1. Measuring the potential predictability of seasonal climate predictions
Michael Tippett, IRI
Richard Kleeman and Youmin Tang CIMS, NYU

2. Predictability Climatology pdf of seasonal precipitation.
Forecast probability distribution based on additional information:
Initial conditions;
Boundary conditions (SST; soil);
ENSO state
If the two distributions are the same:
No additional information in forecast.
Greater difference, more information in forecast.
Predictability often define in relative terms.
With no information, the best forecast is climatology.
Perfect forecast pdf that reflects the true change in distribution due to the additional information.

3. Measuring predictability
Relative entropy measures the difference between forecast p and climatology q pdfs.
Measures change in mean and higher order moments.
Nice properties.
Invariant under nonlinear transformations.
Taking log or square-root does not change R.
Useful for non-Gaussian pdfs.
Relative entropy is an information measure that arises naturally when comparing two distributions.
Don’t know the forecast pdf
Perfect model
Gaussian

4. Outline
Measure relative entropy in two GCM simulations forced by observed SST.
“Perfect model” potential predictabilty
Time-series in three locations
JFM North America precipitation.
How does relative entropy depend on
Ensemble mean?
Ensemble variance?
Perfect model in the sense that the distributions are computed from the GCM ensemble.
3 locations where SST forcing is important.
Using relative entropy to quantify the role of different measures of the pdf.
Complementary to previous work that has looked at changes in pdf depending on ENSO state.

5. South Florida DJF
Black is climatology pdf, gray is forecast pdf with largest RE associated with el nino, string shift to wet conditions.
Pluses mark RE values using Gaussian approximation. Line is 95% significance level (ensemble size).
GCMs are similar.
Strong correlation between RE and square of the ensemble mean.
Weak correlation between RE and variance.

6. Kenya OND Dashed line marks significant values of RE.
One GCM has strong shifts, all years are significant.
Other has fewer years where RE is significant.
Strong correlation with ensemble mean.
One GCM is noisier than the other.

7. NE Brazil MAM
Similar behavior between the two GCMs in NE Brazil.

8. North America JFM precipitation
JFM precipitation totals.
Average RE shows information in usual place, especially SE.
Modest correlation with shift.
Care needed to interpret because it looks like the correlation between the ensemble mean and its square.
Ask is the relation with shift due to the relation with shift2
Need to use partial correlation. Partial correlation of shift, controlling for shift^2, is not significant.
Correlation between RE and spread mostly where there is no skill. Also some is due to variance being correlated with square of mean.

9. North America JFM precipitation
There are modest correlations between RE and the sign of NINO 3.4.
However, care needed with interpretation.
Correlation between nino 3.4 and its square is 0.3.
Semi-partial correlation suggests some of the correlation with NINO3.4 is due to the correlation with NINO3.4^2.

10. Summary
Relative entropy measures the difference between forecast and climatology pdfs.
changes in mean, variance, higher order moments.
For seasonal precipitation total:
RE is more closely related to changes in mean than variance
Model dependence.
Future questions:
Differing utility of predictions during warm/cold events.