Petra Friederichs - Chair of Statistics STAT

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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.<strong>Friederichs</strong> 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.<strong>Friederichs</strong> Extreme weather 17 / 45
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Petra Friederichs - Chair of Statistics STAT

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