. The rections of the two tracks should both be eastward or two tracks within the region can be determined as a westward, while for a meridional pattern, the general result of the first substep (Fig. 3b). Since the two track directions of the two tracks should both be northward or segments are simple, the second substep (‘‘simplification southward. of complex tracks’’) makes no change to the two tracks Generally, we focus on the TC track similarity shown in Fig. 3b. In the second step (‘‘identification of within a specific region or designated region. In this case, track pattern’’), segmentation ratios r of the latitudinal the above considerations can still apply to the segments extreme points of the two tracks are first calculated. For of the TC track. For any two TC tracks, or track seg- the two tracks, r 5 0, which means that neither of the two ments (dotted lines in Fig. 1), if the two initiating and the tracks have any latitudinal extreme points close to the two ending points are connected by two lines (thick endpoints. Then, the conditions for zonal pattern simi- dashed lines in Fig. 1), the two TC tracks or track seg- larity are not met while those for meridional pattern ments constitute a closed region of which the area S can similarity are met. Therefore, in the third step (‘‘track be calculated. The smaller S is, the more similarity there idealization’’), the meridional pattern track idealization is between the two TC tracks, with S 5 0 meaning that is carried out. Due to the characteristics of the two tracks the two tracks or track segments perfectly match each in the designated region, the idealized tracks are the other. Therefore, for any two TC tracks, or track seg- same as those in Fig. 3b without any modification. In the ments, the area of the enclosed scope surrounded by fourth step (‘‘calculation of the similarity index’’), fol- the two TC tracks and the two line segments, which lowing the process of this step, the meridional pattern 2 connect the two initiating and the two ending points, can TSAI Slon is calculated and Slon 5 40 825.9 km .Then, according to the flowchart, the fifth step (‘‘determination 1 See ‘‘General direction’’ in the appendix, section b(1). of TSAI’’) is taken directly. As n 5 0, which means that

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FIG. 2. Calculation ﬂowchart of TSAI, where Slat and Slon are the zonal and meridional pattern track similarity indices, respectively; n is the number of TC tracks whose latitudinal extreme points are not close to the endpoints; and L is the number of slices of the scope.

the two tracks do not have any latitudinal extreme points inﬂuence of the three parameters on the similarity re- that are close to the endpoints, TSAI 5 Slon. sults is discussed. We investigate the sensitivity of these parameters in c. Sensitivity of TSAI to external parameters TSAI sample calculations using the Shanghai Typhoon The calculation of TSAI involves both the simplifying Institute TC best track dataset. tracks and the selections of the three external parame- 1) SIMILARITY REGION ters: the designated region, the threshold r0 of the segmentation ratio of a latitudinal extreme point, and the The method can be applied to both full track similarity threshold c0 of the overlap percentage of two TC tracks and designated region similarity. Full track similarity in the general direction (north–south or east–west). means that the similarity region can be large enough for Considering the simplifying tracks can be carried the two TC tracks of concern, while designated region out automatically when necessary and in most cases it similarity means the similarity region is focused on a does not need to be done, in this section, only the designated area.

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FIG. 3. Examples of results of the two substeps in preprocessing TC tracks for Typhoon Nina (197506) and Typhoon Talim (200513), which are shown in Fig. 4: (a) the two original TC tracks and (b) the designated region, which is indicated by the blue rectangle and the two tracks within it. Meanwhile, (b) also indicates the result of the second substep (simpliﬁcation of complex tracks), which makes no change to that of the ﬁrst substep (determining the tracks within a designated region).

Typhoon Nina (1975) caused serious damage in ratioof0.25leadstothetwosouthwestward-turning tracks Zhumadian in Henan Province after making two land- after landfall (Fig. 5b), whereas a segmentation ratio of 0.2 falls across Taiwan Island and along the coast of Fujian does not (Fig. 5a). Further analysis shows that the seg- Province before moving inland. Figure 4 shows Typhoon mentation ratio of the latitudinal extreme point of Bilis is Nina and the five most similar TCs according to TSAI 0.23, and the segmentation ratios of the latitude extreme within the different similarity regions. Figure 4a pres- points of the two TCs just mentioned before are both less ents the results of full track similarity. All five analog than 0.20. The value of r0 can therefore affect the similarity TCs move in a similar direction (southeast–northwest) results to a certain extent. The reason is that, in step 4 to that of Typhoon Nina, although for full track simi- (determination of TSAI) for the TSAI between Bilis and larity one of the five TCs makes no landfall on Taiwan any of the two TCs, when r0 5 0.25, TSAI 5 Slon,andwhen Island and another makes no landfall at Fujian. r0 5 0.20, TSAI 5 max(Slat, Slon), and this influences the Figure 4b shows the results of similarity before landfall, results directly. with the similarity being assessed by focusing on the blue 3) THRESHOLD c OF THE OVERLAP PERCENTAGE box. All five analog TCs make a first landfall in Taiwan 0 OF THE TWO TC TRACKS and move across north-central Taiwan and then make a second landfall along the central to southern Fujian The overlap percentage of two TC tracks c has the Province, before the tracks diverge. range [0, 1.0]. Based on experience, the suggested

Figure 4c displays the results of similarity after landfall. threshold c0 is between 0.4 and 0.8. All five TCs move across south-central Fujian Province Figure 6 presents the tracks of Supertyphoon Haitang and enter Jiangxi Province, while the tracks diverge be- (2005) and the five most similar TCs based on TSAI with fore the TCs make landfall at Fujian Province. different thresholds c0 for TC tracks over the blue des- Therefore, according to the different similarity regions, ignated region for landfall similarity. When c0 is 0.4 the TSAI can provide different but reasonable TCs. (Fig. 6a), the lengths of the five TC tracks are different in the designated region, where the initiating point of a TC 2) THRESHOLD r0 OF THE SEGMENTATION RATIO track is within the region. When c0 is 0.8 (Fig. 6b), all five OF A LATITUDINAL EXTREME POINT TC tracks move across the designated region and show a The threshold of the segmentation ratio of a latitudinal higher degree of similarity. extreme point can affect whether or not a latitudinal extreme point of a track is close to the endpoints. Therefore, 3. Preliminary application in LTC precipitation this will affect the determination of TSAI. forecasting Figure 5 shows the strong Tropical Storm Bilis (2006) and the five most similar TCs according to TSAI, with In this section we describe an application of TSAI for different thresholds r0 of the segmentation ratio of a lat- the forecasting of accumulated precipitation associated itudinal extreme point under full track similarity. Figures 5a with LTCs. This development has taken place over and 5b show the results with r0 5 0.2 and 0.25, respectively, one year of research, resulting in a technique called and the two results are clearly different. A segmentation the track-similarity-based landfall tropical cyclone

