Hot off the press today, I have calculated the skill of the PDO forecasts produced by some of the leading seasonal forecast models. This is of interest because the PDO is a primary mode of climate variability, and seasonal forecasts - especially for Alaska - often depend on expectations for the PDO phase in the coming months.
I looked at each of the models in the North American Multi-Model Ensemble (NMME) as well as the ECMWF seasonal forecasts. For each model, I calculated the PDO index from the monthly sea surface temperature forecasts from 1982-2010; these are retrospective forecasts that are provided to help with model bias correction, forecast calibration, and skill assessment. The chart below shows results averaged over all months of the year, for 3 different lead times.
As we would expect, the ensemble mean of the NMME models (i.e. all but ECMWF) provides the most skillful prediction of the PDO index and is better than even the best individual model; this is why we look at multi-model ensembles. However, the ECMWF is not far behind in terms of skill, and the CMC2 model is also good. Interestingly, the CFSv2 (NOAA's climate model) is the worst model by some margin; this is a big surprise to me, because I have a high regard for CFSv2 on the whole. Further investigation will be needed to see if there is a particular area of the North Pacific where the CFSv2 temperature forecasts are poor.
Looking at the breakdown of skill by month, the winter PDO index is relatively easy for the models to predict, and the early summer season is the most difficult - see below. This is not too surprising because the winter PDO is linked to tropical Pacific conditions, which the models are quite good at predicting; but the models notoriously struggle with ENSO evolution through the "spring predictability barrier".
Here's the most recent PDO forecast from the same set of models. NCAR's CESM model is an outlier with its very strongly positive PDO phase, but this is one of the less good models according to the skill statistics.