Uncertainty cones deduced from an ensemble prediction system

1. Uncertainty cones deduced from an ensemble prediction system WMO/WWRP Training, Nanjing, dec 2011 Matthieu Plu, Thierry Dupont, Philippe Caroff et Ghislain Faure RSMC La Réunion Laboratoire de l’Atmosphère et des Cyclones

2. Uncertainty cones Motivation • Many RSMC convey an uncertainty information around their track: uncertainty cone Motivation RSMC Tokyo 70% error RSMC Miami 67% error

3. Uncertainty cones Can we refine this uncertainty information using ensemble prediction? The method of JMA RSMC Tokyo (Yamaguchi et al, 2009): Motivation

4. Uncertainty cones The method of JMA RSMC Tokyo (Yamaguchi et al, 2009): Confidence: A=high: spread<40%error B=middle: 40%<spread<80% error C=low: spread>80%error Verification: Motivation

5. Uncertainty cones Motivation Uncertainty cones are useful to convey an uncertainty information RSMC La Réunion did not produce cones yet The uncertainty from ensemble prediction could help to produce a case-dependent cone

6. Uncertainty cones Method of construction: EPS members 48h lead time The circle of probability x% is centered on the ensemble mean and contains x% of the members. Then it is translated to the RSMC forecast position.

7. Calibration • Definitions: • the forecast probability p(y) is given by the number of members inside the circle of radius R • in a large sample, the number of times the verifying position is inside the p(y) circle yields the verifying probability p(o|y) • Sample: 2 recent cyclone seasons • Ensemble: ECMWF EPS

8. Calibration EPS is underdispersive Bias in EPS  simple calibration Reliability diagrams:

9. Verification What verification?

10. Verification • What verification? • … that the EPS cone brings some relevant information with regard to the climatological cone, • p(o|y) and p(y) are available  Probabilistic scores, to be compared with the climatology • does the size of the cone indicate the amplitude of error?

11. Verification • Brier scores as a function of the radius: Climatological error Circle without calibration Calibrated circle

12. Construction of the cone • Circles obtained for the calibrated probability 75% does the size of the cone indicate the amplitude of error?

13. Verification Conditional distributions • The distribution of position error depends on whether the radius R of the uncertainty circle is small or large: If R < quantile(25%) climatological distribution climatological distribution If R > quantile(75%) If R < median If R > median error(km) error(km)

14. Verification Capacity to discriminate between small and large errors: • Error < median : POD : probability of detection [erreur < Q(0.5)] FAR : false-alarm rate [erreur < Q(0.5)] POD Random scores FAR

15. Verification Capacity to detect large errors: • Error > Q(0.75) : POD : probability of detection [erreur > Q(0.75)] FAR : false-alarm rate [erreur > Q(0.75)] Random FAR FAR POD Random POD

16. 3. Validation des cônes d’incertitude Capacity to detect small errors: • Error < Q(0.25) : POD : probability of detection [erreur < Q(0.25)] FAR : false-alarm rate [erreur < Q(0.25)] Random FAR FAR POD Random POD

17. Operational issues • The delay of reception of EPS must be taken into account (12h at 00TU and 12TU, 18h at 06TU and 18TU) • Results are similar if the ensemble tracks are translated at the initial time towards the RSMC analysis Before translation After translation

18. Operational issues • Calibration has been built on 72-hours forecasts  extension to 96-hours using the same regression parameters • Uncertainty cones have been received by forecasters (through SWFDP website) since 2010. • The uncertainty cones will be issued to the public from 2011-2012 season. • Possibility for forecaster to choose the cone (ensemble or climatological).

19. Article: Dupont T., M. Plu, P. Caroff and G. Faure, 2011: Verification of ensemble-based uncertainty circles around tropical cyclone track forecasts, Weather & Forecasting, 26(5), 664-676.