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FIG. 4. Typhoon Nina (1975) and the five most similar TCs according to TSAI within different similarity regions. The green line is the track of Typhoon Nina, the red lines indicate the five TCs, and the blue box is the designated region. (a) Full track similarity, (b) similarity before landfall, and (c) similarity after landfall. precipitation dynamical–statistical ensemble forecast Administration (T639), with horizontal resolutions of model (LTP_DSEF). Here, we present the main idea 0.25830.258,18318, and 1.125831.1258, respectively] is of the LTP_DSEF technique and the key results of selected as the analysis period, with 2012–14 designated experimental prediction. for the training sample and 2015–16 for the independent In the test, we focus on South China (Fig. 7) and TCs sample. There are a total of 27 TCs: 17 in 2012–14 and 10 that produced more than 100 mm of daily precipitation at in 2015–16. The TC dataset, which is for identifying at least one station in the region. For verification of the analog TCs, is the best track data from the CMA Tropi- precipitation forecast for the LTP_DSEF model, we cal Cyclone Database (http://tcdata.typhoon.org.cn/en/ adopted a regional NWP model approach, as these zjljsjj_sm.html) over the period 1958;2016. The train- models have relatively high resolution and perform better ing sample differs from the independent sample in that a when predicting precipitation. However, as no suitable TC of the former can have analog TCs that occur after the regional NWP model’s results are available, three global TC under investigation while a TC of the latter cannot. NWP models are adopted for this work. The period To perform the verification, the precipitation forecasts 2012–16 [during which data are available for three created by the three NWP models are interpolated di- dynamical models: the European Centre for Medium- rectly with the algorithm of inverse–distance-weighted Range Weather Forecasts (ECMWF) model, the Global interpolation onto the 191 stations across South China Forecast System (GFS) run by the National Weather (Fig. 7). Service (NWS), and the global spectral model in To identify TC precipitation, the objective synoptic National Meteorological Center/China Meteorological analysis technique (OSAT; Ren et al. 2001, 2007, 2011),

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FIG. 5. Strong Tropical Storm Bilis (2006) and the five most similar TCs according to TSAI with different thresholds r0 of the segmentation ratio of a latitudinal extreme point under full track similarity for (a) r0 5 0:2and(b)r0 5 0:25. which uses the distance from the TC center and the The LTP_DSEF technique includes four steps: closeness and continuity between neighboring raining 1) Predict the TC track. It is suggested that the TC stations to identify TC-influenced rain belts that may track prediction of an NWP model be absorbed directly. extend from 500 to 1100 km away from a TC center, Based on data availability, the TC track prediction used and the daily precipitation data during 1958;2016 of here is the forecast of the National Meteorological the 191 stations are applied. To assess the forecast effect, it is important to choose a suitable skill mea- Center/China Meteorological Administration, which in sure. Considering that the threat score (TS) is the turn is based on the TC track prediction of the NWP primary operational-forecast verification metric in models. For a predicted track at an initial time, the lead China, TS is selected as the skill measure in this study. time of the track prediction ranges from 12 to 120 h, TS values range between 0 and 1, with 1 indicating depending on the initial time and the status of the TC. a perfect score, and its formula is as follows: TS 5 2) Identify TC track similarity. There are two substeps. hits/(hits 1 misses 1 false alarms) (http://www.cawcr.gov.au/ The first is to construct a complete TC track, which projects/verification/). TS is used for different thresh- consists of the observed and the predicted tracks. The olds (such as 0.1, 10, 25, 50, 100, and 250 mm) of LTC second is to apply TSAI to identify TC track similar- accumulated precipitation over the station network ity within a similarity region, which is a rectangular in Fig. 7. area covering the domain where the predicted track

FIG. 6. The tracks of Supertyphoon Haitang (2005) and the ﬁve most similar TCs according to TSAI with different thresholds c0 of overlap percentages of the two TC tracks under landfall similarity for (a) c0 5 0.4 and (b) c0 5 0.8.

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values of 0.1, 10, 25, 50, 100, and 250 mm) is calculated according to the LTC accumulated precipitation over the station network in Fig. 7. Figure 8 shows the training sample–independent sample TC (r $ 100 mm) cross- section distribution for the 15 552 different schemes in the TC precipitation prediction of the LTP_DSEF model. All the schemes can be sorted into two groups: one is the ensemble mean (gray points), while the other is the maximum value ensemble scheme (orange points), with the average of the orange points (0.170, 0.192) being much better than that of the gray points (0.097, 0.081). This means that the maximum value ensemble is much better than the ensemble mean for intense pre- FIG. 7. Distribution of the 191 stations over South China. cipitation forecasts. From an ensemble scheme per- spective, the maximum value ensemble shares some extends. Then, according to TSAI, a number N of the similarities with the probability matching procedure most similar TC tracks can be identified. outlined by Ebert (2001), which was shown to improve 3) Consider seasonal similarity. Three time periods are precipitation forecast skill in his study. In Fig. 8, the selected (July–September, May–November, and the three open circles represent the three dynamical models whole year) for seasonal similarity. This means that, (ECMWF, GFS, and T639), and the two dotted lines using the results derived by identifying the TC track indicate the highest values of the training sample TSt similarity, the first n (n , N) most similar TCs can be 100 (0.168) and the independent sample TSi (0.238), both determined after considering seasonal similarity. 100 of which are from GFS. A total of 259 schemes are better 4) Develop ensemble predictions of the accumulated than the dynamical models and are located in the first precipitation using ensembles of TCs with the most quadrant of the two dotted lines. similar tracks. Two methodologies are used in the To identify the schemes within the total 259 that have development: the ensemble mean rainfall or selec- better-than-NWP-model performance in the accumu- tion of the maximum rainfall value for each station. lated precipitation $ 250 mm, we prepared Fig. 9. The In this test, there are seven parameters in the two dotted lines represent the highest values of the

