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Predictability of Seasonal Precipitation Using Joint Probabilities

Yılmaz, Mustafa Tuğrul
DelSole, Timothy
This paper tests whether seasonal mean precipitation is predictable using a new method that estimates and analyzes joint probabilities. The new estimation method is to partition the globe into boxes, pool all data within the box to estimate a single joint probability of precipitation for 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 transition probabilities of pixels in a box are homogeneous and stationary. 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, and tested using bootstrap methods. 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. Spring was found to be the most predictable season whereas summer was the least predictable season. Analysis of joint probabilities reveals that though the probabilities are close to climatology, the predictability of precipitation arises from a slight tendency of the state to persist from one season to the next, or if a transition occurs then it is more often from one extreme to normal than from one extreme to the other.