Petra Friederichs - Chair of Statistics STAT

Mesoscale Weather Prediction
Statistical Postprocessing
Applications
Conclusions and Challenges
Predicting High-Impact Weather
Petra Friederichs and Sabrina Bentzien
Meteorological Institute, University of Bonn
in cooperation with
Susanne Theis and Co-workers
German Meteorological National Service (DWD), Offenbach
Marco Oesting and Martin Schlather
Institute of Mathematical Stochastics, Goettingen
Ascona, 11 – 15 July 2011
P.Friederichs Extreme weather 1 / 45

Mesoscale Weather Prediction
Statistical Postprocessing
Applications
Conclusions and Challenges
Why high-impact weather
◮ Mathematically:
Defined as block maxima or excedances of large thresholds.
Events that lie in the tails of a distribution
◮ Perseption:
Rare, exceptional, ”large” and high impact
◮ Problems:
◮
◮
95% quantile of daily precipitation: ≈ 10 − 15mm/d
≈ 2-5 years of data – only few extremes events for verification
P.Friederichs Extreme weather 2 / 45

Mesoscale Weather Prediction
Statistical Postprocessing
Applications
Conclusions and Challenges
Outline
Predicting High-Impact Weather
◮ Atmospheric scales and mesoscale atmospheric dynamics
◮ Numerical weather prediction
◮ Forecast uncertainty and ensemble prediction systems
Ensemble postprocessing
◮ Postprocessing: Extract and calibrate information
Application
◮ Ensemble postprocessing – precipitation
◮ Spatial modelling – wind gusts
P.Friederichs Extreme weather 3 / 45

Mesoscale Weather Prediction
Statistical Postprocessing
Applications
Conclusions and Challenges
Mesoscale Extremes
Predicting high-impact weather
Ensemble Postprocessing
Mesoscale Weather Prediction
◮ Strong and disastrous impact of many weather extremes calls
for reliable forecasts
◮ ”Although forecasters have traditionally viewed weather
prediction as deterministic, a cultural change towards
probabilistic forecasting is in progress.” (T N Palmer, 2002)
◮ Weather extremes do not come ”Out of the Blue”
◮ Numerical weather forecast models provide reliable forecasts
of the atmospheric circulation prone to generate extremes
◮ Combination of dynamical and statistical analysis methods
P.Friederichs Extreme weather 4 / 45

Mesoscale Weather Prediction
Statistical Postprocessing
Applications
Conclusions and Challenges
Mesoscale Extremes
Predicting high-impact weather
Ensemble Postprocessing
Atmospheric scales and mesoscale dynamics
◮ Different scales exhibit different
dominant force balances,
different wave dynamics
◮ Mesoscale on horizontal scales
2km – 2000km
◮ Complex force balances
Steinhorst, Promet 35, 2010
P.Friederichs Extreme weather 5 / 45

Mesoscale Weather Prediction
Statistical Postprocessing
Applications
Conclusions and Challenges
Mesoscale Extremes
Predicting high-impact weather
Ensemble Postprocessing
Mesoscale extremes
Squall-line 14 July 2010
1000
998
A. Kelbch (2010)
35
30
996
25
994
20
Gartenstation MIUB
6 9 12 15 18 21 24
July 2010
P.Friederichs Extreme weather 6 / 45

Mesoscale Weather Prediction
Statistical Postprocessing
Applications
Conclusions and Challenges
Mesoscale Extremes
Predicting high-impact weather
Ensemble Postprocessing
High-impact weather
◮ European mid-latitudes:
Heavy rain and/or violent wind, lightning, hail, . . .
◮ Deep midlatitude convection – Warm season heavy
precipitation clusters
◮ Processes with time scale of ∼1h - 1d
◮ Convective cells – organized and embedded within larger
weather systems – initiated on much smaller scales
www.dwd.de
◮ THORPEX - European Section
P.Friederichs Extreme weather 7 / 45

Mesoscale Weather Prediction
Statistical Postprocessing
Applications
Conclusions and Challenges
Mesoscale Extremes
Predicting high-impact weather
Ensemble Postprocessing
Predictability
◮ Inherent limit of predictability
◮ Fastes error growth at smallest
scales
◮ Predictability strongly depends
on flow regime
◮ Moist convection is primary
source of forecast-error growth
◮ Mesoscale forecasts are issued
for ≤18h-24h
E N Lorenz, Tellus 21, 19 (1969)
P.Friederichs Extreme weather 8 / 45