LTP_DSEF model (Table 1): initial time (P1), sim- training sample TSt250 (0.043) and the independent ilarity region (P2), threshold of the segmentation ra- sample TSi250 (0.0) for the three dynamical models tio of a latitudinal extreme point (P3), threshold of (ECMWF, GFS, and T639), which are also both from the overlap percentage of the two TC tracks (P4), GFS. There are a total of 202 schemes that are better seasonal similarity (P5), number of the most similar than the dynamical models and are located in the first TCs (P6),andanensemblescheme(P7). Considering quadrant of the two dotted lines (Fig. 9). This means these numerous parameters with different values or that the 202 schemes show better-than-NWP-model settings, which are listed in Table 1, ideally there are a performance in the accumulated precipitation of $100 total of 103 680 (5 4 3 15 3 3 3 6 3 3 3 16 3 2) different and $250 mm in the TC precipitation prediction of the schemes. However, because some of the 27 TCs produce LTP_DSEF model. rainfall soon after genesis and those TCs can influence To identify the best choice among the 202 schemes the number of values for parameters P1 and P2, this will and considering precipitation of $100 mm while already result in a decrease in the total number of schemes for including that of $250 mm, we find that TSt100 and the test. To avoid a small total number of schemes oc- TSi100 are suitable for doing this. Figure 10 presents the curring, the 27 TCs have been divided into short-track training sample–independent sample TS (represented

TCs (6) and long-track TCs (21), as in Table 2, where a by TSt100 and TSi100, respectively) cross-section distri- short-track TC is deﬁned as a TC with the number of bution for the 202 schemes. The scheme marked with the values for parameter P1 being 1, and only the 21 long- open circle, which has the largest value of TSt100 1 track TCs (15 for the training sample and 6 for TSi100, is selected as the best scheme. In this scheme, the the independent sample) are used for the test. There- seasonal similarity is the whole year, the number of the fore, the ﬁnal total number of schemes is 15 552. most similar TCs is nine, the ensemble prediction To obtain suitable schemes for both the training and scheme is the maximum, the initial time is the latest one, the independent samples, the TS for the precipitation and the other three parameters are those of TSAI above the different thresholds (r $ R0, where R0 has six (Table 3).

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TABLE 1. Parameters and the total number of schemes in the LTP_DSEF model.

Parameter Method of obtaining a value No. of values Initial time 1200 and 0000 UTC within two days before the ﬁrst day with TC 2 3 2 5 4 precipitation appearing on land Similarity region A parameter of TSAI: TC locations at the initial time (point A) and the 3 3 5 5 15 maximum lead time (point B) are the ﬁrst diagonal points; point A can be the TC locations at 12 or 24 h before the initial time, while point B can be the TC locations at 12, 24, 36, or 48 h before the maximum lead time Threshold r0 of the segmentation A parameter of TSAI; its value can be 0.1, 0.2, or 0.3 3 ratio of a latitude extreme point Threshold c0 of the overlap A parameter of TSAI; its value can be 0.9, 0.8, 0.7, 0.6, 0.5, or 0.4 6 percentage of two TC tracks Seasonal similarity Its value can be the whole year, May;November, or July;September 3 No. of the most similar TCs Its value can be 1;16 16 Ensemble prediction scheme Its value can be the ‘‘mean’’ or ‘‘maximum’’ 2 Total No. of schemes 4 3 15 3 3 3 6 3 3 3 16 3 2 103 680

Figure 11 presents a comparison of the training and in- four TCs, TEST2 using the 14th–17th TCs, TEST3 using dependent sample TSs for precipitation above different the 10th–13th TCs, TEST4 using the 6th–9th TCs, and thresholds for the best scheme of LTP_DSEF and the three TEST5 using the 2nd–5th TCs for training. The best dynamical models. Although the LTP_DSEF model does schemes of the above five tests, noting that is unnecessary not show any advantages over the three dynamical models that they be the same, can be easily identified. Results of at small precipitation thresholds (0.1–25 mm), it shows the best schemes of the five new tests have been compared better prediction ability than the three dynamical models at with these of the three dynamical models (ECMWF, GFS, large precipitation thresholds (100–250 mm) in the training and T639) (figure omitted). Generally, the LTP_DSEF and the independent samples. For example, for $100 mm model shows better performance than do the dynamical precipitation, the TS values for the three dynamical models models, with the results of the training sample being more range between 0.115 and 0.168 (between 0.171 and 0.238) in stable than those of the independent sample, which may the training (independent) sample, while that of the best probably be attributed mainly to the large difference be- scheme of the LTP_DSEF model is 0.198 (0.266). As for tween the sample size (17) in the training sample and in the the reasons for the above results, in addition to the potential independent sample (4). ability of the LTP_DSEF technique for predicting heavy precipitation, part of the reason may be that the dynamical 4. Summary and discussion models limit their abilities to predict heavy precipitation because of low resolution. Based on the above analysis and discussion, we offer To inspect the stability of the above results, a new set of the following conclusions. tests, which randomly choose a set of the TCs for training 1) A new tropical cyclone track similarity index (i.e., and the remainder for testing, have been performed. Based the TSAI) has been developed. For any two TC on the 21 TCs and selecting four consecutive TCs for tracks, TSAI has a simple meaning, which is the area training, there are five new tests, with TEST1 using the last of the enclosed scope surrounded by the two TC tracks and the two line segments connecting the first TABLE 2. List, by year, of the TCs in the training sample and the independent sample. and the last two points of the two TC tracks. The smaller the value of TSAI, the greater the similarity Sample TCs for the two tracks. The detailed calculation pro- Training sample (15 TCs) 2012: Talim, Doksuri, Kai-Tak, cess of TSAI has also been presented, including and Sontinh five steps: preprocessing TC tracks, identification 2013: Bebinca, Soulik, Rumbia, of the track pattern, track idealization, calculation Jebi, Utor, Trami, Usagi, and Haiyan of the similarity index, and determination of TSAI. 2014: Rammasun, Matmo, and In addition, there are three adjustable parameters: Kalmaegi the similarity region, the threshold of the segmenta- Independent sample (6 TCs) 2015: Noul, Linfa, and Mujigae tion ratio of a latitudinal extreme point, and the 2016: Nida, Sarika, and Haima threshold of the overlap percentage of two TC tracks.

