Predictability of Seasonal Precipitation Using Joint Probabilities

This paper tests whether seasonal mean precipitation is predictable using a new method based on joint probabilities. The new method is to partition the globe into boxes, pool all data within the box to estimate a single joint probability of precipitation in two consecutive seasons, and then apply the resulting joint probability to individual pixels in the box. Pooling data in this way allows joint probabilities to be estimated in relatively small sample sizes, but assumes that the characteristics of precipitation in a box are homogeneous. Joint probabilities are estimated from the Global Precipitation Climatology Project data set in 21 land boxes and 5 ocean boxes during the period 1979-2008. The state of precipitation is specified by dry, wet, or normal terciles of the local climatological distribution. Predictability is quantified by mutual information, which is a fundamental measure of predictability that allows for nonlinear dependencies. Spring was found to be the most predictable season whereas summer was the least predictable season, suggesting a “spring barrier” effect. Analysis of joint probabilities shows that the probabilities are close to their climatological values, but with preferences to remain in the same state from season to season, or if a transition occurs it is from one extreme to normal, rather than from one extreme to the other. This predictability was verified by constructing probabilistic and quantitative forecasts directly from the transition probabilities and showing that they have superior cross-validated skill than forecasts based on climatology, persistence, or random selection.