A new Approach to El Niño Prediction beyond the Spring Season

The enormous societal importance of accurate El Niño forecasts has long been recognized. Nonetheless, our predictive capabilities were once more shown to be inadequate in 2014 when an El Nino event was widely predicted by international climate centers but failed to materialize. This result highlighted the problem of the opaque spring persistence barrier, which severely restricts longer-term, accurate forecasting beyond boreal spring. Here we show that the role played by tropical seasonality in the evolution of the El Niño is changing on pentadal (five-year) to decadal timescales and thus that El Niño predictions beyond boreal spring will inevitably be uncertain if this change is neglected. To address this problem, our new coupled climate simulation incorporates these long-term influences directly and generates accurate hindcasts for the 7 major historical El Niños. The error value between predicted and observed sea surface temperature (SST) in a specific tropical region (5°N–5°S and 170°–120°W) can consequently be reduced by 0.6 Kelvin for one-year predictions. This correction is substantial since an “El Niño” is confirmed when the SST anomaly becomes greater than +0.5 Kelvin. Our 2014 forecast is in line with the observed development of the tropical climate.


S1: Mean perturbation wind power
show that the mean perturbation power W mp in the energetics of El Niño and La Niña is approximated as follows, where τ is the zonal wind stress, u surface zonal oceanic velocity, <x> denotes mean component of x, x' its perturbation component. The values here were averaged over the tropical Pacific (5°S-5°N and 150°E-100°W). The quantity W mp loosely represents the work done by the winds on the ocean except that for the maintenance of the climatological mean state.

S2: A possible long-term modulation in a phenomenological low-order conceptual model
The model was originally constructed as a one-dimensional atmospheric model and contains four variables, X 1 , X 2 , X 3 , and X 4 , and is governed by four equations: where k = 1, 2, 3, and 4, and F is an external forcing independent of k. X k is considered to be the value of some unspecified scalar climatological quantity (47) such as atmospheric temperature or zonal velocity.
The variables are scaled so that the nonlinear interaction and linear damping coefficients trend toward unity, where the time unit (assumed to be 1.25 years) is scaled by the dissipative decay time, which roughly represents the time required for the climate mode of a coupled system in the tropical Pacific to decay, as deduced from our coupled data assimilation system. For simplicity, the model is constructed with k = 4. We assume F = 8 for a control run to simulate an ENSO-like oscillator. A fourth-order Runge-Kutta scheme is used to integrate the model. The model time step was 0.01 units, or 4.56 days. We integrate forward for 200 years. This phenomenological model includes many simplifying assumptions. For example, the nonlinear term is simply expressed by quadratic terms subject to the constraint of energy conservation. Nevertheless, the model contains the components that are essential for simulating the behavior of the nonlinear climatological oscillator that is assumed to describe the tropical Pacific. It was used here to examine the behavior of a nonlinear, oscillatory system subject to repeated forcing at a well-defined periodicity.  S1A) and the other a forcing that includes sinusoidal variations with a 1-year periodicity ( Fig. S1B) where F is formulated as the summation of sinusoidal functions with 1-year period and represents the "seasonal" variability: T 1 is 1 year, and F 1 and F 2 are 8, and 12, respectively. The ratio of F 1 to F 2 is roughly estimated from the temporal variability of zonal wind stress in the tropical Pacific.
The result in the case of constant forcing shows natural periodic behavior at the 2.5-year period inherent in the system (Figs. S1A and C), which is assumed to behave like a coupled oscillator defining the basic timescale associated with ENSO variability (2-8 years). The case of a sinusoidal forcing gives an irregular temporal evolution resulting from the interaction between the modeled seasonal and the natural periodic variations. In a basic sense, this simulates the irregular behavior of the ENSO phenomenon in the real climate system (Fig. S1B).
Wavelet analysis of the case with the sinusoidal forcing (Fig. S1D) shows clear modulation of the seasonal variability by the nonlinear interactions. While the seasonal forcing stimulates variations within a waveband centered on one year, the power of these variations changes on a decadal timescale (Fig. S1D). This quasi-decadal modulation is similar to that observed in the tropical climate (Fig. 1C) and demonstrates a modulation of the seasonal variability by nonlinear interactions in the real climate system.

S3: Ensemble forecast experiment for 2014
The numerical experiments were executed with optimized coupling parameters deduced from a coupled data assimilation experiment for the first three months. The prediction therefore starts at 1 st April and 1 st October 2014. The procedure used for the ensemble experiment is the same as that of the hindcast experiment in    and coupled data assimilation (CDA) results from January 2010 to March 2012 with a 3-month assimilation window for recent years (48).