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FIG. 8. Training sample–independent sample TS (represented by

TSt100 and TSi100, respectively, where t, i, and 100 represent the training sample, independent sample, and accumulated precipitation $ 100 mm, respectively) cross-section distribution for the 15 552 schemes in the TC precipitation prediction of the LTP_DSEF model. Gray FIG. 9. Training sample–independent sample TS (represented by and orange points indicate the ensemble scheme ‘‘mean’’ and TSt250 and TSi250, respectively, where ‘‘250’’ means accumulated $ ‘‘maximum,’’ respectively. The three open circles represent the precipitation 250 mm) cross-section distribution for the 259 three dynamical models (ECMWF, GFS, and T639), and the two schemes that have better-than-NWP-model performance in the accumulated precipitation $ 100 mm in the TC precipitation pre- dotted lines represent the highest values of TSt100 (0.168) and diction of the LTP_DSEF model. The three open circles represent TSi100 (0.238) for the three dynamical models (both are from GFS). the three dynamical models (ECMWF, GFS, and T639), and the two

dotted lines indicate the highest values of TSt250 (0.043) and TSi250 (0.0) for the three dynamical models (both are from GFS). Using examples of sensitivity tests for the external parameters, we demonstrate that TSAI has good In practice, and in most cases, simplification is not nec- capability in characterizing TC track similarity. essary, especially for application within a designated re- 2) During the preliminary application of TSAI to de- gion, such as the landfall areas in the examples in Figs. 4 velop dynamical–statistical analog methods for pre- and 6. However, occasionally, for a singular TC track with dicting LTC precipitation, a new technique—the twisting or even spiral parts, TSAIs between this track and LTP_DSEF model—was developed. The LTP_DSEF other TC tracks may be limited due to track simplification, model includes four steps: predict the TC track, such that manual verification is required. Third, in rare identify TC track similarity, consider the seasonal cases, TSAI cannot be calculated when the general di- similarity, and develop an ensemble prediction of the rections of the two tracks are opposite, which means that LTC accumulated precipitation. There are seven pa- there is no similarity between the two TC tracks. For ex- rameters in the LTP_DSEF model. ample, for the zonal similarity pattern, there exists no 3) The forecasting test for the LTP_DSEF model for South similarity between a TC with a general westward direction China during 2012–16, with 2012–14 used as the training and another TC whose general direction of motion is from sample and 2015–16 as the independent sample, reveals west to east. Fourth, TSAI only represents track pattern that, for the LTC accumulated precipitation forecast, similarity. For application in analog rainfall prediction, the LTP_DSEF model is superior to three NWP models additional factors will need to be considered, including (ECMWF, GFS, and T639), especially at large pre- factors of the TC itself, such as landfall seasonal similarity, cipitation thresholds (100 or 250 mm) in the training TC intensity, TC forward speed, and TC structure, as well and independent samples. For example, for $100-mm as environmental factors such as monsoon similarity, precipitation, the TS value for the best scheme of the subtropical high similarity, low-level jet similarity, and LTP_DSEF model is 0.198 (0.266), which is better than vertical wind shear similarity. Further analysis is needed to those of the three dynamical models, at 0.115–0.168 incorporate these effects (Velden and Leslie 1991). (0.171–0.238) in the training (independent) sample. Compared with existing track similarity indices, such as Some issues concerning the calculation of TSAI must Wang et al. (2006), Xu et al. (2013), Liu et al. (2006), be mentioned. First, a similarity region needs to be Zhong (2002),andZhong et al. (2007),TSAIhasthree specified. Generally, there are three types of the similarity distinctive features: (i) it has a clear meaning in that it regions: full track similarity, similarity before landfall, and represents the area of the enclosed scope surrounded by similarity after landfall. Second, application of the TSAI the two TC tracks, (ii) it is objective with a more detailed method does require simplification of the TC tracks. introduction, and (iii) it is easily applied in studies, as well

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FIG. 10. Training sample–independent sample TS (represented by TSt100 and TSi100, respectively) cross-section distribution for the 202 schemes that have better-than-NWP-model performance in the accumulated precipitation of $100 mm and $250 mm in the TC precipitation prediction of the LTP_DSEF model. The scheme marked with the open circle, which has the highest value of

TSt100 1 TSi100, is selected as the best one. as in weather and climate operations. It should be noted that the concept of the area between two TC tracks, which is the core meaning of TSAI, is actually included in the SSI index (Wang et al. 2006). However, since the concept is FIG. 11. Comparison of the TSs at different rainfall levels for the not independently proposed and the calculating technol- best scheme of the LTP_DSEF model (BEST) and the three dy- ogy is GIS, there are limits to the application of SSI. namical models (ECMWF, GFS, and T639). Shown are (top) the For the application of TSAI, the first thing to be thought training sample and (bottom) the independent sample. of is possibly the track forecast. However, as considerable progress has been made by numerical models in However, more complete validation of the performance of track forecasts (Leslie and Fraedrich 1990; Zhang and the LTP_DSEF model is needed, and more factors that Krishnamurti 1997; Goerss 2000; Fraedrich et al. 2003; influence TC precipitation, such as TC characteristics (e.g., Langmack et al. 2012; Cangialosi and Franklin 2015), it is TC intensity and translation speed) and environmental unnecessary to apply TSAI when forecasting TC tracks. characteristics (e.g., intensity of the summer monsoon, Considering the successful preliminary application of status of the WNP subtropical high), should be taken into TSAI, as reported upon in section 3, TC precipitation consideration in the LTP_DSEF model in the future. forecasting is an important field where TSAI can be used. We believe that further studies on the TSAI and its application in dynamical–statistical analog prediction for LTC precipitation will deliver upon its great potential in both research and operational applications. TABLE 3. Values of the parameters for the best scheme of the LTP_DSEF model in the forecast test for South China. Acknowledgments. The authors would like to express Parameter Value their sincere thanks to the two anonymous reviewers; the Initial time First editor, Prof. Dalin Zhang; and Dr. John L. McBride for Similarity region Seventh their helpful suggestions and comments to improve the Threshold r0 of the segmentation ratio of Third manuscript, as well as the Shanghai Typhoon Institute a latitude extreme point and National Meteorological Information Center/China Threshold c0 of the overlap percentage of Third two TC tracks Meteorological Administration for sharing the tropical Seasonal similarity First cyclone best-track dataset and daily precipitation data, No. of the most similar TCs Ninth respectively. This work was supported by the National Ensemble prediction scheme Second Natural Science Foundation of China (Grants 41675042

