1. A comparative study of probabilistic seasonal forecasting techniques over India
Makarand A. Kulkarni
Indian Institute of Technology, Delhi
Michael K. Tippett, Andrew Robertson
International Research Institute for climate and society

2. Objectives:
Learn different multi-model combination techniques that are being used at IRI to make probabilistic seasonal forecasts, and apply them over India.
Study some additional methods to find the mean of the forecast distribution.

3. What probabilistic forecasts represent
Near-Normal
Below Normal
Above Normal
Historical distribution
Forecast distribution
FREQUENCY
Breakpoints of categories are determined by historical observations. The probabilities of this distribution are the climatological probabilities.
Forecast distribution (say of the ensemble members at a point, or over a region) represent a shift in the range of possibilities. Now categorical probabilities are not equal – they differ from climatology.
NORMALIZED RAINFALL
(Courtesy Mike Tippett)

4. Set of GCM retrospective and real-time forecasts used
Model
Ensemble Members
Type
ECHAM4.5-CASST 24
2-tier
ECHAM4.5-GML 12
Semi-Coupled
ECHAM4.5-MOM3
Fully Coupled
SINTEX-F 9
Fully coupled
NCEP CFS 15
Observed data: IMD 1-degree rainfall data
Retrospective forecasts: 1982–2008
SINTEX-F model in collab. With JAMSTEC (Japan)
ECHAM4.5-based models run at IRI, lead by Dave DeWitt

5. Categorical Forecast Made for June-Sept 2009 in June combining the 5 models with equal weight
Observed June-Sept rainfall
Category
probability

6. Different methods for calculating the spread of the forecast distribution
Use GCM ensemble spread directly
Use error residuals between forecast mean and obs.
Use correlations between forecast mean and obs.

7. Reliability Diagram Ensemble Spread Error Residuals Using Correlation
(Averaged for the Spatial domain)
Ensemble Spread
Error Residuals
Using Correlation

8. Ranked Probability Skill Scores
Ensemble Spread
Using Correlation
Error Residuals
Individual model contribution

9. Techniques to find mean of the distribution by weighting individual models
Simple ensemble mean (equal weight)
Correlation weighting
Signal to noise ratio weighting
Bayesian scheme

10. Correlations between GCM ensemble mean (Jun-Sep) precipitation and observations

12. Bayesian approach:
Application of Bayesian approach requires three steps
Selection of prior distribution
Choice of likelihood function and
Estimation of posterior distribution.
Xt|Ot = f(Ot)= α + β Ot
mean =α + βOt and variance Σt 2 = E((Xt - f(Ot))2 |Ot )

13. Application of Bayesian approach on real data
Comparison with various linear regression techniques
Correlations (first Row) and errors skill scores (second Row) between corrected/combined Model predicted June-September precipitation for June start and observed precipitation for June-September season. The data length is The names of the methods used for correcting/combing the models are written on each sub plot.

14. Simple Ensemble
Correlation
SNR
Bayesian

15. Future work Continue this work
Using more complicated Bayesian approach to get the mean of the distribution
Try to forecast anywhere in the distribution

16. Thanks
My sincere thanks to Drs. Tippet, Robertson, Dewitt, Someshwar , Hansen, Ines & Conrad …
Ann ,Thea, Ashley …
I will never forget our local guardians Paul and Amor.
Also My three collogues

18. Brief description All these methods are based on Y = β + ε, where
Y is the forecast to be given,
β is the potentially predictable signal
ε is the error part.
This yields one more
relationship

19. Application of Bayesian approach on synthetic data
When a single model is combined with climatology
Comparison with linear regression
Correlation between observations and their estimations after combination verses correlation between variable and observations.

20. Application of Bayesian approach on synthetic data
When a more than one models are combined with climatology
Comparison with various linear regression techniques
(a)
(b)
(c)
(d)
5 independent variables
10 independent variables
The correlation (subplots (a) and (b)) between observed and estimated values of O, the black color represents fitting or combination without any cross validation while red color represents the fitting or combination under leave one out cross validation mode.
Sub plots (c) and (d) are showing standardized error skill scores for different methods attempted, blue color is for without any cross-validation while dark brown color is for leave one out cross-validation.