My current research is on the predictabilty of precipitation in the contiguous (48) United States. We use a Markov chain model based on weather station data to recreate a stochastic (but stationary from year-to-year) representation of precipitation, and then compare the interannual variability of the stochastic model with the historical record on which it was based.
Since our model is trained on daily data,we are able to recreate the seasonal cycle as well, so that our results make a spatial and temporal map of predictabilty. Some of the possible uses of these results include guiding meteorologists in long-range (greater than annual) forecasting, helping climate scientists decide where to look for evidence of decadal-scale variability patterns or trends, and establishing the connections between the physical processes that lead to climate variability and the places/times at which they occur.
For a quick overview, you might be interested in taking a look at my poster from the American Geophysical Union's 2011 meeting.