Forecasting in CPT Simon Mason [email protected] Seasonal Forecasting Using the Climate...
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![Page 1: Forecasting in CPT Simon Mason simon@iri.columbia.edu Seasonal Forecasting Using the Climate Predictability Tool Bangkok, Thailand, 12 – 16 January 2015.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f155503460f94c29d84/html5/thumbnails/1.jpg)
Forecasting in CPT
Simon [email protected]
Seasonal Forecasting Using the Climate Predictability ToolBangkok, Thailand, 12 – 16 January 2015
![Page 2: Forecasting in CPT Simon Mason simon@iri.columbia.edu Seasonal Forecasting Using the Climate Predictability Tool Bangkok, Thailand, 12 – 16 January 2015.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f155503460f94c29d84/html5/thumbnails/2.jpg)
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
![Page 3: Forecasting in CPT Simon Mason simon@iri.columbia.edu Seasonal Forecasting Using the Climate Predictability Tool Bangkok, Thailand, 12 – 16 January 2015.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f155503460f94c29d84/html5/thumbnails/3.jpg)
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!
![Page 4: Forecasting in CPT Simon Mason simon@iri.columbia.edu Seasonal Forecasting Using the Climate Predictability Tool Bangkok, Thailand, 12 – 16 January 2015.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f155503460f94c29d84/html5/thumbnails/4.jpg)
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
![Page 5: Forecasting in CPT Simon Mason simon@iri.columbia.edu Seasonal Forecasting Using the Climate Predictability Tool Bangkok, Thailand, 12 – 16 January 2015.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f155503460f94c29d84/html5/thumbnails/5.jpg)
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
![Page 6: Forecasting in CPT Simon Mason simon@iri.columbia.edu Seasonal Forecasting Using the Climate Predictability Tool Bangkok, Thailand, 12 – 16 January 2015.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f155503460f94c29d84/html5/thumbnails/6.jpg)
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
![Page 7: Forecasting in CPT Simon Mason simon@iri.columbia.edu Seasonal Forecasting Using the Climate Predictability Tool Bangkok, Thailand, 12 – 16 January 2015.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f155503460f94c29d84/html5/thumbnails/7.jpg)
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.
![Page 8: Forecasting in CPT Simon Mason simon@iri.columbia.edu Seasonal Forecasting Using the Climate Predictability Tool Bangkok, Thailand, 12 – 16 January 2015.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f155503460f94c29d84/html5/thumbnails/8.jpg)
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!
![Page 9: Forecasting in CPT Simon Mason simon@iri.columbia.edu Seasonal Forecasting Using the Climate Predictability Tool Bangkok, Thailand, 12 – 16 January 2015.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f155503460f94c29d84/html5/thumbnails/9.jpg)
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
![Page 10: Forecasting in CPT Simon Mason simon@iri.columbia.edu Seasonal Forecasting Using the Climate Predictability Tool Bangkok, Thailand, 12 – 16 January 2015.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f155503460f94c29d84/html5/thumbnails/10.jpg)
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
![Page 11: Forecasting in CPT Simon Mason simon@iri.columbia.edu Seasonal Forecasting Using the Climate Predictability Tool Bangkok, Thailand, 12 – 16 January 2015.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f155503460f94c29d84/html5/thumbnails/11.jpg)
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
![Page 12: Forecasting in CPT Simon Mason simon@iri.columbia.edu Seasonal Forecasting Using the Climate Predictability Tool Bangkok, Thailand, 12 – 16 January 2015.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f155503460f94c29d84/html5/thumbnails/12.jpg)
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
![Page 13: Forecasting in CPT Simon Mason simon@iri.columbia.edu Seasonal Forecasting Using the Climate Predictability Tool Bangkok, Thailand, 12 – 16 January 2015.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f155503460f94c29d84/html5/thumbnails/13.jpg)
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
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
![Page 14: Forecasting in CPT Simon Mason simon@iri.columbia.edu Seasonal Forecasting Using the Climate Predictability Tool Bangkok, Thailand, 12 – 16 January 2015.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f155503460f94c29d84/html5/thumbnails/14.jpg)
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 ..
![Page 15: Forecasting in CPT Simon Mason simon@iri.columbia.edu Seasonal Forecasting Using the Climate Predictability Tool Bangkok, Thailand, 12 – 16 January 2015.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f155503460f94c29d84/html5/thumbnails/15.jpg)
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
![Page 16: Forecasting in CPT Simon Mason simon@iri.columbia.edu Seasonal Forecasting Using the Climate Predictability Tool Bangkok, Thailand, 12 – 16 January 2015.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f155503460f94c29d84/html5/thumbnails/16.jpg)
16 Seasonal Forecasting Using the Climate Predictability Tool
Low probability of normal
![Page 17: Forecasting in CPT Simon Mason simon@iri.columbia.edu Seasonal Forecasting Using the Climate Predictability Tool Bangkok, Thailand, 12 – 16 January 2015.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f155503460f94c29d84/html5/thumbnails/17.jpg)
17 Seasonal Forecasting Using the Climate Predictability Tool
Low probability of normal
![Page 18: Forecasting in CPT Simon Mason simon@iri.columbia.edu Seasonal Forecasting Using the Climate Predictability Tool Bangkok, Thailand, 12 – 16 January 2015.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f155503460f94c29d84/html5/thumbnails/18.jpg)
18 Seasonal Forecasting Using the Climate Predictability Tool
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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19 Seasonal Forecasting Using the Climate Predictability Tool
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
![Page 20: Forecasting in CPT Simon Mason simon@iri.columbia.edu Seasonal Forecasting Using the Climate Predictability Tool Bangkok, Thailand, 12 – 16 January 2015.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f155503460f94c29d84/html5/thumbnails/20.jpg)
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
![Page 21: Forecasting in CPT Simon Mason simon@iri.columbia.edu Seasonal Forecasting Using the Climate Predictability Tool Bangkok, Thailand, 12 – 16 January 2015.](https://reader035.fdocuments.in/reader035/viewer/2022062321/56649f155503460f94c29d84/html5/thumbnails/21.jpg)
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?