Forecasting in CPT Simon Mason [email protected] Seasonal Forecasting Using the Climate Predictability Tool Bangkok, Thailand, 12 – 16 January 2015.

Forecasting in CPT

Simon [email protected]

Seasonal Forecasting Using the Climate Predictability ToolBangkok, Thailand, 12 – 16 January 2015

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

rain 340 50 NINO4

3 Seasonal Forecasting Using the Climate Predictability Tool

… and can calculate the expected error:Confidence intervals

rain 340 50 NINO4 70

290 70 mm

220 rain 360 68%P

… assuming the model is correct!

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

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There are 3 ways in which the model may be incorrect:2. Sampling errors in the slope

Prediction intervals

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There are 3 ways in which the model may be incorrect:3. Errors in the selection of the predictors

Prediction intervals

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 Seasonal Forecasting Using the Climate Predictability Tool

Using the cross-validated error variance, and the standard errors of the regression parameters:

Prediction intervals

rain 290 75 mm

215 rain 365 68%P

… assuming the model is or is not correct!

9 Seasonal Forecasting Using the Climate Predictability Tool

Using the cross-validated error variance, and the standard errors of the regression parameters:

Prediction intervals

rain 290 75 mm

215 rain 365 68%

rain 365 16%

rain 215 16%

P

P

P

10 Seasonal Forecasting Using the Climate Predictability Tool

But we could use two standard errors …:Prediction intervals

rain 290 150 mm

140 rain 440 96%

rain 440 2%

rain 140 2%

P

P

P

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We can use the prediction intervals to calculate the probabilities of rainfall in the three categories.

Prediction intervals

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

rain 290 0.87 75 mm

290 65 mm

225 rain 355 62%

rain 355 19%

rain 225 19%

P

P

P

rain 355 19%

225 rain 355 62%

rain 225 19%

P

P

P

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Or we could use just the right numbers of standard errors to give the probabilities of exceeding the terciles:

Prediction intervals

rain 290 0.31 75 mm

290 23 mm

267 rain 313 24%

rain 313 38%

rain 267 38%

P

P

P

rain 313 38%P

rain 313 100 38% 62%P

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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 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

rain 313 75 mm

rain 313 50%P

rain 315 75 mm

rain 313 49%P

313 rain 355 22

rain 3

%

55 29%P

P

16 Seasonal Forecasting Using the Climate Predictability Tool

Low probability of normal

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Low probability of normal

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OddsProbabilities 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.

odds1

P

P

0.33 1

odds 0.51 0.33 2

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Relative oddsRelative 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%:

50% 33%relative odds

100 50% 100 33%1 0.5

2

20% 5%relative odds

100 20% 100 5%0.250 0.053

4.750

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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

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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?