1. Identification of Extreme Climate by Extreme Value Theory Approach
Sutikno
Statistics Department
Faculty of Matematics and Natural Sciences
Sepuluh November Institute of Techology Surabaya

2. Outline Introduction Reference Study Sites Results
Summary and further research

3. 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.

4. Introduction Drought Flood in any location
Today we are shocked with many extraordinary events that we never imagine before because it never happen in our life. For the last 2 decades, we are familiar with flooding in big cities like in Jakarta, Bandung, Surabaya and more. 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.
www. its.ac.id

5. Extreme Value Theory
Statistical methods for studying the behavior of the tail distribution. 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.
Heavy Tail Distribution
Normal Distribution
Extreme is a very rare event

6. in Mantingan, Ngawi District, East Java Province
Value Extreme
in Mantingan, Ngawi District, East Java Province
Histogram of rainfall
Plot Indentification of Normal
distribution
Heavy tail

7. in Ngale, Ngawi District, East Java Province
Value Extreme
in Ngale, Ngawi District, East Java Province
Plot Indentification of Normal
distribution
Histogram of rainfall
Heavy tail

8. Method of Determination of the Extreme Value
There are two methods:
Block Maxima
Peaks Over Threshold

9. Block Maxima Method Generallized Extreme Value:
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​​.
Rainfall (mm)
Period
Generallized Extreme Value:
Note:
= location parameter
σ=scala parameter
ξ= shape parameter (tail index)

10. Peaks Over Threshold (POT)
This method uses standard or threshold value.
Data that exceeds standard or threshold value ​​is the sample of extreme value.
Rainfall (mm)
Period
Generallized Pareto Distribution:
Note:
σ=scala parameter
ξ= shape parameter

11. Determination of Threshold Value (u)
The selection of the value of u when there is a point that shows changes in slope.
(1) Means Residual Life Plot
Value u
Selecting some data, eg data above 90 percentile
(2) The percentage method

12. RETURN LEVEL Return Level GEV Return Level GPD
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

13. 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

14. Identification of extreme values
Annually
Monthly Ma n t I g a N g a l e
Extreme value

15. Result (1) Follow GEV Distribution: Weibull (ξ <0)
Extreme sample data by the method
of block maxima at Mantingan Stasion
Parameter Estimation
Period: DJF,MAM,JJA,SON
Identification of the Distribution
Follow GEV Distribution: Weibull (ξ <0)

16. Result (2) Follow GPD Distribution: Exponential (ξ =0)
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)

17. Result (3) Follow GEV Distribution: Weibull (ξ <0)
Extreme sample data by the method
of block maxima at Ngale Stasion
Parameter Estimation
Period: DJF,MAM,JJA,SON
Identification of the Distribution
Follow GEV Distribution: Weibull (ξ <0)

18. Result (4) Follow GPD Distribution: Exponential (ξ =0)
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)

19. Result (5) Station GEV GPD Mantingan 139,7 108,52 Ngale 95,86 78,52
Comparison of RMSE values ​​between GEV and GPD
Station
GEV
GPD
Mantingan
139,7
108,52
Ngale
95,86
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)

20. Result (6) Return Level and Estimation of extreme value rainfall (mm)
Month period
Mantingan Station
Ngale
Station
Jan - Feb 2011
161
153
Jan - May 2011
187
176
Jan - Agust 2011
210
196
Jan - Des 2011
226

21. Summary
There are extremes climate (rainfall) at Ngale and Mantingan Station.
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.
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

22. Further Research
For further research, it is necessary to use other variables (covariates) in the return level.
Multivariate extreme

23. Thanks You
Sutikno