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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
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
(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
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