Prediction of Large Events in Directed Sandpiles

Abstract

The degree of predictability of large avalanche events in the directed sandpile model is studied. This degree is defined in terms of how successfully a strategy can predict such events, as compared to a random guess. A waiting time based prediction strategy which exploits the local anticorrelation of large events is discussed. With this strategy we show analytically and numerically that large events are predictable, and that this predictability persists in the thermodynamic limit. We introduce another strategy which predicts large avalanches in the future based on the present excess density in the sandpile. We obtain the exact conditional probabilities for large events given an excess density, and use this to determine the exact form of the ROC predictability curves. We show that for this strategy, the model is predictable only for finite lattice sizes, and unpredictable in the thermodynamic limit. This behaviour is to be contrasted with previously established numerical studies carried out for Manna sandpiles.