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APPENDIX

TSAI Calculation Method The detailed calculation processes for these steps are outlined in this appendix. a. Preprocessing TC tracks (Fig. 2, top box) In general, we are interested in the TC track similarity within a designated region, and occasionally a TC track may be so singular that it has twisting or even spiral parts. To facilitate the calculation of TSAI, it is necessary to preprocess the original TC tracks. The preprocessing of TC tracks includes two steps: (i) determining the tracks within a designated region and (ii) simpliﬁcation of the complex tracks (Fig. 2).

1) DETERMINING THE TRACKS WITHIN A A1 DESIGNATED REGION FIG. A1. Schematic diagram for determining the track within a designated region. (a) The original TC track and the designated As shown in Fig. A1a, when a designated region region, ABCD. Solid dots are points of intersection of the TC (ABCD) is defined, the track within the region is de- track and the border of the region. (b) The new TC track within the designated region. termined through the following steps. First, identify all the TC points within the designated region (open circles in Fig. A1a). Second, calculate all the points in Fig. A2). Then, exclude all the bizarre points (or points of intersection (filled circles in Fig. A1a)ofthe outliers). Third, to reduce the bending degree of the track, track and the border in the designated region. Third, exclude the short line segment that is divided by the outliers, exclude all the points (open circles with crosses in has less than three points, and does not contain the first or the Fig. A1a) that are outside the designated region. Finally, ending point of the original track (such as CD). Finally, connect the open and filled circles in the original time connect the remaining line segments again in the original order to produce a new track within the designated area time order to produce a simplified track. For example, after (Fig. A1b). the simplification, points A and B become two adjacent 2) SIMPLIFICATION OF COMPLEX TRACKS points in time. Figure A2 is a schematic diagram of the simplification b. Identification of the track pattern of a complex track. For a given TC track that is within the The TC track pattern includes individual TC track shapes designated area and composed of many observation loca- and the relationship between the two TC track shapes. tions (points), the simplification of the track can be com- pleted with the following four steps. First, determine the 1) CONCEPTS bizarre points. Suppose the track has m points in total. For To identify the track pattern, three concepts, or pa- 5 ... point j (j 1, , m) of the track, calculate the distances rameters, are defined. between point j and its two adjacent points (j 2 1and A2 General direction: If the difference between the j 1 1), and select the longer one, dj. If there is another point (k) that makes the distance between itself and point latitude (longitude) of the ending point and that of the initiating point is greater than or equal to j less than or equal to dj, point j is called a bizarre point (filled zero, the general direction of the track is defined as northward (eastward) in the north–south (east– A1 When working with the TC track similarity for the whole west) direction. When the difference is less than lifetime of the TC, this step can be omitted. A2 For the first and ending points of a TC track, the number of zero, the general direction of the track is defined as adjacent points is one. The number of adjacent points is two for the southward (westward) in the north–south (east– other points. west) direction.

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FIG. A2. Schematic diagram of the simplification of a complex track. Solid dots indicate bizarre points, and the dashed line (AB) is a part of the simplified track. (a) The original TC track. (b) The simplified TC track.

Segmentation ratio of a latitudinal extreme point: The value range of c is [0, 1.0], where 0 means that the For a TC track AB with A and B being the two two tracks do not overlap, and 1 indicates that the two endpoints, assume that a latitudinal extreme pointA3 TC tracks overlap completely. (C) divides the track into two parts: AC and BC.

Assume LAB is the length of track AB, and LC is the 2) ZONAL PATTERN SIMILARITY CRITERION length of the shorter of the segments AC and BC. Then, In the identification of track pattern box in Fig. 2, the first the segmentation ratio of a latitudinal extreme point is question addressed is that of zonal pattern similarity. defined as When the two tracks satisfy the following three con- 5 ditions, we move to the middle-left box for zonal pattern r LC/LAB . (A1) track idealization. Otherwise, we move to the middle- By this definition, the value range of r is [0, 0.5], where right box (in Fig. 2) to consider whether there is me- 0 means that the latitudinal extreme point is an ridional pattern similarity. endpoint, and 0.5 means that the latitudinal extreme The three zonal pattern similarity conditions are point is located in the middle of the track. (i) at least one TC track has a latitudinal extreme For a certain threshold r0, if a TC track does not have point that is not close to the endpoints, any latitudinal extreme points with r $ r0, it means that all (ii) the general directions of the two tracks are the the latitudinal extreme points of the track are close to same in the east–west direction, and endpoints. Generally, r0 does not have a typical value, (iii) for a given threshold c0, the overlap percentage c $ c0. and a suitable value of r0 can be gained through a sensi- Generally, c0 does not have a typical value, and a suitable tivity or operational test.

Overlap percentage: For any two TC tracks, assume L0 is the length of the longer track (the track with open circles in Fig. A3). Based on the general direction of this track (in the north–south or east–west directions), assume that the track length of the segment

AB (Fig. A3) that this track overlaps with is Loverlap. Then, the overlap percentage of the two TC tracks in this direction is deﬁned as

5 c Loverlap/L0 . (A2)

A3 ‘‘Latitude extreme point’’ refers to the maximum or minimum of a TC track latitude. FIG. A3. Schematic diagram for calculating the overlap percentage.

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FIG. A4. Schematic diagram of the meridional pattern track idealization. (a) The track after preprocessing of the TC track. (b) The track after the uniﬁcation of the track direction. (c) The new track after the second simpliﬁcation of the track, with the solid thin gray line AB replacing the original dashed one as part of the track.

