1. Forecast Assimilation: A Unified Framework for the
Calibration and Combination of
Multi-Model Weather and Climate Predictions
Caio A. S. Coelho, D. B. Stephenson, F. J. Doblas-Reyes (*) and M. Balmaseda (*)
Department of Meteorology, University of Reading and ECMWF (*)
Aim: To create best probability forecasts from ensemble predictions

2. The analogy with data assimilation
“Forecast Assimilation”

3. Forecast assimilation equations (c.f. 4D-VAR)
Prior:
bias
Likelihood:
Matrices
Posterior:

4. Equatorial Pacific SST anomalies
DEMETER: 7 coupled models; 6-month lead
Forecast
Brier Score (BS)
BSS
(%)
Climatol p=0.5
0.25
Multi-model
0.19 24
FA 58-01
0.17 31
BSS = [1- BS/BS(clim.)]*100%
SST anomalies: Y (°C)
Forecast probabilities: p

5. Brier Score as function of longitude
Forecast assimilation reduces (i.e. improves) the Brier score
in the eastern and western equatorial Pacific

6. Brier Score decomposition
reliability
resolution
uncertainty

7. Reliability as function of longitude
Forecast assimilation improves reliability in the western Pacific

8. Resolution as function of longitude
Forecast assimilation improves resolution in the eastern Pacific

9. South American DJF rainfall anomalies
Forecast
Assimilation
Obs
Multi-model
DEMETER: 3 coupled models
(ECMWF, Meteo-France, UKMO)
1-month lead
Start: Nov DJF
ENSO composites:
• 16 El Nino years
• 13 La Nina years
r=0.51
r=0.97
r=0.28
r=0.82
(mm/day)

10. Brier Skill Score for S. American precip.
Forecast assimilation improves the Brier Skill Score (BSS) in the tropics

11. Reliability component of the BSS
Forecast assimilation improves reliability over many regions

12. Resolution component of the BSS
Forecast assimilation improves resolution in the tropics

13. Conclusions: Forecast assimilation
unified framework for the calibration and combination of multi-model predictions
improves the skill of probability forecasts
Equatorial Pacific SST example:
improved reliability in west and resolution in east
South America precipitation example: improved reliability and resolution in the tropics; improved reliability over subtropical and central regions

14. More information … Available at http://www.met.rdg.ac.uk/~swr01cac
Stephenson, D. B., Coelho, C. A. S., Doblas-Reyes, F. J. and Balmaseda, M.
“Forecast Assimilation: A Unified Framework for the Combination of
Multi-Model Weather and Climate Predictions.”
Tellus A - DEMETER special issue (in press)
Available at