Forecasting in CPT Simon Mason [email protected] Seasonal Forecasting Using the Climate...
-
Upload
griffin-miles -
Category
Documents
-
view
218 -
download
0
Transcript of Forecasting in CPT Simon Mason [email protected] Seasonal Forecasting Using the Climate...
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
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 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 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
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 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
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
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 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
17 Seasonal Forecasting Using the Climate Predictability Tool
Low probability of normal
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
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
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 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?