Petra Friederichs - Chair of Statistics STAT

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