Mesoscale Weather Prediction
Statistical Postprocessing
Applications
Conclusions and Challenges
Mesoscale Extremes
Predicting high-impact weather
Ensemble Postprocessing
COSMO-DE Ensemble Prediction System (EPS)
◮ 2.8 km grid spacing – convection
permitting NWP model
◮ Operational forecasts 0-21 hours (DWD)
◮ EPS with 20 (40) members since 12/10
◮ Uncertainty due to
Initial conditions
Boundary conditions
Model parameterization
◮ High-impact weather
Postprocessing is an integral part of an EPS
GME
COSMO-DE
COSMO-EU
Initial State Boundary Model
Theis, DWD (2010)
P.Friederichs Extreme weather 9 / 45

Mesoscale Weather Prediction
Statistical Postprocessing
Applications
Conclusions and Challenges
Mesoscale Extremes
Predicting high-impact weather
Ensemble Postprocessing
E (κ) [m 3 s 2 ]
1e−02 1e+01 1e+04 1e+07
λ [km]
628 314 125 62 31 12 6
(−5 3)
κ
1e−05 5e−05 2e−04 5e−04
κ [rad/m]
Bierdel, Bentzien, Friederichs (2011)
κ −1.55 21.08.2009
COSMO-DE-EPS
(Experiment 2009, 20 members)
◮ Forecast hour 10
◮ Mesoscale k −5/3 spectrum
◮ No spin-up effect
◮ Effective resolution:
4 to 5 · ∆x
P.Friederichs Extreme weather 10 / 45

Mesoscale Weather Prediction
Statistical Postprocessing
Applications
Conclusions and Challenges
Mesoscale Extremes
Predicting high-impact weather
Ensemble Postprocessing
Ensemble Postprocessing
◮ COSMO-DE forecasts 1 July 2008 – 30 April 2010
◮ lagged average ensemble
12 h accumulated precipitation between 12 and 00 UTC
forecast (LAF)
• Umgebung
• 4x9 member
• 4x25 member
• ...
0 3 6 9 12 15 18 21 lead time
Bentzien, Friederichs (2011)
6
First guess: probability, mean and 0.9-quantile
from 5 × 5 neighborhood and 4 COSMO-DE forecasts
P.Friederichs Extreme weather 11 / 45

Mesoscale Weather Prediction
Statistical Postprocessing
Applications
Conclusions and Challenges
Mesoscale Extremes
Predicting high-impact weather
Ensemble Postprocessing
from Hamill (2006)
Probabilistic forecasting: Maximize sharpness of
the predictive distribution subject to calibration
Calibration:
Raw ensemble data need adjustmend: biased and underdispersive
Gneiting et al. (2005)
P.Friederichs Extreme weather 12 / 45

Mesoscale Weather Prediction
Statistical Postprocessing
Applications
Conclusions and Challenges
Semi-Parametric Approaches
Parametric Approaches
Forecast Verification: Proper Scoring Rules
Statistical postprocessing
◮ Marginal distributions:
Conditional on weather forecast
Standard ensemble postprocessing
◮ Ensemble MOS (e.g., Wilks, 2006; Gneiting et al., 2004)
◮
◮
Ensemble dressing – Ensemle kernel dressing (e.g., Wang and
Bishop, 2004; Broecker and Smith, 200)
Bayesian model averaging (e.g., Hoeting et al, 1999; Raftery et al,
2005)
◮ Dependence structure:
Transformed Gaussian random fields (e.g., Berrocal et al., 2008)
Max-stable random fields (e.g., Kabluchko et al., 20098)
P.Friederichs Extreme weather 13 / 45

Mesoscale Weather Prediction
Statistical Postprocessing
Applications
Conclusions and Challenges
Semi-Parametric Approaches
Parametric Approaches
Forecast Verification: Proper Scoring Rules
Semi-parametric approach
probability
1.0
0.8
0.6
0.4
0.2
F(1)
F(10)
density
1.0
0.8
0.6
0.4
0.2
quantile [mm/12h]
50
10
3
1
0.3
0.5 quantile
0.75 quantile
0.95 quantile
0.0
0.0
0.1
0.1 0.3 1 3 10 50
rain [mm/12h]
0.1 0.3 1 3 10 50
rain [mm/12h]
0.0 0.2 0.4 0.6 0.8 1.0
probability
◮ Logistic regression: π = 1 − F Y (y | X) = logit −1 (β T X)
◮ Censored quantile regression: q = F −1
Y (τ | X) = max(0, βT X)
P.Friederichs Extreme weather 14 / 45

