Predicting the data structure prior to extreme events from passive observables using echo state network

Extreme events are defined as events that largely deviate from the nominal state of the system as observed in a time series. Due to the rarity and uncertainty of their occurrence, predicting extreme events has been challenging. In real life, some variables (passive variables) often encode significant information about the occurrence of extreme events manifested in another variable (active variable). For example, observables such as temperature, pressure, etc., act as passive variables in case of extreme precipitation events. These passive variables do not show any large excursion from the nominal condition yet carry the fingerprint of the extreme events. In this study, we propose a reservoir computation-based framework that can predict the preceding structure or pattern in the time evolution of the active variable that leads to an extreme event using information from the passive variable. An appropriate threshold height of events is a prerequisite for detecting extreme events and improving the skill of their prediction. We demonstrate that the magnitude of extreme events and the appearance of a coherent pattern before the arrival of the extreme event in a time series affect the prediction skill. Quantitatively, we confirm this using a metric describing the mean phase difference between the input time signals, which decreases when the magnitude of the extreme event is relatively higher, thereby increasing the predictability skill.