Transcript Oleh: Wahyudi 1308 100 049 Dosen Pembimbing: Dr. Sutikno

Identification of Extreme Climate
by Extreme Value Theory Approach
Sutikno
[email protected]
Statistics Department
Faculty of Matematics and Natural Sciences
Sepuluh November Institute of Techology
Surabaya
Outline
Introduction
Reference
Study Sites
Results
Summary and further research
Introduction
 Today we are shocked with many extraordinary events
that we never imagined before because it never happens
in our life. For the last 2 decades, we are familiar with
flooding in big cities in Indonesia.
 In agriculture, farmers frequenly complain about the
unpredictable season that really harm their crop, so they
can not harvest it well.
 Thus, to minimalize the serious impacts of extreme
climate, We need to learn the behaviour of this extreme
climate.
 So this subject is studied well in Extreme Value Theory
or EVT.
Introduction
Flood in any location
Drought
www. its.ac.id
Extreme Value Theory
Statistical methods for studying the
behavior of the tail distribution.
Heavy Tail Distribution
Normal Distribution
Extreme is a very rare event
Distribution tail behavior indicates
that in some cases the climate has a
heavy-tail that is slowly declining tail
of the distribution.
As a result the chances of extreme
value generated was very big.
Value Extreme
in Mantingan, Ngawi District, East Java Province
Plot Indentification of Normal
distribution
Histogram of rainfall
350
99,99
300
99
95
80
200
Percent
Frequency
250
150
100
20
5
1
50
0
50
0
60
120
180
CH
240
300
360
Heavy tail
0,01
-200
-100
0
100
CH
200
300
400
Value Extreme
in Ngale, Ngawi District, East Java Province
Plot Indentification of Normal
distribution
Histogram of rainfall
300
99,99
250
99
95
80
Percent
Frequency
200
150
100
50
20
5
1
50
0
0
50
100
150
CH
200
250
300
0,01
-200
-100
0
100
CH
Heavy tail
200
300
Method of Determination of the Extreme Value
There are two methods:
1. Block Maxima
2. Peaks Over Threshold
Block Maxima Method
Rainfall (mm)
Data is divided into blocks of a specific
time period.
Each block is further specified period
formed the highest value.
Highest data is the sample of extreme
values.
Period
Generallized Extreme Value:
Note:
= location parameter
σ=scala parameter
ξ= shape parameter (tail index)
Peaks Over Threshold (POT)
Rainfall (mm)
 This method uses standard
or threshold value.
 Data that exceeds standard
or threshold value is the
sample of extreme value.
Period
Generallized Pareto Distribution:
Note:
σ=scala parameter
ξ= shape parameter
Determination of Threshold Value (u)
(1) Means Residual Life Plot
The selection of the value of u when there is a
point that shows changes in slope.
Value u
(2) The percentage method
Selecting some data, eg data above 90 percentile
RETURN LEVEL
Return level is the maximum value that is expected to exceed one time within a
certain period .
Return Level GEV
Return Level GPD
xm = extreme values that occur once in the observation period m
δu = nu /n; nu = number of data that exceeds the threshold
n = number of data
Study Sites
Study sites in Ngale and Mantingan
Station at Ngawi District, East Java
Province, Indonesia
Rainfall data ten day (“dasaharian”),
period 1989 to 2010.
NGAWI
Identification of extreme values
Annually
400
400
300
Data
300
Data
M
a
n
t
I
n
g
a
n
Monthly
200
100
100
0
0
350
350
300
300
250
250
200
200
Data
Data
89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10
19 19 19 19 19 19 19 19 19 19 19 20 20 20 20 20 20 20 20 20 20 20
N
g
a
l
e
200
150
100
50
50
0
0
Extreme value
PEB
MAR
APR
MEI
JUN
JUL
AGS
SEPT
OKT
NOP
DES
JAN
PEB
MAR
APR
MEI
JUN
JUL
AGS
SEPT
OKT
NOP
DES
150
100
89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10
19 19 19 19 19 19 19 19 19 19 19 20 20 20 20 20 20 20 20 20 20 20
JAN
Result (1)
Extreme sample data by the method
of block maxima at Mantingan Stasion
Parameter Estimation
400
CH
300
200
100
0
0
50
100
150
200
No
250
Period: DJF,MAM,JJA,SON
Identification of the Distribution
Follow GEV Distribution:
Weibull (ξ <0)
Result (2)
Extreme sample data by the method
of Peaks Over Thresshold at Mantingan Stasion
Parameter Estimation
Percentage Method
Identification of the Distribution
Follow GPD Distribution:
Exponential (ξ =0)
Result (3)
Extreme sample data by the method
of block maxima at Ngale Stasion
Parameter Estimation
300
250
CH
200
150
100
50
0
0
50
100
150
200
No
250
Period: DJF,MAM,JJA,SON
Identification of the Distribution
Follow GEV Distribution:
Weibull (ξ <0)
Result (4)
Extreme sample data by the method
of Peaks Over Thresshold at Ngale Stasion
Parameter Estimation
Percentage Method
Identification of the Distribution
Follow GPD Distribution:
Exponential (ξ =0)
Result (5)
Comparison of RMSE values between GEV and GPD
Station
Mantingan
Ngale
GEV
139,7
95,86
GPD
108,52
78,52
POT (GPD) method is more appropriate in determining the extreme values.
It is shown the value of RMSE POT method is smaller than the method
of Block Maxima (GEV)
Result (6)
Return Level and Estimation
of extreme value rainfall (mm)
Month period
 Jan - Feb 2011
 Jan - May 2011
 Jan - Agust 2011
 Jan - Des 2011
Mantingan
Station
161
187
210
226
Ngale
Station
153
176
196
210
Summary
1. There are extremes climate (rainfall) at Ngale
and Mantingan Station.
2. According to the RMSE criterion level return,
Peaks over threshold method is more
appropriate in determining the extreme
values than the method of Block Maxima.
3. Return level at the Mantingan Station is 226
mm with an annual period, while at the Ngale
Station is 210 mm with the same period
Further Research
For further research, it is necessary to use other
variables (covariates) in the return level.
Multivariate extreme
Thanks You
Sutikno
[email protected]
085230203017