Prediction of seasonal rainfall in the north nordeste of Brazil using eigenvectors of sea‐surface temperature

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Abstract
Two statistical techniques, multiple linear regression and linear discriminant analysis, are compared for making hindcasts and real‐time forecasts of north Nordeste (north‐east Brazil) wet season rainfall using only information about sea‐surface temperature. The predictors are strengths of large‐scale patterns of sea‐surface temperature measured just prior to the season being predicted. The patterns are created from non‐rotated covariance eigenvectors of seasonal, basin scale, sea‐surface temperature anomalies for the Atlantic and Pacific Oceans in the years 1901–1980.Separate prediction models are constructed for 1912–1948 and 1949–1985; hindcasts using a given model are made and verified for the set of years not included in the model construction. However, this strategy does not provide hindcast periods that are completely independent of the model construction period (the ‘training period’), because the eigenvector patterns were based on 1901–1980 data. So for the multiple linear regression technique, a second version of the eigenvectors was used to provide predictor sea‐surface temperature patterns derived from data that were independent of one of the testing periods. The results show that skill was maintained when the predictor eigenvector patterns were also independent of the testing period. Hindcast skill is measured with the help of a new type of score, which calculates the linear error of the hindcast in a historical cumulative probability distribution of the seasonal rainfall (linear error in probability space, LEPS). Well‐known scores are also used to allow easy comparisons with the skill of tropical forecasting techniques published elsewhere. At least 50 per cent of north Nordeste wet season rainfall variance appears to be predictable using sea‐surface temperature data alone, with no significant overall bias.Finally, the paper reviews the skill of four, real time, experimental seasonal forecasts issued for the wet season March to May for each year between 1987 and 1990.