The barometer in the port of Papeete on Tahiti and the one in Darwin, Australia, are separated by 7400 kilometers. When one shows high pressure, the other often shows low, and this difference, called the Southern Oscillation, drives rains from India to Brazil. Predicting it even a month ahead is a problem with a century-long history. Classic linear models are like a ruler laid along a winding river: they capture the general slope but miss every turn. The oscillation is nonlinear in nature, so forecasts often miss the mark.

The new approach is like a council of a hundred short experts. Each expert is a small decision tree that knows only a small part of the picture: for example, "if pressure in May dropped by 2 hectopascals and in June rose by 1, then expect a value of 5 in October." One such expert is often wrong, but when a hundred speak and their opinions are averaged, the forecast becomes accurate. The method is called Bayesian additive regression trees, or BART for short. It has been used before for other tasks, but no one had tried applying it to time series, where each value depends on previous ones.

The author took monthly values of the oscillation from January 1876 to August 2009, 1603 observations in all. The trees were built randomly using the Markov chain Monte Carlo method (MCMC), which can be imagined as a drunkard who wanders over a map of probabilities and gradually finds the best spots. To keep the model from overloading, the number of trees was reduced to 20, and it was forced to choose only useful past values, called lags. For predicting the October value from previous months, the best model used just five lags, from May to September. On the training set, the correlation reached 0.90; on the test set, 0.81, with a mean absolute error of 4.89 and a root mean square error (RMSE) of 5.90. If September is excluded to forecast two months ahead, the correlation drops to 0.66.

For forecasts 1 to 12 months ahead, BART with five lags gave a correlation of 0.647 for one month and 0.218 for twelve. The linear model AR(5) on the same data showed 0.620 for one month and 0.112 for twelve. The difference seems small at short horizons, but at long ones BART is twice as accurate. True, after five months BART forecasts degenerate into an almost constant value with small variance, as if the council of experts, seeing no new data, begins to repeat the same thing. This is the method's weakness: it honestly estimates uncertainty one step ahead, but for distant horizons it needs distributed computing, which is still expensive.

The work shows for the first time that a council of a hundred short experts is applicable to climate series and outperforms the linear model in the accuracy of point forecasts. Unlike neural networks, which learn from huge data sets but do not give simple intervals, BART provides a full distribution of uncertainty. This opens the way to nonlinear modeling of climate indices without complex tuning. Hydrologists, agrometeorologists, and climate-risk specialists, who need nonlinear forecasts with uncertainty estimates, can use the method right away. The barometers in Papeete and Darwin will keep measuring pressure, and the council of a hundred experts will now listen to them more attentively.