FIG. A5. Schematic diagram of the zonal pattern track idealization. (a) Cutting lines along the longitude at the latitude ex- value of c canbegainedthroughasensitivityor 0 treme points and the endpoints. (b) Several triangles (D)and operational test. quadrangles (▱) together approximate the enclosed scope for the calculation of TSAI. (c) A quadrangle is divided into two 3) MERIDIONAL PATTERN SIMILARITY CRITERION triangles, and (d) a triangle can be taken as a scope surrounded by two idealized tracks. When the two tracks satisfy both of the following two conditions, they are considered to have meridional pattern similarity: 1) MERIDIONAL PATTERN TRACK IDEALIZATION (i) the general directions of the two tracks are the same Figure A4 shows a schematic diagram of meridional in the north–south direction and pattern similarity idealization. There are two steps: (ii) for a given threshold c (c is generally around 0.5), 0 0 (i) Unification of track direction: Adjust all the points of the overlap percentage c $ c . 0 the track according to latitude in ascending (northward When these conditions are met, we move to the middle- movement) or descending (southward movement) left box in Fig. 2 for meridional pattern track idealization. order, so that the moving direction between any two If they are not met, then the tracks have neither zonal nor points is consistent with the general direction of the meridional similarity, and we move to the bottom-left track (Fig. A4b). corner in Fig. 2: these two tracks are ‘‘not similar.’’ (ii) The second simplification of complex tracks: After the unification of the track direction, the track (Fig. A4b) c. Track idealization may be severely distorted. Therefore, to facilitate the To facilitate the calculation of TSAI, approximation calculation of TSAI, it is necessary to repeat the step in or simplification of the TC tracks (i.e., track idealiza- section a(2) of this appendix, which is called the second tion) is needed. Track idealization can be divided into simplification of complex tracks. The new track after a two types: meridional and zonal pattern. second simplification is presented in Fig. A4c.

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2) ZONAL PATTERN TRACK IDEALIZATION Figure A5 shows the schematic diagram of zonal pattern track idealization. There are four steps in this process: (i) Cut lines along the longitude at the latitudinal extreme points and the endpoints. At each latitudinal extreme point and endpoint, draw a cutting line along the longitude and calculate the points of intersection of the cutting line and the two tracks. At most, there are eight cutting lines, which are shown in Fig. A5a. (ii) Several triangles (D) and quadrangles (▱)together approximate the enclosed scope for the calculation of TSAI. In Fig. A5b, connect the adjacent points of intersection of the same track with line segments. In rare cases, some intersections (represented by the small black boxes) may exist between two line segments. Then, several triangles and quadrangles, which are surrounded by the cutting lines and the line segments, form and they can together approximate the enclosed scope for the calculation of TSAI. (iii) A quadrangle can be divided into two triangles. For a quadrangle (Fig. A5c), its diagonal (fine dotted line segment in Fig. A5c) can divide it into two triangles. (iv) A triangle can be taken as a scope surrounded by FIG. A6. Schematic diagram of using dashed lines to slice the scope two idealized tracks. For any triangle (Fig. A5d, surrounded by two idealized tracks (solid lines with points) and the two left), when the latitude maximum and minimum line segments (thick dashed line) connecting both of the initiating points and both of the ending points of the two tracks. The two dif- points of the triangle are determined, the tri- ferent types of points (a green star and a red ex) indicate the in- angle can be taken as a scope surrounded by two tersections of the cutting lines (thin dashed lines) and the two tracks. idealized tracks of meridional pattern similarity (Fig. A5d,right). 1) SLICING THE SCOPE After the above four steps, the zonal pattern TSAI is For the two idealized tracks, Fig. A6 shows a schematic transformed into a sum of areas of all the triangles, and diagram of slicing the scope surrounded by the two tracks any triangle can be taken as an area surrounded by two and the two line segments connecting the first two and the idealized tracks of meridional pattern similarity. Therefore, last two points of the two TC tracks. the zonal pattern track idealization is finally converted to First, at each point of the two tracks, slice the scope meridional pattern track idealization. with a cutting line and calculate the points of intersection of the cutting line and the two tracks. Then, the scope can d. Calculation of the similarity index (Fig. 2, be divided into a number of slices (Fig. A6), which can be bottom-right box) sorted into three types of geometric graphs: triangle, Based on the above analysis, the TSAI of the two TC trapezoid, and double triangle (Fig. A7). tracks may include a meridional pattern TSAI and a zonal 2) CALCULATION OF THE AREA OF A SINGLE SLICE pattern TSAI, and the calculation of the zonal pattern TSAI depends on the algorithm of the meridional pattern TSAI. For slice i, its area can be calculated as Therefore, once the algorithm of the meridional pattern 8 < AC 3 BD/2, triangle TSAI is established, the zonal pattern TSAI is also solved. S 5 (AP 1 BQ) 3 BD/2, trapezoid , The algorithm of the meridional pattern TSAI includes i : 3 1 3 three steps: (i) slicing the scope, (ii) calculation of the area (AP MD BQ ME)/2, double triangle of a single slice, and (iii) addition of all the slice areas. (A3)

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FIG. A7. The three types of geometric graphs for the slices. The horizontal thin dashed lines are the cutting lines in Fig. A8: (a) triangle, (b) trapezoid, and (c) double triangle.

Equation (A3) shows the three formulas for calcu- y 2 y 1 x k 2 x k x 5 p a a ab p pq and (A6) lating the areas of a triangle (Fig. A7a), trapezoid m 2 kab kpq (Fig. A7b), and double triangle (Fig. A7c). Only the calculation of the area of a double triangle is complex. y 2 y 1 x k 2 x k y 5 y 1 k p a a ab p pq . (A7) First, the location of point M must be calculated. m a ab k 2 k Figure A8 shows a schematic diagram of the in- ab pq tersection of the two line segments AB and PQ, which Then, the area of the double triangle can be easily are assumed to be straight to more readily facilitate determined. TSAI computation. Assume that x and y represent the longitude and latitude, and that the positions of A, B, 3) ADDING ALL THE SLICE AREAS P, and Q are (xa, ya), (xb, yb), (xp, yp), and (xq, yq), re- When the areas of all the slices have been determined, spectively. Then, the location of M (xm, ym)canbede- add all the areas together. Suppose there are L slices in termined by two steps. total, the area of the scope surrounded by the two tracks First, calculate the equations of the straight lines AB can be expressed as and PQ according to the two point formula: L y 5 y 1 k (x 2 x ) and (A4) 5 å a ab a S Si . (A8) i51 5 1 2 y yp kpq(x xp), (A5) where kab 5 (yb 2 ya)/(xb 2 xa)andkpq 5 (yq 2 yp)/ e. Determining TSAI 2 (xq xp). Based on the algorithm of the meridional pattern Second, calculate the location of the intersection M TSAI, the meridional pattern TSAI Slon, and the zonal (xm, ym) of the two straight lines [(A4) and (A5)]: pattern TSAI Slat, the units of which are kilometers squared, are determined. To determine the value of TSAI, we deﬁne the parameter n, which is the size of the subset of the two tracks whose latitude extreme points are not close to the endpoints. Then, the value of TSAI is determined as

