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.

An Objective Index for Identifying Tropical

Cyclone Track Similarity

Fumin Ren1

Wenyu Qiu1,2, Xianling Jiang3, Liguang Wu2, and Yihong Duan1

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

Effect tests

Introduction

The technique

An application of TSAI

Summary

Outline

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.

Chen et al (1979) TC track similarity includes: seasonal similarity, geograph

y similarity, and shift direction and speed similarity

Zhong (2002) and Zhong et al (2007) defined a nonlinear TC track simila

rity index based on multiple similarities including landfall time, initial positi

on of TC, TC central pressure, and environmental fields

Wang et al (2006) proposed a

spatial similarity index (SSI)

based on GIS technology, whic

h is the ratio of the area of the

polygon constituted by two TC t

racks inside a specific region to

the area of the region.

Introduction

Xu et al (2013) proposed a track similarity criterion by averaging the distance simil

arities at all key points.

Liu et al (2006) developed a TC track similarity deviation and gave the specific a

lgorithm of it.

In TC prediction operations in China, whether TCs pass through a fixed regio

n or not is also used as a criterion for identifying TC track similarity.

Introduction

It can be seen that above TC track similarity indices or

criteria are either too complex to calculate, or too sim

ple to be effective in identifying TC track similarity.

Introduction

Question

Can we develop a concise TC track similarity index?

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

0intint firstpolastpo latlatlat

112TCs(about 5.3%) going southward

0lat

in n

orth

-sou

th

directio

n

about 21.2% TCs going zonally

in east-west direction

merid

ional p

attern

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

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

The technique flowchart

(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

),max(0 PQPA ddd

M

If there exists another point M, the distance between P and M

then point P is called a bizarre point (solid points).

0ddPM

The technique step1: Preprocessing TC tracks

(2) Determining tracks within a designated region

Three concepts

General direction ： , northward /eastward; , southward /westward

The technique step2: Identification of track pattern

intint )/()/( firstpolastpo lonlatSlonlatSS

0S 0S

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 】

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

0cc

(1)Meridional pattern similarity criterion

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

0cc

(2) Zonal pattern similarity criterion

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 latitudeascending (descending)

order

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 idealizationThe technique step3: Track idealization

The technique step3: Track idealization

Zonal pattern track

idealization

Meridional pattern track

idealization

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

（ 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

（ 2 ） Calculation of a single slice’s area

The technique step4: Calculation of similarity index Meridional pattern

similarity index

2/)(

2/)(

2/

MEBQMDAP

BDBQAP

BDAC

si

triangle

trapezoid

double triangle

（ 3 ） Accumulation of all the slice areas

L

iiSS

1

The technique step4: Calculation of similarity index Meridional pattern

similarity index

lonS latSand

n: the number of TC tracks whose latitude extreme points

are not close to the endpoints, 0-2.

Base on n, Slat and Slon ， then TSAI

(1)n=2, TSAI=Slat

(2)n=1, TSAI=Max(Slat,Slon) ， i.e. the larger

one

(3)n=0, TSAI=Slon

The technique step5: Determination of TSAI

Effect tests

Typhoon Nina (1975) and

the five most similar TCs

full track similarity

similarity before landfall similarity after landfall

parameter1:

Similarity region

=0.2 =0.25

Bilis

r =0.23

the Two TCsthe 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

=0.4 =0.8

all the five TC tracks move across the

designated region and show a higher

similaritythe 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

A primary application of TSAISuper 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

Rammasun’s process

precipitation amount (mm)

A primary application of TSAISuper typhoon Rammasun (2014)

a prediction scheme:

selecting the maximum of the ten

process precipitation amounts for

individual stations

Prediction

Observation

（ 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

Thanks for your attention!