Mesoscale Weather Prediction
Statistical Postprocessing
Applications
Conclusions and Challenges
Semi-Parametric Approaches
Parametric Approaches
Forecast Verification: Proper Scoring Rules
Parametric approach – Precipitation
probability
1.0
0.8
0.6
0.4
0.2
F(1)
F(10)
density
1.0
0.8
0.6
0.4
0.2
quantile [mm/12h]
50
10
3
1
0.3
0.5 quantile
0.75 quantile
0.95 quantile
0.0
0.0
0.1
0.1 0.3 1 3 10 50
rain [mm/12h]
0.1 0.3 1 3 10 50
rain [mm/12h]
0.0 0.2 0.4 0.6 0.8 1.0
probability
◮ Mixture model:
Y ∼ F y (y; Θ 1 , Θ 2 ) with Θ 1/2 = Θ 1/2 (X)
F y (y; Θ) = π + F Γ (y|y > 0, y ≤ u; Θ 1 ) + F GPD (y|y > u; Θ 2 )
P.Friederichs Extreme weather 15 / 45

Mesoscale Weather Prediction
Statistical Postprocessing
Applications
Conclusions and Challenges
Semi-Parametric Approaches
Parametric Approaches
Forecast Verification: Proper Scoring Rules
Parametric approach – Wind gusts
probability
1.0
0.8
0.6
0.4
0.2
F(1)
F(10)
density
1.0
0.8
0.6
0.4
0.2
quantile [mm/12h]
50
10
3
1
0.3
0.5 quantile
0.75 quantile
0.95 quantile
0.0
0.0
0.1
0.1 0.3 1 3 10 50
rain [mm/12h]
0.1 0.3 1 3 10 50
rain [mm/12h]
0.0 0.2 0.4 0.6 0.8 1.0
probability
◮ Mixture model: Y ∼ F y (y; Θ) with Θ = Θ(X)
F y (y; Θ) = F GEV (y|Θ)
P.Friederichs Extreme weather 16 / 45

Mesoscale Weather Prediction
Statistical Postprocessing
Applications
Conclusions and Challenges
Semi-Parametric Approaches
Parametric Approaches
Forecast Verification: Proper Scoring Rules
Quantile verification score (QVS)
QVS(F −1
Y
(τ), y i) = ∑ i
ρ τ (y i − F −1
Y
(τ | x i))
Brier Score (BS)
BS(F Y (u), y i ) = ∑ i
(F Y (u | x i )) − I u−yi ) 2
Continuous rank probability score (CRPS)
CRPS(F Y , y i ) = ∑ ∫
(F Y (u | x i ) − H(u − y i )du
i
Skill scores
SS =
S(F , y)
S ref (F ref , y)
P.Friederichs Extreme weather 17 / 45

Mesoscale Weather Prediction
Statistical Postprocessing
Applications
Conclusions and Challenges
Ensemble Postprocessing – Precipitation
Case study – 3rd July 2009
Spatial Modelling – Wind Gusts
Ensemble Postprocessing
◮ COSMO-DE forecasts 1 July 2008 – 30 April 2010
◮ 12 h accumulated precipitation between 12 and 00 UTC
n.train
20,30,..,90 Tage
30
T.
!
Jul.08 Okt.08 Jan.09 Apr.09 Jul.09 Okt.09 Jan.10 Apr.10
P.Friederichs Extreme weather 18 / 45

Mesoscale Weather Prediction
Statistical Postprocessing
Applications
Conclusions and Challenges
Ensemble Postprocessing – Precipitation
Case study – 3rd July 2009
Spatial Modelling – Wind Gusts
Radar vs. rain gauge
QVSS (0.9 quantile), training: stations
verification:
radar field
60
52.5
0.6
quantile verification skill score (%)
50
40
30
●
●
latitude
52.0
51.5
51.0
0.5
0.4
0.3
0.2
20
●
verification:
verification:
●
83 stations
83 radar points
●
●
●
●
●
●
●
●
RD ST RD ST RD ●
● ST
●
●
data for statistical model training
●
●
●
●
Bentzien, Friederichs (2011)
50.5
6 7 8 9
longitude
0.1
0.0
Merging rain radar and station data PhD of K. Krebsbach within TR32
P.Friederichs Extreme weather 19 / 45