(i) n 5 2, TSAI 5 Slat; (ii) n 5 1, TSAI 5 max(Slat, Slon); that is, select the larger one; and

(iii) n 5 0, TSAI 5 Slon.

REFERENCES

Bauer, P., A. Thorpe, and G. Brunet, 2015: The quiet revolution of FIG. A8. Schematic diagram of the intersection of the two line numerical weather prediction. Nature, 525, 47–55, https://doi.org/ segments AB and PQ. 10.1038/nature14956.

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Cangialosi, J., and J. Franklin, 2015: 2014 National Hurricane Langmack, H., K. Fraedrich, and F. Sielmann, 2012: Tropical cy- Center Forecast Verification Report. NHC, 82 pp., https:// clone track analog ensemble forecasting in the extended www.nhc.noaa.gov/verification/pdfs/Verification_2014.pdf. Australian basin: NWP combinations. Quart. J. Roy. Meteor. Chen, D., and J. Xue, 2004: An overview on recent progresses Soc., 138, 1828–1838, https://doi.org/10.1002/qj.1915. of the operational numerical weather prediction models (in Lee, C.-S., L.-R. Huang, H.-S. Shen, and S.-T. Wang, 2006: Chinese). Acta Meteor. Sin., 62, 623–633. A climatology model for forecasting typhoon rainfall in Chen, L.-S., and Y. H. Ding, 1979: An Introduction to the Western Taiwan. Nat. Hazards, 37, 87–105, https://doi.org/10.1007/ Pacific Typhoon (in Chinese). Science Press, 491 pp. s11069-005-4658-8. ——, Y. Li, and Z. Q. Cheng, 2010: An overview of research and Leslie, L. M., and K. Fraedrich, 1990: Reduction of tropical cyclone forecasting on rainfall associated with landfall tropical cyclones. position errors using an optimal combination of independent Adv. Atmos. Sci., 27, 967–976, https://doi.org/10.1007/s00376- forecasts. Wea. Forecasting, 5, 158–161, https://doi.org/10.1175/ 010-8171-y. 1520-0434(1990)005,0158:ROTCPE.2.0.CO;2. DeMaria, M., 2009: A simplified dynamical system for tropical Li, B., and S. Zhao, 2009: Development of forecasting model of cyclone intensity prediction. Mon. Wea. Rev., 137, 68–82, https:// typhoon type rainstorm by using SMAT (in Chinese). Mete- doi.org/10.1175/2008MWR2513.1. orology, 35 (6), 3–12. ——, and J. Kaplan, 1994: A Statistical Hurricane Intensity Pre- Liu, C., 2009: The influence of terrain on the tropical rainfall po- diction Scheme (SHIPS) for the Atlantic basin. Wea. Fore- tential technique in Taiwan. Wea. Forecasting, 24, 785–799, casting, 9, 209–220, https://doi.org/10.1175/1520-0434(1994) https://doi.org/10.1175/2008WAF2222135.1. , . 009 0209:ASHIPS 2.0.CO;2. Liu, Y., B. W. Wu, and D. Y. Wang, 2006: Algorithm study on ——, and ——, 1999: An updated Statistical Hurricane Intensity similarity retrieval of typhoon tracks (in Chinese). Meteorol- Prediction Scheme (SHIPS) for the Atlantic and eastern North ogy, 32 (7), 18–24. Pacific basins. Wea. Forecasting, 14, 326–337, https://doi.org/ Lonfat, M., R. Rogers, T. Marchor, and F. D. Marks Jr., 2007: A , . 10.1175/1520-0434(1999)014 0326:AUSHIP 2.0.CO;2. parametric model for predicting hurricane rainfall. Mon. Wea. ——, M. Mainelli, L. K. Shay, J. A. Knaff, and J. Kaplan, 2005: Rev., 135, 3086–3097, https://doi.org/10.1175/MWR3433.1. Further improvements to the Statistical Hurricane Intensity Marchok, T., R. Rogers, and R. Tuleya, 2007: Validation schemes Prediction Scheme (SHIPS). Wea. Forecasting, , 531–543, 20 for tropical cyclone quantitative precipitation forecasts: https://doi.org/10.1175/WAF862.1. Evaluation of operational models for U.S. landfall cases. Wea. Ebert, E. E., 2001: Ability of a poor man’s ensemble to predict the Forecasting, 22, 726–746, https://doi.org/10.1175/WAF1024.1. probability and distribution of precipitation. Mon. Wea. Rev., Marks, F. D., Jr., G. Kappler, and M. DeMaria, 2002: Development 129, 2461–2480, https://doi.org/10.1175/1520-0493(2001)129,2461: of a tropical cyclone rainfall climatology and persistence AOAPMS.2.0.CO;2. (RCLIPER) model. 25th Conf. on Hurricanes and Tropical Me- ——,M.Turk,S.J.Kussion,J.Yang,M.Seybold,P.R.Keehn, teorology, San Diego, CA, Amer. Meteor. Soc., 7D.2, https://ams. and R. J. Kuligowski, 2011: Ensemble tropical rainfall po- confex.com/ams/25HURR/techprogram/paper_35695.htm. tential (eTRaP) forecasts. Wea. Forecasting, 26, 213–224, Ren, F., and Coauthors, 2011: Tropical Cyclones Affecting China https://doi.org/10.1175/2010WAF2222443.1. over the last 60 Years (in Chinese). China Meteorological Fraedrich, K., C. C. Raible, and F. Sielmann, 2003: Analog en- Press, 203 pp. semble forecasts of tropical cyclone tracks in the Australian ——, B. Gleason, and D. R. Easterling, 2001: A technique for region. Wea. Forecasting, 18, 3–11, https://doi.org/10.1175/ partitioning tropical cyclone precipitation (in Chinese). J. Trop. 1520-0434(2003)018,0003:AEFOTC.2.0.CO;2. Goerss, J., 2000: Tropical cyclone track forecasts using an Meteor., 17, 308–313. ensemble of dynamical models. Mon. Wea. Rev., 128, ——, Y. Wang, X. Wang, and W. Li, 2007: Estimating tropical 1187–1193, https://doi.org/10.1175/1520-0493(2000)128,1187: cyclone precipitation from station observations. Adv. Atmos. TCTFUA.2.0.CO;2. Sci., 24, 700–711, https://doi.org/10.1007/s00376-007-0700-y. Huang, W., H. Yu, and X. Liang, 2009: Evaluation of GRAPES- Rozoff, C. M., and J. P. Kossin, 2011: New probabilistic forecast TCM rainfall forecast for China landfall tropical cyclone in models for the prediction of tropical cyclone rapid in- 2006 (in Chinese). Acta Meteor. Sin., 67, 892–901. tensification. Wea. Forecasting, 26, 677–689, https://doi.org/ Kaplan, J., and M. DeMaria, 2003: Large-scale characteristics 10.1175/WAF-D-10-05059.1. of rapidly intensifying tropical cyclones in the North Atlantic ——, C. S. Velden, J. Kaplan, J. P. Kossin, and A. J. Wimmers, basin. Wea. Forecasting, 18, 1093–1108, https://doi.org/10.1175/ 2015: Improvements in the probabilistic prediction of tropical 1520-0434(2003)018,1093:LCORIT.2.0.CO;2. cyclone rapid intensification with passive microwave obser- ——, ——, and J. A. Knaff, 2010: A revised tropical cyclone rapid vations. Wea. Forecasting, 30, 1016–1038, https://doi.org/10.1175/ intensification index for the Atlantic and eastern North Pacific WAF-D-14-00109.1. basins. Wea. Forecasting, 25, 220–241, https://doi.org/10.1175/ Scheitlin, K. N., J. B. Elsner, J. Malmstadt, R. Hodges, and 2009WAF2222280.1. T. Jagger, 2010: Toward increased utilization of historical ——, and Coauthors, 2015: Evaluating environmental impacts on hurricane chronologies. J. Geophys. Res., 115, D3108, https:// tropical cyclone rapid intensification predictability utilizing doi.org/10.1029/2009JD012424. statistical models. Wea. Forecasting, 30, 1374–1396, https:// ——, V. Mesev, and J. B. Elsner, 2013: Polyline averaging using dis- doi.org/10.1175/WAF-D-15-0032.1. tance surfaces: A spatial hurricane climatology. Comput. Geosci., Kidder, S. Q., S. J. Kusselson, J. A. Knaff, R. R. Ferraro, R. J. 52, 126–131, https://doi.org/10.1016/j.cageo.2012.10.012. Kuligowski, and M. Turk, 2005: The tropical rainfall Tuleya, R. E., M. DeMaria, and J. R. Kuligowski, 2007: Evaluation potential (TRaP) technique. Part I: Description and exam- of GFDL and simple statistical model rainfall forecasts for ples. Wea. Forecasting, 20, 456–464, https://doi.org/10.1175/ U.S. landfall tropical storms. Wea. Forecasting, 22, 56–70, WAF860.1. https://doi.org/10.1175/WAF972.1.

