Deutscher Wetterdienst

An Analysis of Changes in the Extremes of Temperature and Precipitation based on

Regional Climate Projections for Germany

Clementine Dalelane & Thomas Deutschländer

European Conference on Applications of Meteorology

Berlin, September 12, 2011

September 12, 2011 DWD - Changes in the Extremes 2

A joint Project of the Working Group on „Climate Change and Civil Protection“ of the Federal German

Agency Alliance

Analysis of the Change

- in the frequency and intensity of:

• heavy precipitation events• storm events

- in the duration of:

• drought periods• precipitation episodes• heat waves

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1. Kernel Estimator of the Point Process Intensity

2. Functional Cluster Analysis

3. Extreme Value Statistics

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Regional Climate Projections for Germany (A1B)

Cutting of the time series at the respective threshold

Non-homogenous Poisson Point Process

Models: CLM, REMO, WETTREG, STAR, HadRM, Aladin (1961-2100)

Variables: daily maximal Temperature, daily total Precipitation

Separation of the seasons (JJA, DJF)

Thresholds: 90th, 95th, 99th percentile from C20 (1961-2000)

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Nonparametric Intensity Estimation

n

ihtt

hiKt

1

1)(̂

No ex ante model selection – flexible and robust estimation

Kernel estimator known from density (Rosenblatt 1956 and Parzen 1962) and regression estimation (Nadaraya 1964)

Kernel estimator for the intensity λ(t) of a Poisson Process (Dia 1990, Mudelsee 2005)

Epanechnikov kernel with bandwidth h=3000 days

WEIGHTED MOVING AVERAGE

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Examples from CLM for q=0.99 Estimated probability of quantile exceedance for several grid points at 10°E

North → South

Temperature (Summer) Precipitation (Winter)

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Functional Cluster Analysis CATS algorithm (Serban & Wassermann 2005) -- Clustering After

Transformation and Smoothing

Functional correlation coefficientKernel Intensity Estimators

Fourier Expansion

Set higher frequency coefficients to 0

k-means procedure

Clustering of Fourier coefficients is equivalent to clustering of curves in time domain

22 )()(

))((),(

ggff

ggffgf

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2 Clusters 3 Clusters 4 Clusters 5 Clusters

Probability of Extreme Precipitation Events (DJF) Criteria for selection of k: spatial fragmentation, discriminatory power

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2 Clusters 3 Clusters 4 Clusters 5 Clusters

Probability of Extreme Temperature Events (JJA)

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Increasing Quantiles q→1

When data become too sparse, kernel intensity estimator no longer possible

Decomposition following Smith & Shively (1995), for u2>u1 high thresholds

1)),;(1()()|()( 121122 uuuGuxPuxuxPuxP

where G is the Generalized Pareto Distribution

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Generalized Pareto Distribution for extreme Temperatures (JJA)

Baltic sea Southwest Northeast (inland)

tt

t yyg

/exp1

);(

tt 10exp

Exponential model with time varying scale parameter

Years 1970 2000 2030 2060 2090 Exceedance of the 0.99th percentile in kelvin (logarithmic scale)

Pro

babi

lity

of e

xcee

danc

e

Temporal evolution of the density

0 1with

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Generalized Pareto Distribution for extreme Precipitation (DJF)

Full model with time varying scale parameter and constant shape parameter

)/11(

11

),;(

ttt

yyg with tt 10exp and const

0 1

Spatial distribution of the shape parameter makes no physical sense (rf. Brown 2010)

Entire modelization questionable

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Evaluation of the Fitted GPD Parameters

)(ˆ99.0 t

9.099.0

)ˆ,ˆ;()(ˆ )9.0()9.0(9.0 uu t dyygt

Kernel intensity for u0.99 Kernel intensity for u0.9+x P(y>u0.99) from GPD with u0.9+x

Precipitation (Winter)

Basic quantile: 90% (left) and 95% (right)

Temperature (Summer)

Basic quantile: 90%

Instationary quantiles, flexible scale model, pooled shape parameter

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Thank you very much for your Attention

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Pointwise Confidence Intervals (α=0.95)

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222/12/1 tttttCIh

z

h

z

Poisson converges to Normal distribution ⇒ parametric confidence intervals

Temperature (Summer)

Precipitation (Winter)