Mesoscale Weather Prediction
Statistical Postprocessing
Applications
Conclusions and Challenges
Ensemble Postprocessing – Precipitation
Case study – 3rd July 2009
Spatial Modelling – Wind Gusts
Reliability
conditional observed frequency
1.0
0.8
0.6
0.4
0.2
0.0
MIX
fgp
(b) 1mm threshold
0.9
0.6
0.3
0.0
0.9
0.6
0.3
0.0
BS=0.094 REL=0.001 RES=0.086
N=47202 (MIX)
0 0.2 0.4 0.6 0.8 1
forecast distribution
BS=0.102 REL=0.008 RES=0.085
N=47202 (fgp)
0.0 0.2 0.4 0.6 0.8 1.0
0 0.2 0.4 0.6 0.8 1
forecast probability
forecast distribution
P.Friederichs Extreme weather 20 / 45

Mesoscale Weather Prediction
Statistical Postprocessing
Applications
Conclusions and Challenges
Ensemble Postprocessing – Precipitation
Case study – 3rd July 2009
Spatial Modelling – Wind Gusts
Reliability
conditional observed frequency
1.0
0.8
0.6
0.4
0.2
0.0
MIX
fgp
(d) 10mm threshold
0.9
0.6
0.3
0.0
0.9
0.6
0.3
0.0
BS=0.019 REL=0.002 RES=0.005
N=47202 (MIX)
0 0.2 0.4 0.6 0.8 1
forecast distribution
BS=0.021 REL=0.004 RES=0.005
N=47202 (fgp)
0.0 0.2 0.4 0.6 0.8 1.0
0 0.2 0.4 0.6 0.8 1
forecast probability
forecast distribution
P.Friederichs Extreme weather 21 / 45

Mesoscale Weather Prediction
Statistical Postprocessing
Applications
Conclusions and Challenges
Ensemble Postprocessing – Precipitation
Case study – 3rd July 2009
Spatial Modelling – Wind Gusts
Quantile forecasts - Skill Score
QVSS for q 0.90 QVSS for q 0.99
52.5
0.6
52.5
0.8
52.0
0.5
52.0
0.6
0.4
latitude
51.5
0.3
latitude
51.5
0.4
51.0
0.2
51.0
0.2
50.5
0.1
50.5
0.0
0.0
6 7 8 9
longitude
6 7 8 9
longitude
P.Friederichs Extreme weather 22 / 45

Mesoscale Weather Prediction
Statistical Postprocessing
Applications
Conclusions and Challenges
Ensemble Postprocessing – Precipitation
Case study – 3rd July 2009
Spatial Modelling – Wind Gusts
Quantile forecasts - Skill Score
QVSS
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
●
0.99 quantile
●
+
●●● ●●●●●●●● +
+
+
+
+ +
+
+
● + +
+ + + ++ ●●●●●●●●●●●●● ++ +
+
+
++ + ++ + + + +
+ +
+ + ++
+
++ + ●●●● ●●●●●●●●●●●●●●●●●●
+++ + ++
++
+
+ +
+
+++
+
+ + +
+
+ +
+
++ ● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● +++ +
+
+
+ + +
+ + +
+ + +
+ + ++ + +
+ +
+ +
++ +
+
+
+
+
++ + ++ + +
+ ++
+ +
++
+
+ + + +
+
●
+
+ +
●
+
+ +
+
●
+
+
+
+ + +
●
+
+ +
QR
MIX
MIX.t
GPD
QR MIX MIX.t GPD
0 10 20 30 40 50 60 70 80
P.Friederichs Extreme weather 23 / 45

