1. Forecasting in CPT Simon Mason simon@iri.columbia.edu Seasonal Forecasting Using the Climate Predictability Tool Bangkok, Thailand, 12 – 16 January 2015

2. 2 Seasonal Forecasting Using the Climate Predictability Tool If we construct a regression model, we can get a best guess estimate of Y given new X: Prediction

3. 3 Seasonal Forecasting Using the Climate Predictability Tool … and can calculate the expected error: Confidence intervals … assuming the model is correct!

4. 4 Seasonal Forecasting Using the Climate Predictability Tool There are 3 ways in which the model may be incorrect: 1. Sampling errors in the intercept Prediction intervals

5. 5 Seasonal Forecasting Using the Climate Predictability Tool There are 3 ways in which the model may be incorrect: 2. Sampling errors in the slope Prediction intervals

6. 6 Seasonal Forecasting Using the Climate Predictability Tool There are 3 ways in which the model may be incorrect: 3. Errors in the selection of the predictors Prediction intervals

7. 7 Seasonal Forecasting Using the Climate Predictability Tool Prediction intervals CPT takes the cross-validated error variance, and the standard errors of the regression constant and coefficient(s) to calculate the prediction error variance. We then have the best guess value, plus or minus one standard error in prediction, giving a prediction interval in which we can state there is about a 68% probability.

8. 8 Seasonal Forecasting Using the Climate Predictability Tool Using the cross-validated error variance, and the standard errors of the regression parameters: Prediction intervals … assuming the model is or is not correct!

9. 9 Seasonal Forecasting Using the Climate Predictability Tool Using the cross-validated error variance, and the standard errors of the regression parameters: Prediction intervals

10. 10 Seasonal Forecasting Using the Climate Predictability Tool But we could use two standard errors …: Prediction intervals

11. 11 Seasonal Forecasting Using the Climate Predictability Tool We can use the prediction intervals to calculate the probabilities of rainfall in the three categories. Prediction intervals

12. 12 Seasonal Forecasting Using the Climate Predictability Tool Or we could use just the right numbers of standard errors to give the probabilities of exceeding the terciles: Prediction intervals

13. 13 Seasonal Forecasting Using the Climate Predictability Tool Or we could use just the right numbers of standard errors to give the probabilities of exceeding the terciles: Prediction intervals

14. 14 Seasonal Forecasting Using the Climate Predictability Tool Prediction intervals Or we could use just the right numbers of standard errors to give the probabilities of: More than 500 mm A 1-in-10 year drought Less than 50% of average More than 100 mm above average Less than last year etc..

15. 15 Seasonal Forecasting Using the Climate Predictability Tool If the best guess value is right on the lower tercile, the below-normal category will have 50% probability. Prediction intervals

16. 16 Seasonal Forecasting Using the Climate Predictability Tool Low probability of normal

17. 17 Seasonal Forecasting Using the Climate Predictability Tool Low probability of normal

18. 18 Seasonal Forecasting Using the Climate Predictability Tool Odds Probabilities can be expressed as odds: i.e., the probability of an event happening divided by it not happening. The odds indicate how much more likely the event is to occur than not to occur. For the climatological categories: i.e., the odds are 2 to 1 against: for every time that category occurs, it will not occur twice.

19. 19 Seasonal Forecasting Using the Climate Predictability Tool Relative odds Relative odds are the odds relative to the climatological odds. If the climatological probability is 0.33, and the forecast indicates a probability of 50%, the odds have doubled: The relative odds are useful for indicating changes in the risk of rare events. Consider a forecast indicating a 20% risk of an extreme event that has a climatological probability of 5%:

20. 20 Seasonal Forecasting Using the Climate Predictability Tool Summary From the prediction error variance we can tailor forecasts in many different ways. Uncertainty in the forecast can be expressed as: – Probabilities – Odds – Prediction intervals

21. 21 Seasonal Forecasting Using the Climate Predictability Tool Exercises Using gridded or station rainfall data, construct a prediction model using CCA and a predictor of your choice. Produce a probabilistic forecast map using predictors for MAM 2015, and then select a location of your choice. Now try to tailor this forecast to answer questions such as: – Will it be exceptionally wet? – Will there be less than 100 mm? – Will there be less than 80% of average? – Will it be drier than last year; will it be wetter than 2010?