Fig. 1
One-day ahead forecasts for daily maximum wind speed at Frankfurt Airport valid on 19 March 2011. The ECMWF ensemble forecasts are indicated in black, the observation in red. The solid blue and green lines indicate the median of the truncated normal (TN) and the GEV predictive distribution, respectively. The dashed lines indicate the corresponding central 80% prediction intervals.
Fig. 2
Map of Germany showing the locations of the 228 synoptic observation stations used in this study. The station at Frankfurt Airport is indicated with +, the station at Greifswalder Oie is indicated with ×, and the station at Kap Arkona is indicated with *.
Fig. 3
The post-processed forecast median for: (a) the truncated normal (TN) model, (b) the generalised extreme value (GEV) model, and (c) the regime-switching combination method as a function of the median ensemble prediction for 20000 randomly selected forecast cases in the test set. The red lines indicate the line x=y.
Fig. 4
One-day ahead forecasts for daily maximum wind speed at Greifswalder Oie and Kap Arkona under the combination method valid on 19 March 2011. The ECMWF median forecasts are indicated by the short bars. The ECMWF median forecast at Greifswalder Oie is 7.4 m s−1 resulting in a TN predictive distribution, while the ECMWF median forecast of 7.95 m s−1 at Kap Arkona results in a GEV predictive distribution. The locations of the two stations are indicated in Fig. 2.
Table 1. Mean continuous ranked probability score (CRPS), mean absolute error (MAE), average coverage and width of 80% prediction intervals of probabilistic one-day ahead forecasts of daily maximum wind speed at 228 synoptic stations in Germany from 1 May 2010 to 30 April 2011. The best score for each performance measure is indicated in bold
Fig. 5
Mean continuous ranked probability score (CRPS) for the regime-switching model as a function of the model threshold θ. The results are based on a rolling training period of 30 d during the out-of-sample time period from 1 February 2010 to 30 April 2010.
Fig. 6
Calibration checks for probabilistic one-day ahead forecasts of wind speed over Germany aggregated over 1 May 2010 to 30 April 2011 and the 228 stations: (a) verification rank (VR) histogram for the ECMWF ensemble forecasts; (b) PIT histogram for the TN model; (c) PIT histogram for the GEV model; (d) PIT histogram for the regime-switching combination technique.
Fig. 7
Station-specific comparisons of the continuous ranked probability score (CRPS) for the three post-processing methods as a function of the average observed daily maximum wind speed at the station. The plots compare (a) the TN and the GEV models, (b) the TN and the regime-switching combination models, and (c) the GEV and the regime-switching combination models. The horizontal dashed lines indicate equal predictive performance.
Table 2. Mean threshold-weighted continuous ranked probability score (twCRPS) for one-day ahead forecasts of daily maximum wind speed at 228 synoptic stations in Germany from 1 May 2010 to 30 April 2011 using an indicator weight function for different values of r. The best score for each threshold value is indicated in bold
Fig. 8
Threshold-weighted continuous ranked probability skill score of probabilistic one-day ahead forecasts of daily maximum wind speed at 228 synoptic stations in Germany from 1 May 2010 to 30 April 2011 as a function of the threshold r in the indicator weight function , using the forecasts produced by the TN method as reference. The grey dashed vertical lines indicate the 50th, 90th, 95th and 99th percentile of the marginal distribution of the observations.
Table 3. Mean continuous ranked probability score (CRPS), mean absolute error (MAE), average coverage and width of 80% prediction intervals of daily maximum wind speed forecasts at 228 synoptic stations in Germany from 1 May 2010 to 30 April 2011. The best score for each performance measure is indicated in bold
Climatology1.552.1464.46.6Ensemble1.221.4738.81.6TN1.071.4380.54.1GEV1.061.4382.54.7Combination1.061.4380.64.2Three-day ahead
Climatology1.552.1464.46.6Ensemble1.221.5248.02.1TN1.101.4780.44.3GEV1.091.4782.34.8Combination1.091.4780.74.3
[i] GEV=generalised extreme value; TN=truncated normal.
[ii] The upper half shows results for two-day ahead forecasts, the lower half results for three-day ahead forecasts.
Table 4. Mean threshold-weighted continuous ranked probability score (twCRPS) of daily maximum wind speed forecasts at 228 synoptic stations in Germany from 1 May 2010 to 30 April 2011 using an indicator weight function for different values of r. The best score for each threshold value is indicated in bold
Climatology0.2500.1280.045Ensemble0.2090.1130.043TN0.2020.1110.043GEV0.1980.1080.041Combination0.1960.1060.040Three-day ahead
Climatology0.2500.1280.045Ensemble0.2090.1130.043TN0.2040.1120.043GEV0.2000.1090.041Combination0.1990.1070.041
[i] GEV=generalised extreme value; TN=truncated normal.
[ii] The upper half shows results for two-day ahead forecasts, the lower half shows results for three-day ahead forecasts.