Mesoscale Weather Prediction
Statistical Postprocessing
Applications
Conclusions and Challenges
Ensemble Postprocessing – Precipitation
Case study – 3rd July 2009
Spatial Modelling – Wind Gusts
Quantile forecasts - Skill Score
QVSS
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
−0.1
−0.2
−0.3
0.99 quantile
● +
+
+
+ + + +
●●●●●●●●● ●● ●● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● +
++
+ +
+
+ +
+
+ + +
+ ++ + + + +
+ + +
+
+ + + +
+
++ +
++
+
+++
+ +
+ ++
+++ + ++
+ + + + +
+ + +
+ +++ ++
+
+
+ + + + +
+ + +
+
+ +
+
+ +
+
● ●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●● +
+
+ + +
+ + +
++ ++
+ +
+ +
+ +
+ + +
+
+ +
+
+ +
+ + ++ + +
+
++
+ + + + ++ +
+
+ + +
●
+
+ +
++ ++ + QR
MIX
MIX.t
GPD
QR MIX MIX.t GPD
0 10 20 30 40 50 60 70 80
P.Friederichs Extreme weather 24 / 45

Mesoscale Weather Prediction
Statistical Postprocessing
Applications
Conclusions and Challenges
Ensemble Postprocessing – Precipitation
Case study – 3rd July 2009
Spatial Modelling – Wind Gusts
Quantile forecasts, station and radar measurements
rain [mm/12h]
50
40
30
20
10
0
●
Kleve
●
● ● ● ● ● ● ● ●
●
● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
●
●
●
rain gauge
radar
q0.99
q0.95
q0.90
q0.75
Bentzien, Friederichs (2011)
Jul 05 Jul 15 Jul 25 Aug 04
P.Friederichs Extreme weather 25 / 45

Mesoscale Weather Prediction
Statistical Postprocessing
Applications
Conclusions and Challenges
Ensemble Postprocessing – Precipitation
Case study – 3rd July 2009
Spatial Modelling – Wind Gusts
03.07.2009, init 12 UTC
rain [mm/12h]
03.07.2009, init 09 UTC
rain [mm/12h]
03.07.2009, radar
rain [mm/12h]
52.5
52.5
52.5
80
80
80
52.0
52.0
52.0
60
60
60
51.5
latitude
51.5
latitude
51.5
latitude
40
40
40
51.0
51.0
51.0
20
20
20
50.5
50.5
50.5
longitude
longitude
longitude
6 7 8 9
03.07.2009, init 06 UTC
rain [mm/12h]
6 7 8 9
03.07.2009, init 03 UTC
rain [mm/12h]
6 7 8 9
03.07.2009, 0.99 quantile (mixture model)
rain [mm/12h]
52.5
52.5
52.5
140
80
80
120
52.0
52.0
52.0
60
60
100
51.5
latitude
51.5
latitude
51.5
latitude
80
40
40
60
51.0
51.0
51.0
40
20
20
50.5
50.5
50.5
20
longitude
6 7 8 9
Bentzien, Friederichs (2011)
longitude
6 7 8 9
longitude
6 7 8 9
P.Friederichs Extreme weather 26 / 45

Mesoscale Weather Prediction
Statistical Postprocessing
Applications
Conclusions and Challenges
Ensemble Postprocessing – Precipitation
Case study – 3rd July 2009
Spatial Modelling – Wind Gusts
Forecasting + Verification – German Weather Service
type of gust threshold m/s km/h knots
near gale > 14 50-60 28-33
gale 18 − 24 65-85 34-47
storm 25 − 28 90-100 48-55
violent storm 29 − 32 105-125 56-63
hurricane force > 33 > 120 > 64
P.Friederichs Extreme weather 27 / 45

Mesoscale Weather Prediction
Statistical Postprocessing
Applications
Conclusions and Challenges
Ensemble Postprocessing – Precipitation
Case study – 3rd July 2009
Spatial Modelling – Wind Gusts
Spatial modeling of peak wind speed observations
◮ Marginal distributions:
Spatial interpolation of marginal distribution
- conditional on large scale weather situation
- conditional on local conditions (surface roughness,
altitude,. . .)
→ Transform marginals to standard Fréchet
◮ Dependence structure:
Gaussian random fields to construct max-stable processes
P.Friederichs Extreme weather 28 / 45

