1. Predictability of Indian monsoon rainfall variability
Michael K. Tippett, IRI
Timothy DelSole, COLA

2. Issues & Questions
Interannual variability of Indian monsoon rainfall has a large societal impact.
How predictable is IMR given SST?
GCM simulations forced by observed SST.
Ability to reproduce observations is limited by
predictability
GCM deficiencies
How to account for (and correct) systematic model error in seasonal forecasts?
Variability of IMR has a large impact on society. Provided the motivation for some the earliest seasonal forecasts.
A usual method of quantifying predictability due to SST forcing is with GCM simulations forced with observed SST.
However, failure to reproduce observations can be due to either genuine lack of predictability or model deficiencies.
If model errors have a systematic character, it may be possible to account for and correct model errors.

3. Seasonal forecasting Two-tier seasonal forecast system
(1) predict SST.
(2) predict response to SST
GCM ensembles forced with dynamical/statistical predicted and persisted SST anomalies.
Grid-point post-processing to account for model error.
Categorical probability forecasts for temperature and precipitation.
Computing the response to SST is key part of seasonal forecasting.
Predictability limits the extent that probability forecasts can differ from climatology.
Check how well model reproduce observations when given observed SSTs.
There are inconsistencies, same in the forecast and AMIP runs.

4. GCM JJAS anomaly correlation
Model present varying skill, suggesting the value of a multi-model approach.
Here, focus on the ECHAM model being run at IRI, more data available.
Relatively low skill.
Observed SST

5. IRI Net Assessment 2002
Seasonal forecasts may in May 2002 for JJA and JAS failed to capture any increased likelihood of below normal precipitation.

6. Predictability and imperfect models
Inherent lack of predictability vs. model deficiency
Is predictability being obscured by systematic errors?
Can additional information be extracted from the model?
Information theory approach (DelSole 2003).
Account for systematic model error by finding the expected outcome given a forecast.
Predictable component analysis of the regression forecast equivalent to CCA between model outputs and observations.
Correction tool.
Model deficiency includes the lack of feedback between GCM and prescribed SST.

7. Seasonal forecasting Two-tier seasonal forecast system
(1) predict SST.
(2) predict response to SST
GCM ensembles forced with dynamical/statistical predicted and persisted SST anomalies.
Pattern-based statistical correction.
Grid-point post-processing to account for model error.
Categorical probability forecasts for temperature and precipitation.
Use the correspondence between model and observed predictable patterns to correct model output.

8. Relating model and observations
Which model variables?
Regional (India) precipitation?
Pacific precipitation?
Vertical wind shear (dynamical monsoon indices)?
Zonal component?
Meridional component?
How many predictable patterns (CCA modes)?
Many choices of model outputs to associated with observed IMR.
Also choice of number of predictable pattern.

9. Model selection by cross-validation
Use cross-validation to choose predictors and number of modes
Leave-1-out
Leave-10-out
Pacific GCM precipitation has most skill.
Avoids region where heat flux inconsistency may be an issue.
Pick the correction model with the most predictive skill.
General problem. Danger of selecting a model whose superior CV skill is by chance. Don’t look at too many models. For some problems leaving out many years can help.
Find that GCM precipitation in the Pacific is the most skillful predictor.
Regional predictors, both precipitation and vertical wind shear, have skill. However, the lack of interaction between atmosphere and SST can be a problem.

10. Correlation of local SST with
Observed precipitation
Model precipitation
In observations, there is a negative correlation between local SST and rainfall anomalies.
In simulations, that is mostly the case. However, there are some regions where there is positive correlation.
Statistical correction can correct this in simulations.
However, such a correction might be of little use in a forecast setting where local SST, a response to convection, are not known.
Local SST
Local SST

11. First CCA mode Observations GCM precip. pattern
Time-series associated with these patterns is highly correlated with ENSO.
Negative IMR precipitation anomalies associated with precipitation anomalies like ENSO. Westward shift.

12. Correction skill estimates
Leave-1-out CV
Hindcasts made May 1 using persisted (Apr) SST.
Correction is trained on all simulation data and applied to hindcast data.
Not cross-validated.

13. Categorical probability forecasts
2002
At each grid point.
Convert forecast anomalies to probability shifts.
Assume forecast error variance is constant and interpret anomalies as shifts of a Gaussian PDF.
Similar results using observed SST.
Did not get the right answer for the wrong reason.
2003
Corrected May forecasts
using forecast SST.

14. Observations
2002
2003
From Monsoon On Line

15. Conclusions Some GCM deficiencies can be corrected.
Enhanced skill levels for IMR.
Care required with statistics.
Forecast corrections dependent on SST forecast.
Potential to predict other variables.
hydrology
Agriculture
Next: identify dynamical mechanisms associated with predictable components.