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Forecasting the El Nino-Southern Oscillation (ENSO) has been a subject ofvigorous research due to the important role of the phenomenon in climatedynamics and its worldwide socioeconomic impacts. Over the past decades,numerous models for ENSO prediction have been developed, among whichstatistical models approximating ENSO evolution by linear dynamics havereceived significant attention owing to their simplicity and comparableforecast skill to first-principles models at short lead times. Yet, due tohighly nonlinear and chaotic dynamics (particularly during ENSO initiation),such models have limited skill for longer-term forecasts beyond half a year. Toresolve this limitation, here we employ a new nonparametric statisticalapproach based on analog forecasting, called kernel analog forecasting (KAF),which avoids assumptions on the underlying dynamics through the use of fornonlinear kernel methods for machine learning and dimension reduction ofhigh-dimensional datasets. Through a rigorous connection with Koopman operatortheory for dynamical systems, KAF yields statistically optimal predictions offuture ENSO states as conditional expectations, given noisy and potentiallyincomplete data at forecast initialization. Here, using industrial-eraIndo-Pacific sea surface temperature (SST) as training data, the method isshown to successfully predict the Nino 3.4 index in a 1998-2017 verificationperiod out to a 10-month lead, which corresponds to an increase of 3-7 monthsover a benchmark linear inverse model (LIM), while significantly improving uponthe ENSO predictability "spring barrier". An analysis of a 1300-yr controlintegration of a comprehensive climate model (CCSM4) further demonstrates thatthe enhanced predictability afforded by KAF holds over potentially much longerleads, extending to 24 months versus 18 months in the benchmark LIM.

Extended-range statistical ENSO prediction through operator-theoretic techniques for nonlinear dynamics