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 Miami
67% error
RSMC Tokyo
70% error

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

4. Uncertainty cones
Motivation
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:

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 Reliability diagrams: EPS is underdispersive Bias in EPS
 simple calibration

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. Predicted radius < Q(0.5)
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)]
36h
Predicted radius < Q(0.5)
Predicted radius  Q(0.5)
Error < Q(0.5)
34%
16%
Error  Q(0.5)
POD
Random scores
FAR

15. Predicted radius > Q(0.5)
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)]
36h
Predicted radius > Q(0.5)
Predicted radius  Q(0.5)
Error > Q(0.5)
12%
13%
Error  Q(0.5)
62%
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)]
36h
Predicted radius < Q(0.25)
Predicted radius  Q(0.25)
Error < Q(0.25)
13%
12%
Error  Q(0.25)
63%
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 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),