Identification of Extreme Climate by Extreme Value Theory Approach   Sutikno sutikno@statistika.its.ac.id 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 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

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

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

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

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

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)

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 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

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 Monthly Ma n t I g a N g a l e Extreme value

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)

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)

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)

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)

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)

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

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   Sutikno sutikno@statistika.its.ac.id 085230203017