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Velden, C. S., and L. M. Leslie, 1991: The basic relationship Xu, Z., L. Zou, X. Z. Lu, and Z. Ai, 2013: Fast prediction of typhoon between tropical cyclone intensity and the depth of the tracksbasedonasimilaritymethodandGIS.Disaster Adv., 6 (6), environmental steering layer in the Australian region. Wea. 45–51. Forecasting, 6, 244–253, https://doi.org/10.1175/1520-0434(1991) Zhang, Z., and T. N. Krishnamurti, 1997: Ensemble forecasting of , . 006 0244:TBRBTC 2.0.CO;2. hurricane tracks. Bull. Amer. Meteor. Soc., 78, 2785–2795, https:// Wang, T., and D. Chen, 2007: A brief overview of ensemble fore- doi.org/10.1175/1520-0477(1997)078,2785:EFOHT.2.0.CO;2. casts (in Chinese). J. Meteor. Res. Appl., 28, 6–12. Zhong, Y., 2002: The objective analogue prediction model for Wang, Y., X. Shen, and D. Chen, 2012: Veriﬁcation of tropical tropical cyclone track with comprehensive assessment of the cyclone rainfall predictions from CMA and JMA global environment. J. Trop. Meteor., 8 (2), 207–217. models. J. Trop. Meteor., 18, 537–542. ——, D. F. Wang, and H. Yu, 2007: An objective forecast tech- Wang, Y. F., T. Lu, H. Y. Zhu, J. H. Sun, and W. Zhang, 2006: GIS nique for post landfall track of tropical cyclones (in Chi- based tropical cyclone similar path query and analysis (in Chinese). Sci. Surv. Mapp., 31 (5), 124–128. nese). Zhejiang Daxue Xuebao Lixue Ban, 34, 585–592. Woo, W. C., W. Hogsett, M. Mohapatra, K. Nagata, P. Otto, L. Qi, ——, H. Yu, W. Teng, and P. Chen, 2009: A dynamic similitude V. H. Vo, and Y. Xu, 2014: Challenges and advances related to scheme for tropical cyclone quantitative precipitation forecast TC rainfall forecast. Third Int. Workshop on Tropical Cyclone (in Chinese). J. Appl. Meteor. Sci., 20, 17–27. Landfall Processes, Jeju, South Korea, World Weather Re- ——, W. Teng, B. Hu, X. Huang, Z. Teng, and M. Dong, 2012: search Programme, https://www.wmo.int/pages/prog/arep/wwrp/ Dynamic similarity prediction for mid-term track of tropical new/documents/T8.2_WCWoo.pdf. cyclone (in Chinese). Mar. Forecasts, 29 (6), 8–21.

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