clementine dalelane & thomas deutschländer european conference on applications of meteorology
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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. - PowerPoint PPT PresentationTRANSCRIPT
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
September 12, 2011 DWD - Changes in the Extremes 3
1. Kernel Estimator of the Point Process Intensity
2. Functional Cluster Analysis
3. Extreme Value Statistics
September 12, 2011 DWD - Changes in the Extremes 4
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)
September 12, 2011 DWD - Changes in the Extremes 5
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
September 12, 2011 DWD - Changes in the Extremes 6
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)
September 12, 2011 DWD - Changes in the Extremes 7
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
September 12, 2011 DWD - Changes in the Extremes 8
2 Clusters 3 Clusters 4 Clusters 5 Clusters
Probability of Extreme Precipitation Events (DJF) Criteria for selection of k: spatial fragmentation, discriminatory power
September 12, 2011 DWD - Changes in the Extremes 9
2 Clusters 3 Clusters 4 Clusters 5 Clusters
Probability of Extreme Temperature Events (JJA)
September 12, 2011 DWD - Changes in the Extremes 10
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
September 12, 2011 DWD - Changes in the Extremes 11
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
September 12, 2011 DWD - Changes in the Extremes 12
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
September 12, 2011 DWD - Changes in the Extremes 13
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
September 12, 2011 DWD - Changes in the Extremes 14
Thank you very much for your Attention
September 12, 2011 DWD - Changes in the Extremes 15
Pointwise Confidence Intervals (α=0.95)
)(ˆ)(ˆ,)(ˆ)(ˆ,0max)(
222/12/1 tttttCIh
z
h
z
Poisson converges to Normal distribution ⇒ parametric confidence intervals
Temperature (Summer)
Precipitation (Winter)