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Statistics DepartmentFaculty of Matematics and Natural SciencesSepuluh November Institute of Techology
Surabaya
Sutikno
Identification of Extreme Climate by Extreme Value Theory Approach
Introduction
Reference
Study Sites
Results
Summary and further research
Outline
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
www. its.ac.id
Flood in any location Drought
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.
Normal Distribution
Heavy Tail Distribution
Extreme is a very rare event
Value Extreme in Mantingan, Ngawi District, East Java
Province
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CH
Frequency
4003002001000-100-200
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0,01
CH
Perc
ent
Heavy tail
Histogram of rainfall Plot Indentification of Normal distribution
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CH
Frequency
3002001000-100-200
99,99
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0,01
CH
Perc
ent
Heavy tail
Histogram of rainfall Plot Indentification of Normal distribution
Value Extreme in Ngale, Ngawi District, East Java
Province
Method of Determination of the Extreme Value
There are two methods:
1. Block Maxima2. Peaks Over Threshold
Block Maxima Method
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 .
Generallized Extreme Value:
Note:= location parameterσ=scala parameterξ= shape parameter (tail index)
Period
Rain
fall
(mm
)
Peaks Over Threshold (POT)
This method uses standard or threshold value.
Data that exceeds standard or threshold value is the sample of extreme value.
Generallized Pareto Distribution:
Note:σ=scala parameterξ= shape parameter
Period
Rain
fall
(mm
)
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
(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 mδu = 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
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Data
DESNOPOKTSEPTAGSJULJUNMEIAPRMARPEBJAN
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Data
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Data
DESNOPOKTSEPTAGSJULJUNMEIAPRMARPEBJAN
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0Data
Extreme value
MantIngan
Ngale
Annually Monthly
Result (1)Extreme sample data by the method of block maxima at Mantingan Stasion
Period: DJF,MAM,JJA,SON
Follow GEV Distribution: Weibull (ξ <0)
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No
CH
Identification of the Distribution
Parameter Estimation
Result (2)
Percentage Method
Extreme sample data by the method of Peaks Over Thresshold at Mantingan Stasion
Identification of the Distribution
Follow GPD Distribution: Exponential (ξ =0)
Parameter Estimation
Result (3)Extreme sample data by the method of block maxima at Ngale Stasion
Period: DJF,MAM,JJA,SON
Follow GEV Distribution: Weibull (ξ <0)
Identification of the Distribution
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No
CH
Parameter Estimation
Result (4)
Percentage Method
Extreme sample data by the method of Peaks Over Thresshold at Ngale Stasion
Identification of the Distribution
Follow GPD Distribution: Exponential (ξ =0)
Parameter Estimation
Result (5)
Station GEV GPDMantingan 139,7 108,52Ngale 95,86 78,52
Comparison of RMSE values between GEV and GPD
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 periodMantingan
StationNgale Station
Jan - Feb 2011 161 153 Jan - May 2011 187 176 Jan - Agust 2011 210 196 Jan - Des 2011 226 210
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