Mesoscale Weather Prediction
Statistical Postprocessing
Applications
Conclusions and Challenges
Ensemble Postprocessing – Precipitation
Case study – 3rd July 2009
Spatial Modelling – Wind Gusts
Conditional marginal distribution
Non-stationary process is characterised by atmospheric circulation
◮ COSMO-DE forecasts: wind velocity 10m above ground
◮ Diurnal and annual cycle
◮ Topography and surface roughness
◮ Spatially and temporally constant hyperparameters (MLE)
µ t = Z(X t ) T γ ; σ t = Z(X t ) T ρ ; ξ t = ξ
→ Diploma thesis of S. Memmel: BHM to spatially model parameter surfaces
P.Friederichs Extreme weather 29 / 45

Mesoscale Weather Prediction
Statistical Postprocessing
Applications
Conclusions and Challenges
Ensemble Postprocessing – Precipitation
Case study – 3rd July 2009
Spatial Modelling – Wind Gusts
∼400 (139) weather stations
◮ 6-hourly wind maxima in 1m/s
◮ from April 2003 to May 2011
COSMO-DE forecasts
◮ 10m wind velocity, 6 hour mean
◮ surface maximum wind velocity
◮ January 2010 to April 2010
(available until now)
Forecasts and observations 28 Feb 2010
P.Friederichs Extreme weather 30 / 45

Mesoscale Weather Prediction
Statistical Postprocessing
Applications
Conclusions and Challenges
Ensemble Postprocessing – Precipitation
Case study – 3rd July 2009
Spatial Modelling – Wind Gusts
Max-stabile Prozesse
A stochastic process {Y (r), r ∈ Z} is called max-stable, if its
scaled maxima follow the same distrinution.
P.Friederichs Extreme weather 31 / 45

Mesoscale Weather Prediction
Statistical Postprocessing
Applications
Conclusions and Challenges
Ensemble Postprocessing – Precipitation
Case study – 3rd July 2009
Spatial Modelling – Wind Gusts
Construction of max-stable process – Smith (1990)
( ∫
)
Prob(Y i ≤ y i , ∀i ∈ N) = exp − {y −1 f (r, R i )}dr
R d max
i∈N
where f (r, R i ) = f 0 (r − R i ), f 0 is a multivariate normal distribution
i
P.Friederichs Extreme weather 32 / 45

Mesoscale Weather Prediction
Statistical Postprocessing
Applications
Conclusions and Challenges
Ensemble Postprocessing – Precipitation
Case study – 3rd July 2009
Spatial Modelling – Wind Gusts
Construction of max-stable process – Schlather (2002)
W i : stationary, standard Gaussian random process in R d
Poisson point process (U i ) on (0, ∞) with intensity u −2 du
Y (r) = √ 2π max{U i max{0, W i }}, r ∈ R d
i∈N
is stationary and max-stable with standard Fréchet marginals
P.Friederichs Extreme weather 33 / 45

Mesoscale Weather Prediction
Statistical Postprocessing
Applications
Conclusions and Challenges
Ensemble Postprocessing – Precipitation
Case study – 3rd July 2009
Spatial Modelling – Wind Gusts
Construction of max-stable process – Kabluchko (2009)
W i : zero-mean Gaussian random process R d with variance σ 2 (x)
Poisson point process (U i i) on (0, ∞)
with intensity u −2 du
Z(r) = e −σ2 (r)/2 max{U i e W i (r) }, r ∈ R d
i∈N
is stationary and max-stable with standard Fréchet marginals
P.Friederichs Extreme weather 34 / 45

Mesoscale Weather Prediction
Statistical Postprocessing
Applications
Conclusions and Challenges
Ensemble Postprocessing – Precipitation
Case study – 3rd July 2009
Spatial Modelling – Wind Gusts
Extremal coefficient
Extremal coefficient Θ N defined as
with Θ N = V (1, . . . , 1)
Prob(Y (r i ) ≤ y, ∀i ∈ N) = exp
(
− Θ )
N
,
y
Measure for degrees of freedom
P.Friederichs Extreme weather 35 / 45

Mesoscale Weather Prediction
Statistical Postprocessing
Applications
Conclusions and Challenges
Ensemble Postprocessing – Precipitation
Case study – 3rd July 2009
Spatial Modelling – Wind Gusts
Madogram
F -Madogram: Cooley (2007)
ν F (r i , r j ) = 1 2 E [|F (Y (r i)) − F (Y (r j ))|] ,
F -Madogram determines extremal coefficient
Θ 2 (r i , r j ) = 1 + 2ν F (r i − r j )
1 − 2ν F (r i − r j ) .
P.Friederichs Extreme weather 36 / 45

