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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.

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Identification of extreme climate by extreme value theory approach

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



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
Introduction

Drought

Flood in any location

www. its.ac.id


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


Value Extreme

in Mantingan, Ngawi District, East Java Province

Histogram of rainfall

Plot Indentification of Normal

distribution

Heavy tail


Value Extreme

in Ngale, Ngawi District, East Java Province

Plot Indentification of Normal

distribution

Histogram of rainfall

Heavy tail


Method of Determination of the Extreme Value

There are two methods:

Block Maxima

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)

  • 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


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


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, IndonesiaRainfall data ten day (“dasaharian”), period 1989 to 2010.

NGAWI


Identification of extreme values

Annually

Monthly

Ma

n

t

I

n

g

a

n

N

g

a

l

e

Extreme value


Result (1)

  • 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)


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

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

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)


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


Further Research

For further research, it is necessary to use other variables (covariates) in the return level.

Multivariate extreme


Thanks you

Thanks You

Sutikno

[email protected]

085230203017


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