1. An Objective Index for Identifying Tropical Cyclone Track Similarity Fumin Ren 1 Wenyu Qiu 1,2, Xianling Jiang 3, Liguang Wu 2, and Yihong Duan 1 1 State key laboratory on Severe Weather, Chinese Academy of Meteorological Sciences, Beijing 100081, China; 2 The Department of atmospheric sciences, Nanjing University of Information Science and Technology, Nanjing 210044, China; 3 Hainan Meteorological Observatory, Haikou 570203, China Jan. 21, 2015. Ningbo

2. Effect tests Introduction The technique An application of TSAI Summary Outline

3. Introduction Although numerical prediction of tropical cyclones (TCs) has made great progress, analog forecast as an important supplementary means is still irreplaceable. Meanwhile, track similarity is an important topic of TC analog forecast.

4. Chen et al (1979) TC track similarity includes: seasonal similarity, geography similarity, and shift direction and speed similarity Zhong (2002) and Zhong et al (2007) defined a nonlinear TC track similarity index based on multiple similarities including landfall time, initial position of TC, TC central pressure, and environmental fields Wang et al (2006) proposed a spatial similarity index (SSI) based on GIS technology, which is the ratio of the area of the polygon constituted by two TC tracks inside a specific region to the area of the region. Introduction

5. Xu et al (2013) proposed a track similarity criterion by averaging the distance similarities at all key points. Liu et al (2006) developed a TC track similarity deviation and gave the specific algorithm of it. In TC prediction operations in China, whether TCs pass through a fixed region or not is also used as a criterion for identifying TC track similarity. Introduction

6. It can be seen that above TC track similarity indices or criteria are either too complex to calculate, or too simple to be effective in identifying TC track similarity. Introduction Question Can we develop a concise TC track similarity index ?

7. The technique 2115 TCs totally during 1949-2012 in the Western North Pacific(WNP) latitude extreme (maximum or minimum) point Being the endpoints (the first point and the last point of a TC track) 1092 TCs, about 51.6% close to the endpoints [ the segmentation rate of latitude extreme point is smaller than 0.2 ] 1667 TCs, about 78.8% idea 2003 TCs(about 94.7%) going northward 112TCs(about 5.3%) going southward in north-south direction about 21.2% TCs going zonally in east-west direction

8. meridional pattern tropical cyclone Track Similarity Area Index, TSAI The technique idea Schematic diagram of the enclosed scope (shaded area) surrounded by two TC tracks (dotted line) and the two line segments (thick broken line) connecting the two first points and the two last points of the two TC tracks zonal pattern

9. Five steps ： step1: Preprocessing TC tracks step2: Identification of track pattern step3:Track idealization step4: Calculation of similarity index step5: Determination of TSAI The technique flowchart

10. The technique flowchart

11. (1) Simplification of complex tracks bizarre point: For point P: the larger distance between P and its adjacent points The technique step1: Preprocessing TC tracks P Q M If there exists another point M, the distance between P and M then point P is called a bizarre point (solid points).

12. The technique step1: Preprocessing TC tracks (2) Determining tracks within a designated region

13. Three concepts General direction ：, northward /eastward;, southward /westward The technique step2: Identification of track pattern Segmentation rate of a latitude extreme point (C) r : where is length of track AB, and is length of the shorter one of segments AC and BC. ~ 【 0.0,0.5 】 ( two TC tracks’ ) Overlap rate ： where is the length of the longer track, and is the length of the overlap segment. ~ 【 0.0,1.0 】

14. Both the two conditions are satisfied ？ The technique step2: Identification of track pattern （ 1 ） General directions of the two tracks are the same in north-south direction （ 2 ） For a given threshold ( generally takes 0.4 ~0.8), the overlap rate (1)Meridional pattern similarity criterion

15. All the three conditions are satisfied ？ The technique step2: Identification of track pattern （ 1 ） At least one TC track has a latitude extreme point that isn’t close to endpoints （ 2 ） General directions of the two tracks are the same in east-west direction （ 3 ） For a given threshold ( generally takes 0.4 ~0.8), the overlap rate (2) Zonal pattern similarity criterion

16. Meridional pattern track idealization the second simplification of the track The technique step3: Track idealization a track after step1 unifying track direction According to the general direction, adjust all the points of the track in latitude ascending (descending) order

17. a“ ” can be taken as a scope surrounded by two idealized tracks of meridional pattern similarity Cutting lines along longitude at the latitude extreme points and the endpoints With a diagonal, a“ ”can be changed into two“ ” Several triangles ( ) and quadrangles ( ) enclosed by the cutting lines and the line segments between the points of intersection Zonal pattern track idealization The technique step3: Track idealization

18. The technique step3: Track idealization Zonal pattern track idealization Meridional pattern track idealization

19. The technique step4: Calculation of similarity index Meridional pattern similarity index （ 1 ） Slicing the scope slice the scope with a cutting line and calculate the points of intersection of the cutting line and the two tracks the scope can be divided into a number of slices, which can be sorted into three types of geometric graphs

20. （ 2 ） Calculation of a single slice’s area The three types of geometric graphs for the slices triangle trapezoid double triangle The technique step4: Calculation of similarity index Meridional pattern similarity index

21. （ 2 ） Calculation of a single slice’s area The technique step4: Calculation of similarity index Meridional pattern similarity index triangle trapezoid double triangle

22. （ 3 ） Accumulation of all the slice areas The technique step4: Calculation of similarity index Meridional pattern similarity index and

23. n: the number of TC tracks whose latitude extreme points are not close to the endpoints, 0-2. Base on n, S lat and S lon ， then TSAI (1)n=2, TSAI=S lat (2)n=1, TSAI=Max(S lat,S lon ) ， i.e. the larger one (3)n=0, TSAI=S lon The technique step5: Determination of TSAI

24. Effect tests Typhoon Nina (1975) and the five most similar TCs full track similarity similarity before landfall similarity after landfall parameter1: Similarity region

25. =0.2 =0.25 Bilis r =0.23 the Two TCs r < 0.2 Effect tests Strong tropical storm Bilis (2006) and the five most similar TCs parameter2: Threshold of segmentation rate of a latitude extreme point

26. =0.4 =0.8 all the five TC tracks move across the designated region and show a higher similarity the first point of a TC is within the designated region Effect tests Super-typhoon Haitang (2005) and the five most similar TCs parameter3: Threshold of overlap rate of two TC tracks

27. A primary application of TSAI Super typhoon Rammasun (2014) The intensity of Rammasun is 35m/s at 8:00 on 17 July 2014 Super typhoon Rammasun (2014) and the ten most similar TCs

28. Rammasun’s process precipitation amount (mm) A primary application of TSAI Super typhoon Rammasun (2014) a prediction scheme: selecting the maximum of the ten process precipitation amounts for individual stations Prediction Observation

29. （ 1 ） A tropical cyclone Track Similarity Area Index (TSAI), which has a clear physical meaning, is preliminarily developed. (2) The calculation process of TSAI is divided into five steps: preprocessing TC tracks, identification of track pattern, track idealization, calculation of similarity index, and determination of TSAI. （ 3 ） Effect tests show that TSAI has a good capability to characterize TC track similarity. According to TSAI, the most similar TCs of a certain TC track can be identified by adjusting the three adjustable parameters. （ 4 ） A primary application of TSAI to super typhoon Rammasun (2014) shows that analog forecast for Rammasun’s process precipitation amount is much succesful. Summary

30. Thanks for your attention!