Mesoscale Weather Prediction
Statistical Postprocessing
Applications
Conclusions and Challenges
Ensemble Postprocessing – Precipitation
Case study – 3rd July 2009
Spatial Modelling – Wind Gusts
Extremal coefficient
1.0 1.2 1.4 1.6 1.8 2.0
DWDnorth
F−Madogram
Smith
Schlather
Whittle−Matern
Powered Exponential
Cauchy
Brown−Resnick
0 50 100 150 200 250 300
Distance in km
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Mesoscale Weather Prediction
Statistical Postprocessing
Applications
Conclusions and Challenges
Ensemble Postprocessing – Precipitation
Case study – 3rd July 2009
Spatial Modelling – Wind Gusts
Extremal coefficient
1.0 1.2 1.4 1.6 1.8 2.0
DWDnorth
F−Madogram
Smith
Schlather
Whittle−Matern
Powered Exponential
Cauchy
Brown−Resnick
0 50 100 150 200 250 300
Distance in km
P.Friederichs Extreme weather 38 / 45

Mesoscale Weather Prediction
Statistical Postprocessing
Applications
Conclusions and Challenges
Ensemble Postprocessing – Precipitation
Case study – 3rd July 2009
Spatial Modelling – Wind Gusts
Extremal coefficient
1.0 1.2 1.4 1.6 1.8 2.0
DWDnorth
F−Madogram
Smith
Schlather
Whittle−Matern
Powered Exponential
Cauchy
Brown−Resnick
0 50 100 150 200 250 300
Distance in km
P.Friederichs Extreme weather 39 / 45

Mesoscale Weather Prediction
Statistical Postprocessing
Applications
Conclusions and Challenges
Ensemble Postprocessing – Precipitation
Case study – 3rd July 2009
Spatial Modelling – Wind Gusts
Extremal coefficient
1.0 1.2 1.4 1.6 1.8 2.0
DWDeast
F−Madogram
Smith
Schlather
Whittle−Matern
Powered Exponential
Cauchy
Brown−Resnick
0 50 100 150 200 250 300
Distance in km
P.Friederichs Extreme weather 40 / 45

Mesoscale Weather Prediction
Statistical Postprocessing
Applications
Conclusions and Challenges
Ensemble Postprocessing – Precipitation
Case study – 3rd July 2009
Spatial Modelling – Wind Gusts
Thanks to M. Oesting and M. Schlather for the simulations of the BR
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Mesoscale Weather Prediction
Statistical Postprocessing
Applications
Conclusions and Challenges
Conclusions
◮ Weather forcasts provide information that conditions occurence of
extremes
◮ Linear (non-linear) statistical modeling extracts information
◮ Extreme value theory provides distributions tailored for extremes
◮ Parametric method less uncertain than non-parametric method and
non-linear dependecy (shape parameter) is not parsimony
◮ High-impact weather: insufficient data available for training and for
validation
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Mesoscale Weather Prediction
Statistical Postprocessing
Applications
Conclusions and Challenges
Challenges
◮ Improve physical understanding of generation processes of extremes
◮ Application to multi-variable and spatio-temporal predictionswhich
◮
◮
◮
Combine spatial statistics with model postprocessing (Berrocal
et al., 2007)
Develop methods for multivariate postprocessing
Develop ensemble methods tailored to extremes
◮ Verification tailored to extremes
◮ Verification for probabilistic multivariate and spatial forecasts
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Mesoscale Weather Prediction
Statistical Postprocessing
Applications
Conclusions and Challenges
Towards a next-generation mesoscale prediction system
for extreme weather
VolkswagenStiftung funded project:
◮ Physical understanding of mesoscale weather extremes
◮ Theory and methodology for spatial and multivariate statistical
modeling, uncertainty assessment and verification of extremes
◮ Operational ensemble prediction system
◮ Postprocessing for multivariate and spatial weather variables
PhD position on “Conditional statistical modeling of spatial extremes
using non-homogeneous marked point processes” (M. Schlather)
go to www.wex-mop.uni-bonn.de
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Mesoscale Weather Prediction
Statistical Postprocessing
Applications
Conclusions and Challenges
Thank you for your attention!
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