Forecasting Long-Lead Rainfall Probability with Application to Australia’s Northeastern Coast

Abstract

The authors develop a method for the long-lead forecasting of El Niño?influenced rainfall probability and illustrate it using the economically important prediction, from the beginning of the year, of September?November (SON) rainfall in the coastal sugarcane producing region of Australia?s northeastern coast. The method is based on two probability distributions. One is the Gaussian error distribution of the long-lead prediction of the El Niño index Niño-3.4 by the Clarke and Van Gorder forecast method. The other is the relationship of the rainfall distribution to the Niño-3.4 index. The rainfall distribution can be approximated by a gamma distribution whose two parameters depend on Niño-3.4. To predict the rainfall at, say, the Tully Sugar, Ltd., mill on the north Queensland coast in SON 2009, the June?August (JJA) value of Niño-3.4 is predicted and then 1000 possible ?observed? JJA Niño-3.4 values calculated from the error distribution. Each one of these observed Niño-3.4 values is then used, with the Niño-3.4-dependent gamma distribution for that location, to calculate 1000 possible SON rainfall totals. The result is one million possible SON rainfalls. A histogram of these rainfalls is the required probability distribution for the rainfall at that location predicted from the beginning of the year. Cross-validated predictions suggest that the method is successful.