Linear Regression Simon Mason Seasonal Forecasting Using the Climate Predictability Tool Bangkok, Thailand, 12 – 16 January 2015

2 Seasonal Forecasting Using the Climate Predictability Tool Seasonal prediction How do we know how the oceans will affect the weather? – How have they affected it in the past? – What causes them to have an effect?

3 Seasonal Forecasting Using the Climate Predictability Tool Seasonal forecasting I: empirical Area-average MAM rainfall for 10° – 20°N, 98° – 105°E (Thailand)

4 Seasonal Forecasting Using the Climate Predictability Tool Ocean-based ENSO Indices Niño1+20°–10°S, 90°W–80°W Niño35°N–5°S, 150°W–90°W Niño3.45°N–5°S, 170°W–120°W Niño45°N–5°S, 160°E–150°W Niño55°N–5°S, 120°E–140°E Niño616°N–8°N, 140°E–160°E

5 Seasonal Forecasting Using the Climate Predictability Tool Seasonal forecasting I: empirical MAM rainfall, and NIÑO4 SSTs (5°S – 5°N, 160°E – 150°W).

6 Seasonal Forecasting Using the Climate Predictability Tool Seasonal forecasting I: empirical MAM rainfall, and NIÑO4 SSTs (5°S – 5°N, 160°E – 150°W).

7 Seasonal Forecasting Using the Climate Predictability Tool We can use simple linear regression to predict rainfall using a single predictor such as NIÑO4. Feb NIÑO4 SSTs as a predictor of MAM rainfall over Thailand Linear regression

8 Seasonal Forecasting Using the Climate Predictability Tool Forecasting vs describing The correlation (-0.48) does not tell us how well good the forecasts will be; it tells us how well we can describe the past relationship. The goodness index estimates how good the forecasts will be rather than how well the historical relationship is described. (NB. We want the goodness index to be positive, because it compares the observations with the forecasts. However, the correlation correlation with the predictor can be positive or negative.)

9 Seasonal Forecasting Using the Climate Predictability Tool Cross-validation

10 Seasonal Forecasting Using the Climate Predictability Tool Seasonal prediction How do we know how the oceans will affect the weather? – How have they affected it in the past? – What causes them to have an effect?

11 Seasonal Forecasting Using the Climate Predictability Tool Seasonal forecasting II: dynamical ECHAM4.5 MAM rainfall for Thailand from Feb (purple).

12 Seasonal Forecasting Using the Climate Predictability Tool Seasonal forecasting II: dynamical ECHAM4.5 rainfall for 21° – 27°N, 88° – 93°E (Bangladesh)

13 Seasonal Forecasting Using the Climate Predictability Tool Summary A simple linear regression equation for predicting rainfall has two parameters: – constant: how much rainfall can we expect on average when the value of the predictor is 0. – coefficient: how much can we expect rainfall to increase or decrease when the predictor increases by 1. How well we can describe a historical relationship is not the same as how well we can predict future values. We have to test the predictions using independent data. We can use regression to correct (“recalibrate”) dynamical model predictions.

14 Seasonal Forecasting Using the Climate Predictability Tool Exercise Select a season of interest and download ENSO indices for that season. How strongly related to Thailand rainfall is ENSO? Compare the goodness index with the correlation. Repeat using successively earlier ENSO values (e.g., MAM from Feb, Jan, Dec etc.). How much does the skill weaken? Repeat using different rainfall seasons. How well can we predict rainfall for Thailand for different seasons? Repeat for the best predictors using the gridded data or your own station data for Thailand as predictands. Where is the correlation strongest, and at what time of year?