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We apply Gaussian density neural network and quantile regression neural network ensembles to predict the El Nino-Southern Oscillation. Both models are able to assess the predictive uncertainty of the forecast by predicting a Gaussian distribution and the quantiles of the forecasts, respectively. This direct estimation of the predictive uncertainty for each given forecast is a novel feature in the prediction of the El Nino-Southern Oscillation by statistical models. The predicted mean and median, respectively, show a high-correlation skill for long lead times (r=0.5, 12 months) for the 1963-2017 evaluation period. For the 1982-2017 evaluation period, the probabilistic forecasts by the Gaussian density neural network can better estimate the predictive uncertainty than a standard method to assess the predictive uncertainty of statistical models.

Plain Language Summary We apply, for the first time, machine learning models that can directly estimate the uncertainty of the given forecasts of the El Nino phenomenon. Usually, machine learning models for the prediction of the El Nino phenomenon only forecast one value of the so-called Oceanic Nino Index. In contrast, our models predict which values are likely to be observed and which are not. We find that the models have high-correlation skill for long lead times for an evaluation between 1963 and 2017. Moreover, the estimation of the predictive uncertainty is superior to simpler methods for an evaluation between 1982 and 2017.