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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. Uncertainty cones. Motivation.
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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
Uncertainty cones Motivation • Many RSMC convey an uncertainty information around their track: uncertainty cone Motivation RSMC Tokyo 70% error RSMC Miami 67% error
Uncertainty cones Can we refine this uncertainty information using ensemble prediction? The method of JMA RSMC Tokyo (Yamaguchi et al, 2009): Motivation
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
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
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.
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
Calibration EPS is underdispersive Bias in EPS simple calibration Reliability diagrams:
Verification What verification?
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?
Verification • Brier scores as a function of the radius: Climatological error Circle without calibration Calibrated circle
Construction of the cone • Circles obtained for the calibrated probability 75% does the size of the cone indicate the amplitude of error?
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)
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
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
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
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
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).
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.